Strategic Network Design for Parcel with Drones under Competition

Gohram Baloch, Fatma Gzara Department of Management Sciences, University of Waterloo, ON Canada N2L 3G1 [email protected] [email protected]

This paper studies the economic desirability of UAV parcel delivery and its effect on e-retailer distribution

network while taking into account technological limitations, government regulations, and customer behavior.

We consider an e-retailer offering multiple same day delivery services including a fast UAV service and

develop a distribution network design formulation under service based competition where the services offered

by the e-retailer not only compete with the stores (convenience, grocery, etc.), but also with each other.

Competition is incorporated using the Multinomial Logit market share model. To solve the resulting nonlinear

mathematical formulation, we develop a novel logic-based Benders decomposition approach. We build a case

based on NYC, carry out extensive numerical testing, and perform sensitivity analyses over delivery charge,

delivery time, government regulations, technological limitations, customer behavior, and market size. The

results show that government regulations, technological limitations, and service charge decisions play a vital

role in the future of UAV delivery.

Key words : UAV; drone; market share models; facility location; logic-based benders decomposition

1. Introduction

Unmanned aerial vehicles (UAVs) or drones have been used in military applications as early as 1916

(Cook 2007). As the technology improved, their applications extended to surveillance and moni- toring (Maza et al. 2010, Krishnamoorthy et al. 2012), weather research (Darack 2012), delivery of medical supplies (Wang 2016, Thiels et al. 2015), and emergency response (Adams and Friedland

2011). Yet, when in 2013 revealed its plan for “Prime Air” service to deliver packages using UAVs within 30 minutes, it was faced with significant skepticism. The idea that our skies

1 Baloch and Gzara: UAV service with competition 2 would be crowded with UAVs sounded like science fiction. While being confident that UAVs will be as common as delivery trucks in a few years, Amazon’s CEO Jeff Bezos admitted in a 2014 interview with The Telegraph (Quinn 2015) that regulations lag behind and pose a serious obstacle.

Logistics practitioners also stated technology limitations, safety, privacy, and public perception as major issues that may hinder the use of UAV technology for parcel delivery (Lewis 2014a, Keeney

2016, Wang 2016). Despite these hurdles, Amazon’s announcement started a race among compa- nies like , Walmart, DHL, and Zookal to develop the technology and the logistics strategies to enable the use of UAVs not only in last mile parcel delivery but also in first mile delivery, inter- and intra-facility distribution, and delivery to remote and difficult to access regions (Butter

2015, Hovrtek 2018). A remarkable application is that by DHL’s “Parcelcopter 3.0” making 130 successful parcel deliveries in remote areas of Bavaria, Germany in 2017 (Burgess 2017). Recently,

Amazon has successfully delivered its first Prime Air package containing a TV streaming stick and a bag of popcorn to a customer in UK (Hern 2016). Other successful applications include hybrid truck-UAV delivery by UPS in Florida, USA (Stewart 2017), and UAV package delivery to islands by Chinese e-commerce giant, Alibaba (Xinhua 2017). Despite these promising applications, UAV parcel delivery is not yet a full scale reality. Whether the attractiveness of the technology will overcome the regulatory and social obstacles is yet to be determined.

Unlike trucks, autonomous UAVs fly without a human pilot, are fast as they do not use congested road networks (Lewis 2014b, Wang 2016), and are significantly cheaper (Welch 2015, D’Andrea

2014, Hickey 2014, Keeney 2016). Hence they provide a perfect solution for the e-retail industry.

The latter captured 11.7% of the total U.S retail sales in 2016 with a growth rate of 8-12% (Statista

2016, Intelligence 2017). Similar growth is observed globally. For example, in 2016, the Chinese e- retail market captured 15.5% of the total retail sales with a growth rate of 26.2% (ECN 2017). This growth is largely due to millennials who embrace online shopping but are ever more sensitive to delivery time and delivery charge (Hsu 2016). Yet, it is not clear how customer preferences and their sensitivity to delivery charge and delivery time affects their choice of a fast UAV delivery service Baloch and Gzara: UAV service with competition 3 versus traditional in-person shopping. On the other hand, UAVs are limited by package weight, travel range, and landing area. For example Air can carry a package weighing up to 2.5 kg and travels up to 24 km (Keeney 2016). DHL’s Parcelcopter carries a package of up to

2 kg with a travel range of 16 km (Franco 2016). Regulations require that an UAV is monitored by a certified operator even though UAVs like Prime Air and Parcelcopter are autonomous and can operate without human intervention. These limitations together with customer preferences are expected to play a crucial role in determining the future of UAV parcel delivery.

In this paper, we study the economic feasibility of UAV parcel delivery in terms of its impact on an e-retailer’s distribution network while taking into account customer preferences, locational decisions, and regulatory and technological limitations. These research questions are of most inter- est to an e-retailer like Amazon, that already offers a set of delivery services such as Same day and delivery services, and that plans to introduce a new and expedited UAV delivery service: Prime Air. While UAVs may be integrated in a hybrid truck-UAV delivery system, the distinctive feature of instant delivery is compromised and a hybrid system may not yield as fast a delivery as direct drone delivery from the warehouse to the customer location. In order to achieve short delivery times, direct UAV delivery from the e-retailer facilities is required, which may in turn require the redesign of the distribution network partly due to the limited flight range of UAVs. On the other hand, analysis of the top ordered products by Prime Now service reveals that these are mostly consumer products bought for immediate use and are otherwise available at convenience and grocery stores (Chronicle 2015). As such, an expedited UAV delivery service does not only compete with other services offered by the e-retailer but also with physical stores in close proximity to the customer.

We investigate the questions that an e-retailer faces when deciding whether or not to offer a UAV parcel delivery service. The decision depends on social, regulatory, and technological challenges facing UAVs. We incorporate social challenges by modelling the market share captured by UAV service as a function of customer preferences for the different online services and in-person shopping, Baloch and Gzara: UAV service with competition 4 as well as their sensitivity to delivery time and delivery cost. We use the Multinomial Logit (MNL) market share model (Cooper, Nakanishi, and Eliashberg 1988) where the market share captured by a service is probabilistic and a function of the utility derived from that service relative to the other services available in the market. We model utility with five attributes: inherent attractiveness of the service, travel time, travel cost, delivery charge, and delivery time. If regulation requires human monitoring of UAVs, their operating cost, and consequently the corresponding delivery charge, would increase. Furthermore, we incorporate technological limitations through allowing different types of packages: those that may be delivered by UAVs and those that may not. Landing area requirements like building type are incorporated in estimating the maximum market share that

UAV service may attract. Finally, the flying range is factored into the design of the distribution network to determine whether a customer may be offered a UAV service. Ultimately, we model the following key decisions (1) how many facilities to open and where, (2) which services to offer at an open facility, and (3) which services to be made available to each customer zone.

The main contributions of this paper are as follows. To the best of our knowledge, this is the first attempt to pose the above research questions in relation to UAV parcel delivery and its impact on the e-retail industry, and to develop a quantitative model to answer these questions. The model is also generic in nature and several possible extensions are proposed in Section4. We develop a logic-based Benders decomposition (LBBD) approach to solve the nonlinear mixed integer model to optimality and within very short time, a few seconds in most cases. The proposed algorithm is also applicable to existing models in competitive facility location (CFL) literature. Also, our work is the first to use a multionominal logit market share model in CFLP to locate multiple facilities with a profit maximization objective, and present an exact solution approach for such a model. Finally, we construct a new case study based in New York City and perform extensive numerical testing to analyze the economic feasibility and added value of UAV delivery under varying levels of technological limitations, regulatory requirements, and customer preferences. The modelling and analysis presented in this paper may be used not only by e-retailers but by any Baloch and Gzara: UAV service with competition 5 retail business to assess the added value of offering UAV delivery. For example, a business concept under development is to offer a UAV leasing service to local businesses such as pizza restaurants, pharmacies, convenience stores, etc., who would independently operate UAVs to deliver customer orders (Luci 2017). It may also be used by regulating bodies to assess the impact of regulations before putting them in effect. We would like to note that we do not exclude the possibility of using hybrid UAV-truck delivery as that may still be used for existing e-retailer services and would only impact the delivery cost and/or delivery charge of these services, which are parameters in our modelling.

The outline for the paper is as follows. In Section2, we present the problem statement, develop the nonlinear mixed integer formulation and the market share model. Section3 presents a novel logic-based Benders decomposition approach, derives strong Benders cuts, and details the solution of the subproblems. Section4 details several model extensions that could be solved using the proposed solution approach. In Section5, we carry out extensive numerical testing using a new case study based in New York City (NYC), and perform sensitivity analyses over delivery charges, delivery time, government regulations, technological limitations, customer behavior, and market size. In Section6, we show the effectiveness of the proposed Benders algorithm by comparing it to an equivalent mixed integer formulation that we develop. Finally, concluding remarks and future research directions are presented in Section7.

1.1. Related Work

The industry interest in UAVs sparked a similar interest in the research community and led to a significant increase in research output. Substantial research is ongoing to address technical issues associated with commercial UAVs such as safety issues including hijacking threats and collision with nearby obstacles, limited endurance, and payload capacity (Mahony, Kumar, and Corke 2012,

Kahn et al. 2017, Pounds, Bersak, and Dollar 2012, Allen 2005). Studies on the economics of

UAVs are mostly limited to industry reports (Hickey 2014, Keeney 2016, Wang 2016). An excellent economic analysis is presented by ARK Invest (Keeney 2016) and attempts to determine unit UAV Baloch and Gzara: UAV service with competition 6 delivery cost by taking into account facility upgrade costs, operator salary, fuel cost, and UAV and battery purchase costs. D’Andrea(2014) models UAV fuel cost using energy consumption functions. In the Management Science/Operations Research literature, Campbell, Sweeney II, and

Zhang(2017) and Carlsson and Song(2017) analyze the economic feasibility of a hybrid truck-

UAV delivery system using continuous approximation models. Murray and Chu(2015) are the first to address operational challenges associated with truck-UAV delivery and introduce two delivery systems that are modelled as extensions of the traveling salesman problem (TSP). In one system, truck deliveries form a tour and UAVs depart from and land on the truck as it makes delivery stops. In the second system, UAVs make direct deliveries from a distribution center while the truck makes deliveries to customers that are not within UAV maximum range. Subsequent works by Ha et al.(2015), Agatz, Bouman, and Schmidt(2018), Poikonen, Wasil, and Golden(2018) consider a similar problem and propose efficient heuristic approaches for TSP with drones (TSP-D). Ferrandez et al.(2016) use k-means clustering to find the optimal location of drone launch sites from the truck and present a genetic algorithm to solve the TSP-D. The overall delivery time and cost for a hybrid truck-drone network are compared against stand-alone truck and drone systems. Other researchers extended TSP-D to vehicle routing problem with multiple trucks and drones (Ulmer and Thomas 2017, Wang, Poikonen, and Golden 2016, Gambella, Naoum-Sawaya, and Ghaddar

2018).

Other than Hong, Kuby, and Murray(2017), researchers are more focused on the operational challenges associated with drones without addressing key network design questions. Hong, Kuby, and Murray(2017) develop a maximal coverage location model with a given number of warehouses and charging stations. The objective is to maximize drone coverage while minimizing the aver- age network distance between the warehouse and charging stations. However, the location of the warehouses is fixed and the model only decides on locating charging stations. To the best of our knowledge, none of the research addresses the economic feasibility of UAV parcel delivery in terms of its impact on an e-retailer’s distribution network while taking into account customer preferences, locational decisions, and regulatory and technological limitations. Baloch and Gzara: UAV service with competition 7

Studies within the marketing literature primarily focus on investigating customer behaviour. In this regard, the work by Hsiao(2009) and Schmid, Schmutz, and Axhausen(2016) are relevant in our context as they attempt to estimate customer sensitivity to travel time, travel cost, delivery time, and delivery charges based on market surveys. Schmid, Schmutz, and Axhausen(2016) focus on grocery and electronic goods while Hsiao(2009) focuses on books. Both use market survey results in MNL models to determine the utility derived by customers from online shopping and in-store shopping. We use similar market share modelling but within an optimization modelling framework. The market share model parameters allow an analysis of different customer segments and how the e-retailer decision to offer UAV delivery changes as a result.

Our work closely relates to competitive facility location (CFL) literature where locational deci- sions are based on competition in the market. We present a new variant of CFL problem where there is no competition between an e-retailer’s own facilities but rather the services offered by an e-retailer are competing against each other and nearby stores. Farahani et al.(2014) provide a comprehensive review of the existing literature on facility location problems under three main types of competition: static, dynamic, and foresight. Static competition is when the new entrant assumes that the attributes of existing competitors do not change following its entrance into the market. Dynamic competition is when the new entrant makes decisions assuming that competitive characteristics of existing rivals may change following its entrance into the market. Competition with foresight is when the rivals (follower) soon join the market once the new entrant (leader) enters the market. Table1 classifies/lists papers on CFL according to each type of competition and compared to our work based on model assumptions, competitive characteristics, strategic decisions, objective function, and solution approach.

In static competition, nearly all the papers use utility based attraction models (multionomial logit or multiplicative competitive interaction market share models), also referred to as gravity models, to capture probabilistic customer behavior. These works consider same service being offered and players (facilities) in the market compete on facility characteristics such as travel distance, Baloch and Gzara: UAV service with competition 8 Approach(5) LBBD Max. P Max. MSMax. MSMax. MSMin. H DLMax. TLA TU + H Max. TLA P + H Max. FC MIP Max. GA MSMax. P MIP MIPMax. + P H SAMax. + TD AA Max. CBP H +Min E max PO E Max. MIP MS E Max. GT PMax. P H Max. PMax. P MIP GA E GA Capacity Objective (4) Solution X alloca- tion X X X X XXX X XXXX X XX X X X X X X XXXXXX Location Services Customer 1 1 F F F F F F F F U U U U U U U U U to open(3) X X X X X X X X X X X X X X XX X X X XX X XXX Competitive characteristics Strategic decisions Price/ cost Time distance weight # facilities A Demand Model(2) C UAUA UUU LF LF LF U Customer behavior(1) Table 1: Review of competitive location problem literature X X X X X X X Demand Paper Elastic Our paper Aboolian, Sun, and Koehler( 2009 )C Berman and Krass ( 1998 )UAAboolian, Berman, and Krass ( 2007a ) Aboolian, Berman, and Krass ( 2007b ) ReVelle, Murray, and Serra ( 2007 )CZhang and( 2008 )UA Rushton Fern´andezet al. ( 2007b )CWu and Lin ( 2003 )UADrezner, Drezner, and Salhi ( 2002 )UAFern´andezet al. ( 2007a )UAPlastria and( 2008 ) Vanhaverbeke Shiode and Drezner ( 2003 )CChawla et al. ( 2006 )CDrezner and Drezner ( 1998 )UARezapour and( 2014 ) Farahani Nasiri et al. ( 2018 )CRhim, Ho, and( 2003 ) Karmarkar Meng, Huang, and Cheu ( 2009 ) Static Dynamic Foresight Competion type Acronyms: (1): U - uncertain,(2): C A - - certain attraction(3): model, F LF - - fixed,(4): linear U MS function - - unknown market(5): (model share, LBBD decides) DL - - Logic(5): demand based E lost, Benders - P decomposition exact - LA solution profits, - methodolgy, TU linear GT - approximation, - total MIP game utility, - TD theory, mixed SA - integer - total program, simulated demand, GA annealing, CBP - AA - genetic - captured algorithm, ascent buying algorithm, power, H PO - - other payoff, heuristic FC - approaches flow captured Baloch and Gzara: UAV service with competition 9 travel time, etc. In such cases, the profit maximization objective is equivalent to the market share maximization objective when facility costs are constrained by a budget. This is because profit margins are the same for all competing players. Under market share maximization, the objective function is a non-decreasing concave function, and easy to deal with. However, since we consider multiple services with different profit margins, profit maximization makes more sense. A profit maximization objective function is more difficult to deal with because it yields a non-concave objective function and piece-wise linear approximation techniques (Aboolian, Berman, and Krass

2007a,b) used to solve conventional CFL problems do not apply. We are not aware of any work other than Fern´andezet al.(2007a) that considers a profit maximization objective function with attraction models. Fern´andezet al.(2007a) present exact and heuristic solution approaches to solve the CFLP for profit maximization. However, the model decides only on locating a single facility which greatly limits the applicability of the solution methodology in general context of locating multiple facilities. On the other hand, the literature dealing with competition with foresight and dynamic competition consider linear demand models for profit maximization problems (Rezapour and Farahani(2014), Rhim, Ho, and Karmarkar(2003), Meng, Huang, and Cheu(2009), Nasiri et al.(2018)). In linear models, the market share captured by a player (e.g. facility, firm, or service) is a linear function of the attributes of all competing players. However, Cooper, Nakanishi, and

Eliashberg(1988) correctly point out that such models do not meet logical consistency requirements.

To the best of our knowledge, this makes our work the first to use a multionominal logit (MNL) market share model in a competitive facility location problem to locate multiple facilities with a profit maximization objective. The proposed demand model in this paper is different from the ones used in the CFL literature in terms of the competitive characteristics. Although, some of these characteristics are frequently studied in the marketing literature, we are not aware of any work that incorporates delivery price, delivery time, travel time, travel cost, and package weight in the demand model.

To solve the challenging nonlinear nonconcave optimization models, we develop an efficient logic- based Benders decomposition (LBBD) approach and show that it is equally applicable to market Baloch and Gzara: UAV service with competition 10 share maximization problems under budget constraint. Logic-based Benders decomposition gener- alizes the classical Benders decomposition approach by relaxing the linear subproblem requirement

(Hooker 2000, Hooker and Ottosson 2003). In this approach, the original problem is divided into a master problem and subproblem(s). In the master problem, some decision variables and constraints are fixed/removed. Optimal solutions of the master problem are used in the subproblem(s) to gener- ate Benders cuts that are added back to the master problem. This iterative process continues until an optimal solution is found. Unlike classical Benders decomposition where standardized cuts are added using dual information of the subproblem, the cuts in LBBD are problem-specific (Hooker

2007). Therefore, while deriving optimality or feasibility cuts, the modeler needs to ensure that the cuts are strong and may be computed with little computational effort. Logic-based Benders decom- position has been used in a variety of applications including scheduling (Jain and Grossmann 2001), network design (Garg and Smith 2008), and location (Fazel-Zarandi and Beck 2012, Fazel-Zarandi,

Berman, and Beck 2013, Wheatley, Gzara, and Jewkes 2015). Within location problems, LBBD is applied to facility location and vehicle assignment problems Fazel-Zarandi and Beck(2012),

Fazel-Zarandi, Berman, and Beck(2013), and location-inventory problems Wheatley, Gzara, and

Jewkes(2015). Unlike the literature on location problems using logic-based Benders, we define

LBBD cuts using location decision variables as opposed to assignment variables which significantly improves the computational efficiency by reducing the number of binary decision variables in the master problem. A novel approach is also proposed to compute stronger cut coefficients with little computational effort using the properties of MNL model. To the best of our knowledge, our work is the first to use LBBD in a competitive facility location (CFL) problem.

2. Problem Definition

Consider an e-retailer that offers a set of same day delivery services {1, ..., n − 1} and plans to offer a new UAV service n. Let S = {1, ..., n} be the set of all e-retailer services. Amazon, for example has 2-hour and 12-hour same day delivery services and plans on offering 30-minute UAV delivery service. The e-retailer competes with existing stores e.g., retail, convenience, and department, Baloch and Gzara: UAV service with competition 11 that offer in-person shopping service n + 1. The e-retailer wants to decide on optimal network configuration by opening facilities from a set of discrete candidate locations J offering same services in S = {1, ..., n}. We assume that the network is designed from scratch which allows us to present a comparative study between networks with and without UAVs to investigate how offering a UAV service affects the network design. Later in Section 4.3, we show how a UAV service could be added to an existing network. Opening a facility at location j ∈ J incurs a fixed cost Lj. An additional

fixed service cost Fs is incurred for offering service s ∈ S. We assume that facilities have ample capacity to service all assigned demand regions. The capacity limitation is dealt with through stocking and replenishment decisions.

Customer demand originates from a set of finite customer zones I with two types of packages P =

{0, 1} where p = 0 denotes packages that are not deliverable by UAV and p = 1 refers to packages that may be delivered by UAVs. A package is defined as a bundle of products a customer buys in one order. A package cannot be delivered by a UAV due to two reasons: its weight exceeds UAV weight limit or landing at the customer location is not possible. A binary parameter asp is calculated apriori which indicates whether service s ∈ S can deliver package p ∈ P . As per FAA regulations,

UAV weight including the package must not exceed 55 lbs. This regulation is incorporated within parameter asp which equals zero for the packages that exceeds the weight limit. Another binary parameter, rijs, indicates whether delivery to customer zone i ∈ I from facility j ∈ J using service s ∈ S is possible, and is calculated based on the distance metric (Euclidean or Manhattan) being used. The parameter rijs takes into account maximum delivery range of services as well as other regulatory limitations such as airspace restrictions and dedicated paths. Current FAA regulations prohibit UAVs to fly over people and require the flight path to be limited within class G airspace.

As such, UAVs are required to fly in dedicated airspace, for instance, flying over the road network.

In our modelling approach, these restrictions only impact the reachibility which is captured by rijs.

However, the regulation to keep UAV within visual line-of-sight must be relaxed by the government for commercial use of UAVs. Until then, UAVs cannot operate. FAA regulations also require that Baloch and Gzara: UAV service with competition 12 an UAV is monitored by a certified operator and must fly under 100 mph. Hiring certified operators increases operator cost while flying speed affects the number of UAVs an e-retailer has to purchase.

As such, these regulations impact UAV delivery cost and are incorporated within the unit delivery cost parameter cijs. Refer to Section 5.1 for detailed calculations.

Three sets of binary decision variables (wj, xjs, and yijs) are defined where wj takes value 1 when facility j ∈ J is open and xjs takes value 1 when service s ∈ S is offered at location j ∈ J while yijs equals 1 if customer zone i ∈ I is assigned facility j for service s ∈ S. We also define two sets of continuous decision variables Disp and dijsp, where Disp denotes the demand captured by service s ∈ S for package p ∈ P in zone i ∈ I and dijsp is the portion serviced by facility j ∈ J.

The demand Disp, captured by a service depends on the other competing services available to the customers. The competition between the services is modelled using a multinominal logit (MNL) model detailed next.

2.1. Market share model

We use a multinomial logit (MNL) model to predict the demand captured by each service in a competitive environment. Customer zone i ∈ I has a maximum market size Nip for package p ∈ P which is distributed between the services in S0 = S ∪{n + 1} which compete on five distinct factors:

(1) inherent attractiveness, β0s (2) travel time, TTi, (3) travel cost, TCi, (4) delivery charge, qs, and

(5) delivery time DTs. To incorporate social resistance against UAVs, we may set β0n < β0s, ∀s ∈

S0\{n}, i.e., the inherent attractiveness of UAV service is, possibly significantly, less than that of other services.

We assume that there is no competition between the stores and customers visit their nearest store. It is further assumed that there is static competition between services offered by the e-retailer and stores, i.e., the characteristics of the services offered will not change once delivery by UAV service is made available.

The utility function of customer zone i ∈ I for package p ∈ P is: ! ! X X Uip = aspyijs exp(β0s − βdtDTs − βdcqs) + exp(β0,n+1 − βttTTi − βtcTCi) (2.1) s∈S j∈J Baloch and Gzara: UAV service with competition 13

where βtt, βtc, βdt, and βdc are sensitivity parameters to travel time, travel cost, delivery time, and delivery charges, respectively. The first expression on the left of (2.1) is the utility captured by the services offered by the e-retailer. The second expression is the utility captured by stores where customer i ∈ I visits the nearest store. The market share captured by service s ∈ S in customer zone i ∈ I for package p ∈ P is: ! X aspyijs exp(β0s − βdtDTs − βdcqs) j∈J MSisp = (2.2) Uip

The standard market share model assumes that market size is perfectly inelastic which limits the applicability of the model to capture market expansion or shrinkage. When more services are available to the customers, the probability of lost sales decreases. As a result, the overall market size increases. Similarly, a proportion of the market is lost since not all competing services in the market are included in the model. Hence, we use an exponential expenditure function (Berman and Krass 2002) to determine the proportion of the maximum market size Nip that is captured by all services offered by the e-retailer and the store. The expenditure function is

g(Uip) = 1 − exp(−λUip) (2.3)

and market size is Nip ×g(Uip). Parameter λ represents the elasticity of market size with respect to total utility Uip. When elasticity λ → ∞, g(Uip) → 1, and the maximum market size is fully captured.

When λ is low, the market size is small. Basuroy and Nguyen(1998) suggest a conceptually similar

θ expenditure function to estimate market size as MSZ0(Uip) , where MSZ0 is the base market size and 0 ≤ θ < 1 reflects the size of market expansion with respect to utility. This function is also applicable to our modelling approach and solution methodology. The demand captured by service s ∈ S in customer zone i for package p is Disp = Nip × g(Uip) × MSisp, or

! X Nip (1 − exp(1 − λUip)) aspyijs exp(β0s − βdtDTs − βdcqs) j∈J Disp = ! ! . (2.4) X X aspyijs exp(β0s − βdtDTs − βdcqs) + exp(β0,n+1 − βttTTi − βtcTCi) s∈S j∈J Baloch and Gzara: UAV service with competition 14

Network Representation S set of e-retailer services S = {1, . . . , n} where n is the new UAV service S0 set of services offered in the market, S0 = S ∪ {n + 1} where n + 1 is instore service J set of candidate Locations I set of customer zones P set of Packages, P = {0, 1} asp equals 1 if service s ∈ S can deliver package p ∈ P rijs equals 1 if zone i ∈ I is within the maximum range of service s ∈ S from facility j ∈ J

Cost Parameters Lj cost of opening facility j ∈ J Fs cost of offering service s ∈ S at a facility α profit margin (in percentage) πp package value cijs delivery cost per unit to zone i ∈ I from facility j ∈ J using service s ∈ S qs delivery charge for service s ∈ S

Market share model Parameters Nip maximum market size (in units) in zone i ∈ I for package p ∈ P DTs delivery time for service s ∈ S qs delivery charge for service s ∈ S TTi travel time for customers in zone i ∈ I to the nearest store TCi travel Cost for customers in zone i ∈ I to the nearest store β0s inherent attractiveness of service s ∈ S βdt delivery time (in hours) senstivity parameter βdc delivery charge (in dollars) senstivity parameter βtt travel time (in hours) senstivity parameter βtc travel cost (in dollars) senstivity parameter g(Uip) expenditure function λ elasticity of market size w.r.t to Uip

Decision variables wj equals 1 if facility j ∈ J is open. xjs equals 1 if service s ∈ S is offered at facility j ∈ J. yijs equals 1 if zone i ∈ I is assigned to facility j ∈ J for service s ∈ S Uip utility function of zone i ∈ I for package p ∈ P Disp Demand captured by service s ∈ S for package p ∈ P in zone i ∈ I dijsp Portion of Disp serviced by facility j ∈ J Table 2 Model parameters and decision variables

The expressions of Disp = f(yi11, ..., yijn+1) and Uip = u(yi11, ..., yijn+1) are functions of the deci- sion variable yijs. In fact, Disp and Uip are decision variables, and equations (2.1) and (2.4) are constraints to e-retailer’s problem detailed next.

2.2. Mathematical formulation

In this section, we formally define the complete mathematical formulation for e-retailer’s problem

[NP] using the modelling parameters and decision variables listed in Table2. Model [NP] is

X X X X X X X [NP]: max (απp + qs − cijs)dijsp − Fsxjs − Ljwj (2.5) i∈I j∈J s∈S p∈P j∈J s∈S j∈J Baloch and Gzara: UAV service with competition 15

X s.t. yijs ≤ 1 i ∈ I, s ∈ S, (2.6) j∈J

yijs ≤ rijsxjs i ∈ I, j ∈ J, s ∈ S, (2.7)

xjs ≤ wj j ∈ J, s ∈ S (2.8)

dijsp ≤ Myijs i ∈ I, j ∈ J, s ∈ S, p ∈ P, (2.9) X dijsp ≤ Disp i ∈ I, s ∈ S, p ∈ P, (2.10) j∈J (2.1), (2.4)

yijs ∈ {0, 1} i ∈ I, j ∈ J, s ∈ S, (2.11)

wj ∈ {0, 1} j ∈ J, (2.12)

xjs ∈ {0, 1} j ∈ J, s ∈ S, (2.13)

dijsp,Disp,Uip ≥ 0 i ∈ I, j ∈ J, s ∈ S, p ∈ P. (2.14)

The objective function (2.5) maximizes the overall profitability of the e-retailer expressed as the difference between revenues, delivery costs, fixed facility costs, and fixed service costs. Constraint

(2.6) ensures that customer zone i ∈ I is served using service s ∈ S by only one facility. Service s ∈ S may be offered from facility j ∈ J if delivery to the customer zone i ∈ I is possible i.e., rijs = 1, and it is available i.e., xjs = 1, as indicated by constraint (2.10). Constraint (2.8) ensures that a facility j ∈ J can offer services only if it is open. Constraint (2.9) ensures that demand serviced dijsp for package p ∈ P using service s ∈ S can only be satisfied by facility j ∈ J if the customer zone i ∈ I is assigned to it, where M is a large number to ensure that the constraint is nonbinding X for yijs=1. Constraint (2.10) limits the demand serviced by all facilities dijsp to customer zone j∈J i ∈ I for package p ∈ P using service s ∈ S to the demand captured by that service Disp. The latter depends on the utility that the customer zone i ∈ I derives from that service relative to the utility derived from other services and is completely defined when equations (2.1), and (2.4) of the market share model equations are added as constraints. Constraints (2.11), (2.12), and (2.13) are binary requirements for variables wj, xjs, and yijs respectively. Constraints (2.14) are the nonnegativity requirements for variables dijsp,Disp,Uip.

Note that the capacity for UAV deliveries in a given time period is factored in delivery costs, see

Table B3 for detailed calculations of unit UAV delivery cost. At facility j, the yearly demand for X X UAV service n is YDj = dijnp, where dijnp is the solution to model [NP]. The average hourly i∈I p∈P Baloch and Gzara: UAV service with competition 16

YDj demand Hj for UAV service at facility j is calculated as Hj = 365×14 . Based on average hourly

Hj ×ss demand, the number of UAVs required at facility j ∈ J is calculated as NFj = Φ , where ss is a safety factor set by the e-retailer to have sufficient additional UAVs, and Φ is the minimum number of deliveries a UAV can make within one hour. Safety factor ss takes into account fluctuations in hourly demand and the time associated with different overhead activities such as battery charging, battery swap, and delivery time under different weather conditions.

Although the safety factor takes into account fluctuations in hourly demand, the demand during certain days may be much higher. To consider this variability in demand, Hjt is defined as the demand at facility j on day t ∈ Y. Let Πt be the proportion of the demand on day t ∈ Y. The

YDj ×Πt average hourly demand Hjt for UAV service at facility j on day t is then calculated as Hjt = 14 .

Hjt×ss Similarly, the number of UAVs required at facility j ∈ J on day t is calculated as NFjt = Φ .

As such, the total number of UAVs required at facility j equals max{NFjt}. t∈Y

3. A Logic-Based Benders Decomposition Approach

When the services offered at the facilities are known, the problem reduces to assigning each cus- tomer zone to the nearest open facility offering a given service s ∈ S, and to decide whether this service s is offered or not. We exploit this feature to decompose [NP] into a location-service mas- ter problem (LSMP) that makes locational decisions, and a set of |I| customer service-assignment subproblems [SPi] where the assignment decisions are made. We develop a Location-Assignment

Benders (LAB) algorithm that iterates between the master problem and subproblems to solve the nonlinear formulation to optimality. First, the master problem LSMP is solved to make locational decisions:

X X X X [LSMP]: max Zi − Fsxjs − Ljwj (3.1) i∈I j∈J s∈S j∈J X X X s.t. (απp + qs − cijs)dijsp − Zi = 0 i ∈ I, (3.2) j∈J s∈S p∈P X max dijsp ≤ Disp i ∈ I, s ∈ S, p ∈ P, (3.3) j∈J max dijsp ≤ rijsDisp xjs i ∈ I, j ∈ J, s ∈ S, p ∈ P, (3.4) Baloch and Gzara: UAV service with competition 17

X X max dijsp ≤ TDip i ∈ I, p ∈ P, (3.5) j∈J s∈S cuts, (3.6) (2.8), (2.13), (2.12), (2.14),

Zi ≥ 0 i ∈ I (3.7)

where decision variable Zi captures the total revenue minus the delivery cost associated with serving customer zone i ∈ I, as defined by constraint (3.2). The objective function maximizes the total profit, which is the same as (2.5). Constraints (3.6) are Benders optimality cuts that are generated each time the subproblem is solved. Deriving optimality cuts from the subproblem solution is explained in detail in Section 3.2. Constraints (3.3), (3.4) and (3.5) are valid constraints, and are added to tighten the relaxation. Constraint (3.3) ensures that the demand serviced by all X facilities, dijsp, does not exceed the maximum demand that can be captured by service s ∈ S, j∈J max Disp . Constraint (3.5) ensures that for package p ∈ P in customer zone i ∈ I, demand serviced

X X max dijsp, must not exceed the maximum total demand TDip that e-retailer can capture. By j∈J s∈S max Lemma1, Disp is achieved when only that service is made available to the customer zone i ∈ I for

max package p ∈ P and TDip is achieved when all services in S are offered. These results are proven in

AppendixA and follows from properties of the MNL models (Cooper, Nakanishi, and Eliashberg

1988).

Lemma 1 For customer zone i ∈ I and package p ∈ P ,

max 1. the maximum demand that service s ∈ S may capture, denoted by Disp , is achieved when only that service is made available; and

max 2. the maximum total demand that the e-retailer may capture, denoted by TDip , is achieved when all services s ∈ S are made available.

3.1. Customer Service-Assignment Subproblems

One of the advantages of logic-based Benders decomposition approach is that the subproblem can take any form including an optimization problem or a feasibility problem (Jain and Grossmann

2001, Hooker 2005, Fazel-Zarandi and Beck 2012, Fazel-Zarandi, Berman, and Beck 2013, Wheatley, Baloch and Gzara: UAV service with competition 18

Gzara, and Jewkes 2015, Roshanaei et al. 2017). In contrast to the methodologies in literature, the subproblem in our case is a nonlinear optimization problem. When the location and service decisions are known, [NP] reduces to |I| customer-service assignment subproblems [SPi]:

X X [SPi] : max (απp + qs − cijs)dijsp (3.8) j∈J s∈S

s.t. yijs ≤ rijsxjs, j ∈ J, s ∈ S, (3.9) (2.7) − (2.9), (2.11), (2.14), (2.1), (2.4)

where xjs is [LSMP] solution. Subproblem [SPi] finds an optimal assignment of customer zone i ∈ I to offered services at open facilities. Such an assignment depends on the demand values determined by constraints (2.1), and (2.4). Since the latter are nonlinear, [SPi] remains challenging to solve.

We explain two main characteristics of [SPi] and develop a fast enumeration based algorithm to solve industry-scale instances. We also present special cases where the resulting optimization problem has a non-decreasing concave objective function that can be solved without enumerating over all scenarios. When xjs and wj are known, customer zone i ∈ I is assigned to the nearest open facility offering that service to minimize delivery costs, cijs. If rijsxjs = 0 ∀j ∈ J, customer zone i ∈ I is assigned to a dummy facility with sufficiently large penalty to ensure that service s ∈ S is not offered. When all customer zones are assigned, we need to decide on the optimal set of services to be made available to each zone which is a binary non-convex nonlinear optimization problem. We use an enumeration based approach to solve the problem. Note that the decomposition reduces the original problem to a point where only service decisions need to be optimized for each customer zone separately. Moreover, the services offered by an e-retailer are limited in practice.

For instance, Amazon offers a total of six main delivery services (Prime Now (2-hour), Same-Day

Delivery, One-Day Delivery, Release-Date Delivery, Free Shipping, and ) and not all of these services are offered at all customer locations (Amazon 2018). As such, the enumeration based approach performs extremely well for industry-scale instances.

Let P(S) be the power set of S. For zone i ∈ I and package p ∈ P , the demand captured by service s ∈ S when the set of services e ∈ P(S) is offered is precalculated as

Dispe = Nip(1 − exp(−λpU ipe))MSispe ∀ i ∈ I, s ∈ S, p ∈ P, e ∈ P(S) (3.10) Baloch and Gzara: UAV service with competition 19

where U ipe is the utility of customer zone i ∈ I for package p ∈ P when the set of services e ∈ P(S) is available. MSispe calculates the market share of package p ∈ P from customer zone i ∈ I captured by service s ∈ S when the set of services available is e ∈ P(S). The optimal solution of [SPi] is then

X X SP i = max { (απp + qs − MCis)Dispe} ∀i ∈ I (3.11) e∈ (S) P s∈S p∈P where MCis denotes minimum cost to deliver a package to zone i ∈ I using service s ∈ S. Note that Dispe is computed only once at the start of the LAB algorithm and the resulting subproblem

(3.11) is solved in |P(S)| iterations to find the set of services e ∈ P(S) to be offered to customer zone i ∈ I which maximizes operating profits SP i.

Under a special case, when the objective function coefficients (απp + qs − MCis) are same for all services in S and products in P , the resulting subproblem objective is a non-decreasing concave function and is therefore solvable in polynominal time. If ∃j ∈ J, s ∈ S: rijs ×xjs = 1, then by Lemma P 1 j∈J yijs = 1 i.e., service s must be offered to customer zone i by some facility to maximize the total demand captured. As such, enumerating over all possible set of services is not required and the optimal solution is to offer each service when ∃j ∈ J, s ∈ S: rijs × xjs = 1.

3.2. Logic-based Benders cuts

This paper presents a novel way to define cuts using location-service decision variables and inde- pendent of the assignment variables. This allows to remove assignment variables from the master problem, making it extremely efficient to solve repeatedly. The number of binary decision variables in the master problem reduces from |J|(|S|(|I| + 1)) to |J|(|S| + 1) when location-service based

Benders cuts are used instead of assignment-based cuts. The cut coefficients are also tailored to the location-service decisions variables and are calculated with little computational effort. Previous work in the facility location literature (Fazel-Zarandi and Beck 2012, Fazel-Zarandi, Berman, and

Beck 2013, Wheatley, Gzara, and Jewkes 2015), however, use assignment variables in defining the cuts.

Consider a solution (xjs, wj, Zi) obtained from [LSMP]. [LSMP] provides an upper bound to X X X X the original problem, and a lower bound is calculated as SP i − Fsxjs − Ljwj. Since i∈I j∈J s∈S j∈J Baloch and Gzara: UAV service with competition 20 market share constraints are dropped in the master problem [LSMP] and are replaced by an upper bound on Disp, at any given iteration, Zi ≥ SP i. When the operating profits Zi, in [LSMP] equal the operating profits calculated in subproblem SP i, ∀ i ∈ I, an optimal solution is reached. At a given iteration k, let Ok = {j ∈ J, s ∈ S : xjs = 1}. If ∃i ∈ I : Zi > SP i, we add Benders optimality cuts to the master problem [LSMP]. A valid Benders cut is defined by Chu and Xia(2004) as any logical expression that eliminates the current master solution (x, w, Z) if it is not feasible to the original problem [NP], and it must not eliminate any solution that is feasible to the original problem

[NP]. At each iteration, either optimality or feasibility cuts are added to the master problem. When the subproblem is feasible, optimality cuts are added to improve the lower bound (Roshanaei et al.

2017). If the subproblem is infeasible, feasibility cuts are added to the master problem (Jain and

Grossmann 2001, Hooker 2005, Fazel-Zarandi and Beck 2012, Wheatley, Gzara, and Jewkes 2015,

Fazel-Zarandi, Berman, and Beck 2013). In our problem, the subproblem is always feasible and feasibility cuts are therefore not required. We define optimality cut

X X X X Zi ≤ SP i + γijs(1 − xjs) + δijsxjs i ∈ I (3.12)

j∈Ok s∈Ok j∈ /Ok s/∈Ok where γijs and δijs are cut coefficients. The effectiveness of cut (3.12) depends on the cut coefficients.

A large value is likely to result in total enumeration. A significant contribution of the paper is in calculating effective cut coefficients with little computational effort. We present a novel approach that calculates right cut coefficients in (3.12) without eliminating any solution that is feasible to the original problem and is computationally efficient.

The cut coefficients are designed to capture the change in operating profits where γijs captures the minimum possible decrease in SP i when an available service s ∈ S at facility j ∈ J (i.e. xjs = 1) is closed. For a given service s at a facility j, minimum decrease in SP i is achieved when only

max max max max xjs = 0. We define γijs = Mijs − Mi where Mijs = SP i when only xjs = 0, and Mi = SP i when xjs = 1 ∀ j ∈ J, s ∈ S. Similarly, δijs captures the maximum possible increase in SP i when a

min service s ∈ S that is not offered at facility j ∈ J (i.e. xjs = 0) is opened. δijs = Mijs − Mi where

min Mijs = SP i when only xjs = 1, and Mi = 0 when xjs = 0 ∀ j ∈ J, s ∈ S. As such, γijs is the Baloch and Gzara: UAV service with competition 21

minimum decrease in SP i when only service s at facility j is closed and δijs is the maximum increase in SP i when only service s at facility j is open. In the same fashion, valid Benders optimality cuts can also be computed for the market share maximization problem. X X X X If the same set of services are offered in subsequent iterations, (1 − xjs) and xjs

j∈Ok s∈Ok j∈ /Ok s/∈Ok equal 0, reducing the cut to Zi ≤ SP i which is violated if Zi takes a value greater than SP i. As such, cut (3.12) ensures that either the current solution is changed or the operating profit is reduced to SP i, i ∈ I, i.e., it eliminates the current solution if it is infeasible. This proves that the cut satisfies the first condition. Since the maximum change is considered to calculate cut coefficients,

(3.12) does not remove any feasible solution and is a valid Benders cut.

LAB algorithm is an iterative process that alternates between [LSMP] and [SPi]. At a given iteration k, an optimal solution (x, w, Z) to [LSMP] is used to solve subproblems [SPi]. If ∀i ∈ I :

Zi = SP i, the solution (w, x, Z) is optimal. This rarely happens in early iterations since Disp in

[LSMP] is overestimated. If ∃i ∈ I : Zi =6 SP i, |I| optimality cuts (3.12), are calculated and added to [LSMP]. The algorithm stops when Zi = SP i, i ∈ I. The overall iterative algorithm (LAB) is shown in Figure1. Baloch and Gzara: UAV service with competition 22

Initialize k = 1

Compute

Dispe, γijs, δijs

Zi Solve LSMP

xjs optimal

[SP1] [SP2] [SP|I|]

SP i

Add Opti- no ∀ i ∈ I : Zi = SP i? mality cuts to

LSMP, k++

yes

Stop, optimal

solution found

Figure 1 Location-Assignment Benders Algorithm (LAB) Baloch and Gzara: UAV service with competition 23

Algorithm 1 Pseudo code for LAB Algorithm

Require: Benders cut coefficients γijs, δijs and demand values Dispe

Initialization 1: k ← 0 2: Z ← ∞ 3: SP ← 0

Main Loop X X 4: while Zi =6 SP i do i∈I i∈I 5: Solve [LSMP] . obtain solution (x, Z) 6: Z ← Z 7: x ← x 8: for customer zone i ∈ I do 9: for service s ∈ S do 10: MCis ← ∞ 11: for facility j ∈ J do 12: if rijs × xjs = 1 & cijs < MCis then 13: MCis ← cijs . Assigns zone to the nearest open facility offering service s 14: end if 15: end for 16: end for 17: Solve [SPi], . obtain (SP) 18: SP i ← SPi 19: Derive the optimality cut and add to [LSMP] 20: end for 21: k ← k + 1 22: end while Baloch and Gzara: UAV service with competition 24

4. Model Extensions

In this section, we discuss extensions to account for market share maximization objective, facility costs with economies of scale, and redesign of an existing network to add UAV service. We spec- ify the changes in the modelling and explain when and how the solution method is modified to accommodate the extensions.

4.1. Market Share Maximization Problem

In competitive facility location problems (CFLP), the problem is often modelled as market share maximization under budget constraint. The e-retailer’s market share maximization problem [MS] can easily be modelled as

X X X X [MS]: max dijsp (4.1) i∈I j∈J s∈S p∈P s.t. (2.1), (2.4), (2.6) − (2.14), X X X Fsxjs + Ljwj ≤ B, (4.2) j∈J s∈S j∈J

where (4.2) is the budget constraint ensuring that total fixed facility and service costs do not X X X exceed the available budget B. Model [LSMP] is modified by defining Zi = dijsp as the j∈J s∈S p∈P X total demand captured from customer zone i and the objective is to maximize Zi under budget i∈I constraint (4.2). For the market share maximization problem [MS], if ∃j ∈ J, s ∈ S: rijs × xjs = P 1, then by Lemma1 j∈J yijs = 1 i.e., service s must be offered to customer zone i by some facility to maximize the total demand captured. Disp is then simply calculated using Equation X X (2.4) and subproblem solution is SP i = Disp. Note that under market share maximization, s∈S p∈P the subproblem is solvable in polynomial time without a need for enumeration.

4.2. Facility costs with economies of scale

Model [NP] assumes a fixed cost Lj for opening a facility, and a fixed cost Fs for offering service s.

This assumes that the fixed costs are independent of the number of services offered. Often times, substantial cost savings might be achieved through economies of scale by offering multiple services at the same location. Economies of scale may be captured by defining fixed facility cost as a piece- wise linear function of the number of services offered. We define a new decision variable ηj that Baloch and Gzara: UAV service with competition 25

counts the number of services offered at facility j. The facility fixed cost Lj = fj(ηj) is then a nonlinear concave function. Let T = {0, 1, ..., |S|} be the set of possible values that ηj can take. The nonlinear function may be linearized by defining SOS1 variables σtj ∀ t ∈ T, j ∈ J. A parameter btj = t ∀t ∈ T , is also defined representing breakpoints of the number of services. The modified model with economies of scale [NPE] is as follows.

X X X X X X X X [NPE]: max (απp + qs − cijs)dijsp − Fsxjs − fj(btj)σtj (4.3) i∈I j∈J s∈S p∈P j∈J s∈S j∈J t∈T s.t. (2.1), (2.4), (2.5) − (2.7), (2.9) − (2.13), (2.14), X ηj = xjs j ∈ J, (4.4) s∈S X ηj = btjσtj j ∈ J, (4.5) t∈T X σtj = 1 j ∈ J, (4.6) t∈T

σtj ≥ 0, σtj → SOS1 t ∈ T, j ∈ J, (4.7)

where Constraint (4.4) counts the number of services offered at facility j ∈ J. Constraints (4.5) and (4.6) defines ηj as convex combination of two consecutive breakpoints of the number of services P and t∈T fj(btj)σkj is a convex combination of two breakpoint service costs.

4.3. Facility location and relocation Problem

So far, we consider the design of a network from scratch. However, when a network already exists the question may be whether a redesign is necessary. We now show how to modify model [NP] to allow for possibly closing existing facilities and opening new ones. We partition the candidate locations into two sets J = J E ∪ J N , where J E be the set of existing facilities, J N be the set of new candidate facilities. Let Sj be the set of services that are already offered at the existing facility j ∈ J E. The objective function is then modified as

X X X X X X N X N max (απp + qs − cijs)dijsp − Fs xjs − Lj wj (4.8) i∈I j∈J s∈S p∈P j∈JN s∈S j∈JN X E X X X E X X E − Lj wj − CLj (1 − wj) − Fjsxjs − CSs (1 − xjs) j∈JE j∈JE j∈JE s∈S j∈JE s∈Sj

N N where Fs is the fixed cost of offering service s ∈ S at a new facility, Lj cost of opening the new

N E facility j ∈ J , Lj is the fixed cost of operating an existing facility, CLj is the cost of closing an Baloch and Gzara: UAV service with competition 26

E E existing facility j ∈ J , Fjs is the fixed service cost (could be a new or an existing service) at the

E E existing facility j ∈ J , and CSs are the costs associated with closing service s ∈ Sj at an existing facility. The above objective function takes into account two important factors while deciding on relocation of the facilities, first, it considers the cost of closing a facility or a service, and secondly,

E if the facility is not closed, it would incur fixed cost of Lj to operate it and is expected to be less

N E than Lj since there are no initial setup costs. Note that fixed service costs Fjs depends on whether the service is already being offered at the facility j ∈ J E or it has to be added.

5. The case of NYC

An actual network, shown in Figure2, is constructed for New York City (NYC), the most populated city in the USA with a population of around 8.5 million, and is spread over a land area of 789 km2 (NYC 2016). There are several reasons that motivate selecting NYC for the case study. First, the world’s largest e-retail company, Amazon.com, first started its 2-hour delivery operations in

NYC. UAV service shares similar characteristics with 2-hour delivery service to make instantaneous deliveries. Selecting a city where such a service is already offered allows for investigating the effects of introducing UAV delivery service. Second, NYC’s land area allows the possibility of multiple facilities to open. NYC also poses challenges because of high rises. There is ongoing research as how apartment buildings should be designed or updated to accommodate UAV deliveries. One such concept is “DragonFly” by UK-based industrial design studio where packages are dropped on landing pads installed on the sides of buildings allowing direct delivery to customer apartments

(PriestmanGoode 2018). Our study helps answer the question of whether advancing the technology to allow delivery to tall buildings is worth it and how this impacts the overall design of the network.

Finally, availability of data online was a major reason in using NYC and Amazon in the case study.

Data available on Amazon.com is used to estimate market share model parameters and other cost

figures. Section 5.1 details the data used.

5.1. Data used

Physical network and facility costs NYC consists of five boroughs that are divided into

Neighborhood Tabulation Areas (NTAs) as shown in Figure2(NTA 2015). The centroid of each Baloch and Gzara: UAV service with competition 27

Bronx Legend Facility ● ● ● ● Stores ●● ● ● ● ● ● ● ● ● ● ● Population ● ● ● ● ● ● 125000 ● ● 100000 ● ● ● Manhattan● ● ● 75000 ●●● ● ● ● ● ● ● 50000 ● ● ●● ● ● Queens 25000 ●● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ●

● ●

● Brooklyn

Staten Island

Figure 2 New York City Network

NTA is used as a customer zone. To locate competitive stores (retail, grocery and departmental), we use Google Earth software to find their exact locations. Moreover, 20 candidate facility locations are selected such that they are evenly distributed over the network. In practice, there already exists a network with open facilities. For the sake of simplicity, we assume that the network is designed from scratch and no such facilities are open. However, we can easily design a UAV network given an existing network by forcing wj = 1 for already open facilities in the model. Each facility is assumed to be 50,000 sq.ft based on the fact that Amazon has 50,000 sq.ft distribution center in Manhattan to offer same day delivery services in NYC. To estimate yearly facility cost Lj, we consider warehouse lease rates, labor and miscellaneous costs. Yearly labor and miscellaneous costs for a 50,000 sq.ft facility are estimated to be $1.5 million based on the study conducted by Boyd Company (Boyd 2014). To calculate the lease rate of a facility j ∈ J located in a given borough b, we use Jll(2015) report and online leasing website LoopNet (LoopNet 2017) to estimate minimum (minb) and maximum (maxb) lease rates ($/sq.ft) in each borough b. Yearly facility cost Baloch and Gzara: UAV service with competition 28

Lj = 50, 000 ∗ U(minb, maxb) + 1, 500, 000, where U(minb, maxb) randomly generates a lease rate for a facility in a given borough b. Each facility can offer three types of services S = {1, 2, 3}. The maximum range of 2-hour (s = 1), 12-hour (s = 2), and UAV (s = 3) services are assumed to be

20 km, 40 km, and 10 km, respectively. Amazon’s Prime Air travels up to 24 km while DHL’s

Parcelcopter has a maximum flying range of 16 km which averages to 20 km. Since the UAV must

20 return back to the facility, its maximum range is set to 2 = 10 km. For UAV service, we set rij3 = 0 for all customer zones that are within short distance to the airport and is shaded in grey in Figure

2. For 2-hour and 12-hour services, the maximum ranges are estimated by calculating the distance between Amazon’s current distribution center in Manhattan and the farthest location (based on zip code) where each service is available. It turns out that 12-hour service is available to all boroughs in New York City while 2-hour service is not offered in Staten Island. The distances between the nodes are calculated using geosphere package in R (Hijmans 2017). The yearly additional cost of offering service s = 1 or s = 2 at a facility, Fs = $250, 000. Yearly cost of offering UAV service s = 3 is estimated to be $1, 000, 000 based on the ARK Invest industry report (Keeney 2016).

Package delivery costs and service charges Unit delivery costs cijs for each service s ∈ S are presented in Table3. To estimate UAV delivery cost cij3, we use a similar methodology as presented by ARK Invest (Keeney 2016). Detailed calculations are shown in Table C3, where the amortized UAV and battery costs are used along with operator salary cost to estimate cost per delivery. To do so, we estimate the number of UAVs and batteries an e-retailer has to purchase to meet its yearly demand YD. The maximum hourly demand Hmax is the average hourly demand multiplied by a safety factor ss. The latter accounts for fluctuations in hourly demand, the time associated with overhead activities such as battery charging and battery swap, and fluctuations in delivery time because of weather conditions. The value of the safety factor is estimated based on two industry reports. In a market survey by Statista(2015), out of four time windows, 48% of the respondents shop online during the peak-time window. Based on these figures, the ratio of peak

48% time demand to average demand is estimated as ss = 1 = 1.92. Using the data from Albright 4 Baloch and Gzara: UAV service with competition 29

(2015) who reports the percentage of hourly online retail sales, we estimate ss = 1.6. We round up the estimated values and set the safety factor to ss = 2.0 to take into account other operational

fluctuations.

Assuming that a UAV flies at a speed of 40 km/h and has a range of 10 km, it can make atleast

Hmax two deliveries per hour and as such, we set the number of UAVs required to 2 . We further assume that the number of extra batteries required equals the number of UAVs to ensure zero charging time. Using the number of UAVs and batteries, the purchasing cost PC, is calculated and amortized over a period of five years (rate, r = 20%) to estimate yearly amortized cost, AC = r × PC. Several reports suggest that FAA new regulations for delivery by UAVs would require certified operators to monitor the UAV activity (Wang 2016, Keeney 2016). However, the number of UAVs ND, an operator can manage simultaneously are highly speculated ranging from 1 to 30.

For the base case scenario, we assume that ND = 10, i.e., 10 UAVs per operator are allowed. To calculate the number of UAV operators required, we assume that the delivery process is automated and operators’ role is to monitor flight operations from a central control room in the city. In case of an emergency, however, an operator flies the UAV manually. An operator can make two deliveries

Hmax per hour and as such, the number of operators required per hour then equals 2×ND and is used to estimate yearly operator salary cost, OC. The total yearly cost, TC = AC + OC, and unit delivery

TC cost, cij0 = YD + 0.10 = $2.62, where $0.10 is the battery charging cost per delivery.

For 2-hour service s = 1, Amazon uses its Flex Program where independent drivers are paid $20 per hour to make deliveries (Chuang 2016). We estimate cij1 = $10 if a driver makes 4 deliveries in a two hour window. For 12-hour service s = 2, cij2 = $6 based on the analysis presented by Wohlsen

(2013). These cost figures are well aligned with Amazon’s delivery charges. For each service s ∈ S, delivery charges qs are assumed to be equal to the unit delivery cost cijs as e-retailers usually do not earn profits from delivery charges. In fact, Amazon reports revenue earned from delivery to be less than delivery costs incurred (Statista 2018). Baloch and Gzara: UAV service with competition 30

Lj : 50000 × U(minb, maxb) + 1, 500, 000 yearly facility costs

π0 = π1 = 20, α = 0.30 package price and profit margin f1 = $250, 000 2-hour delivery - yearly facility costs f2 = $250, 000 same-day delivery - yearly facility costs f3 = $1, 000, 000 30-minute delivery by UAV - yearly facility costs cij1 = q2 = $10 delivery cost and charges per package using 2-hour service cij2 = q3 = $6 delivery cost and charges per package using same-day service cij3 = q1 = $2.62 delivery cost and charges per package using UAV service r1 : 20km Range of two-hour delivery at a facility r2 : 40km Range of same day delivery at a facility r3 : 10km Range of delivery-by-UAV

β04 = 0.00, β01 = −2.00, β02 = −2.00, β03 = −2.22, Inherent attractiveness of the services available.

βtt = 1.4 Travel time (in hours) sensitivity parameter.

βtc = 0.035 Travel cost sensitivity parameter.

βdt = 0.092 Delivery time (in hours) sensitivity parameter.

βdc = 0.34 Delivery charges (in dollars) sensitivity parameter. λ = 0.5 Demand elasticity parameter, elastic. Table 3 NYC example input parameters

Market share model parameters As pointed out earlier, for same day delivery, products that are readily available at convenience and retail stores are frequently ordered. We therefore use US grocery sales 2015 (Bender 2016) to estimate maximum market size Nip in customer zone i ∈ I for package p ∈ P . Grocery sales (in dollars) are converted into units by assuming that average package value πp = 20, p = {0, 1}. The total grocery sales (in units) in a given customer zone are then estimated based on its population relative to US population. We assume that UAV delivery is not possible to apartment buildings (i.e., the number of units in the building µ ≤ 9, for UAV delivery), and only 86% of the packages meet UAV weight capacity based on an interview of Amazon’s CEO

Jeff Bezos in 2014 (Quinn 2015). Building size data is retrieved from American Community survey data (ACS 2015) which presents housing characteristics for all customer zones (NTAs). As such, in a customer zone i ∈ I, total grocery demand is divided between packages p = 0 and p = 1 to estimate maximum market size Nip.

Sensitivity parameters of the market share model are usually estimated based on market surveys or POS data (refer to Cooper, Nakanishi, and Eliashberg(1988)) which does not fall within the scope of this work. We therefore use the sensitivity parameters as estimated in (Schmid, Schmutz, and Axhausen 2016). Schmid, Schmutz, and Axhausen(2016) study consumer choice behavior Baloch and Gzara: UAV service with competition 31

Bronx Legend Bronx Facility Stores

Population 125000 100000 Manhattan Manhattan 75000 [1,2,3] [3]

50000 Queens [1,2] Queens 25000

[1,3]

Brooklyn Brooklyn Staten Island Staten Island

(a) Without UAVs (b) With UAVs Figure 3 NYC optimal network configuration

for online grocery shopping versus in-store. The inherent attractiveness for online shopping β0s =

−2.00 relative to in-store shopping (β04 = 0.0). β0s < 0 indicates negative attraction towards online shopping. For UAV service, we assume β03 = −2.2 to account for social resistance. Schmid, Schmutz, and Axhausen(2016) calculate average value of the travel time VOTT = βtt = 40.0$/hr and travel βtc cost sensitivity βtc = 0.035. As such, travel time sensitivity βtt = VOTT × βtc = 40.0 × 0.035 = 1.4.

βdt The study estimates the value of delivery time VODT = = $6.5/day = $0.27/hr. We set βdt = βdc

0.27βdc in the utility function (2.1) and calculate βdc such that the percentage of the grocery market that is captured by e-retailers equals US online grocery market share. Based on our calculations,

βdc = 0.34 and βdt = 0.092. We use demand elasticity λ = 0.5 so that on average, the expenditure function (2.3) equals Amazon’s online grocery market share (41%). When estimating βdc and λ from utility and expenditure functions, we do not include UAV service. This is because the market share figures and the study conducted by Schmid, Schmutz, and Axhausen(2016) are based on same day delivery without UAVs.

5.2. Analysis of the base case

To study the effect of UAVs on network design, we solve the NYC instance under two scenarios. In scenario 1, UAV service is dropped from the model and the resulting optimal network is shown in Baloch and Gzara: UAV service with competition 32

● ● ● 100% 50 ● ● ● 40 75%

● 30 50% ● ● ● ● ● 20 ● UAV coverage (%) coverage UAV ● 25%

Revenue/Costs (in millions) Revenue/Costs Net Profits ● Area coverage 10 ● Operating Profits ● Population coverage Facility costs 0% ● 0 2 4 6 0 2 4 6 Nb. of UAV facilities Nb. of UAV facilities (a) Operating Profits vs facility costs (b) UAV coverage Figure 4 Trade-offs between net revenue, costs and coverage

Figure 3a. A single facility is open and it offers both 2-hour and 12-hour services. While 12-hour service is available to all customer zones, only 95% of the customer zones can use the 2-hour service as shown by the region in the red circle in Figure 3a. In scenario 2, the model is solved with all three services. In the optimal design, three facilities are open, each offering UAV service to the customers within its 10 km radius as depicted by the blue circles in Figure 3b. The facility opened in scenario

1 is no longer optimal for scenario 2. This shows that incorporating a UAV service may require the relocation of existing facilities. We also observe that under scenario 2, 2-hour service (s = 1) is made available at two facilities which improves its coverage from 95% to 98%. UAV service may also improve the coverage of other services. In this example, the coverage of 2-hour service s = 1 improves from 95% to 98%. Offering UAV service increases facility costs by $11.2 million while it increases operating profit by $27.7 million from $18 million to $45.7 million. Higher facility costs are compensated by increased operating profits due to the increase in market share captured by the e-retailer from 3.0 million to 7.6 million packages.

To further investigate the effect of the number of facilities open on the operating profits and costs and on UAV coverage, we add a constraint to the model to fix the number of UAV facilities Baloch and Gzara: UAV service with competition 33

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 75% ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 50% ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 25% ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● UAV population coverage UAV ● ● ● ● ● ● ● 0% ● ● µ ≤ 2 µ ≤ 4 µ ≤ 9 µ ≤ 20 µ ≤ ∞ UAV building size µ constraint

Figure 5 UAV population coverage vs building size µ constraint open to a specific number and vary it between 0 and 7. Figure 4a plots the operating profits and costs in function of the number of UAV facilities open and Figure 4b shows UAV coverage. “Area coverage” denotes the percentage of customer zones that are within 10 km radius of an opened facility offering UAV service. However, not all customers within 10 km can be served by UAVs due to technological limitations including building size and package weight. Population coverage takes these limitations into account and gives the percentage of the population for which UAV delivery is possible. As expected, facility cost increases linearly with the number of open facilities. Operating profits, on the other hand, increase at a decreasing rate. The net profit is maximized with three open UAV facilities covering 75% of the NYC area and 34% of the population. Opening a fourth facility increases area and population coverage to 84% and 38% respectively, but the increase in operating profit is not sufficient to cover additional facility costs.

5.3. Technological limitations and network design

Currently, UAV technology is in the development phase and it is hard to predict technological constraints associated with it. In this paper, we take into account two types of technological limitations that a UAV delivery will face: parcel weight limit, and building size. Many reports suggest that a UAV cannot deliver parcels weighing more than 5 lbs (Wang 2016, Rezapour and Baloch and Gzara: UAV service with competition 34

Farahani 2014). Consequently, population coverage cannot exceed 86% due to the weight limit.

However, the type of buildings where UAV delivery would be possible is not clear yet. In our analysis, we assumed that UAV delivery is only possible to buildings with units µ ≤ 9. In this section, we relax the assumption. Figure5 is a box-plot of UAV population coverage in all customer zones under different building size requirements and shows that as the building requirement is relaxed, the coverage increases. Coverage is maximized when delivery is possible to all building types and reaches 86%. As the building requirement is relaxed, more facilities are open as illustrated in Figure6. When building requirement is µ ≤ 4, a densely populated area like Manhattan is not offered UAV service because 95% of the population live in buildings with 5 or more units. In Staten

Island, 100% of the population live in buildings with 4 units or less. However, Staten Island is not offered UAV service due to low demand. Brooklyn and Queens are the most favorable boroughs for UAV delivery due to high population living in buildings with fewer number of units. The above analysis shows that advancement in technology will play a vital role in shaping the future of UAV delivery.

5.4. Government regulations

Government regulations are expected to play a vital role in determining the future of UAVs in last-mile delivery. These regulations may require firms to hire certified operators to monitor UAV activity leading to higher delivery costs and delivery charges which would in turn reduce customer attraction towards the UAV service.

5.4.1. Analysis of UAV’s target market The number of operators a firm needs to hire depends on the number of UAVs, ND, an operator is allowed to monitor simultaneously. In the base case scenario in Section 5.2, we set ND = 10. However, this value is highly speculative as some reports suggest only 1 to 2 UAVs per operator (Lewis 2014a) will be allowed while others believe this value may be as high as 30 (Keeney 2016). To determine the effect of government regulations on UAV delivery, we solve the model under different values of ND.

Based on our calculations in Table C3, Figure 7a illustrates the relationship between ND and

UAV delivery cost cij3 which decreases at a decreasing rate as ND increases and varies significantly Baloch and Gzara: UAV service with competition 35

Bronx UAV Bronx UAV Bronx Population Coverage Coverage 125000 50000 60000 100000 40000 40000 75000 30000 50000 20000 20000 25000 10000 Manhattan Manhattan Manhattan

[1,3] Queens [1,3] Queens

[1,2] Queens

[1,2,3] [1,2,3]

Brooklyn Brooklyn Brooklyn Staten Island Staten Island Staten Island

(a) Without UAVs (b) µ ≤ 2 (c) µ ≤ 4

UAV UAV UAV Coverage Bronx Coverage Bronx Coverage Bronx 60000 60000 90000 40000 40000 60000 [3]

20000 20000 30000 Manhattan[1,2,3] Manhattan[1,2,3] Manhattan[1,2,3] Queens Queens [3] [3] [3] Queens

[1,3] [1,3] [1,3]

Brooklyn Brooklyn Brooklyn

Staten Island Staten Island Staten Island

(d) µ ≤ 9 (e) µ ≤ 20 (f) µ ≤ ∞ Figure 6 UAV building size µ constraint

from $24 for ND = 1 to $1 for ND = 30. Since UAV delivery charge q3 is determined by the delivery cost, ND would impact the demand captured by the UAV service. As such, government regulations will have significant impact on value-added by UAVs. To study this, we solve the model by varying market size using elasticity parameter λ between 0.01 to 1.3. under four different values of ND: 2, 5, 10, and 30. Currently, FAA regulations allow only one UAV per operator which is too restrictive to make UAVs economically feasible. For ND = 1, UAV service is not offered by the e-retailer due to low demand and high service costs. However, these regulations are expected to be relaxed in the future and we therefore vary ND between 2 to 30. Figure 7b plots e-retailer’s profits against the market size under different government regulations where “No UAV” denotes e-retailer’s profit in the absence of UAV service. As the market size increases, profits increase due to Baloch and Gzara: UAV service with competition 36

120 25 No UAV ● ND = 2 ND = 5 20

3 90 ND = 10 ij

c ND =

30

15 60

10 Profits (in millions)

Unit delivery cost, Unit delivery ● ● 30 ● ● ● ● ● ● ● ● ● 5 ● ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● 0 0 ●●●●●●●●●● 0 4 8 12 16 20 24 28 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Nb. of UAVs per operator, ND Market size, λ

(a) UAV delivery cost as a function of Nb. of (b) UAVs per operator effect under different

UAVs per operator market sizes

Figure 7 Effect of regulations for UAVs on same day delivery market βtt

0.100 ● 47.5 ● 500 ● ● 1000 45.0 ● 0.075 ● 400 800 42.5 ● ● 0.050 ● ● 300 ● ● ● ● ● ● 600 40.0 ● ● ● PVAD(%) ● ● ● ● ● ● 0.025 ● ● 200 ● ● 400 37.5 ● ● ● ● ● ● ● ● ●●●●●●●●● ● ● ● ● ●●●●● ● ●●●●●●●●●●●●● ●● ●● ●●● ● ●●●●●● ●●●●● ●●●●● ●●●●●● 0.000 ●●●●●●●●●●●●●●●●●●●●●●●●●●● 35.0 100 200 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Market size, λ Market size, λ Market size, λ Market size, λ

(a) ND=2 (b) ND=5 (c) ND=10 (d) ND=30 Figure 8 Effect of government regulations on PVAD higher demand captured and profit curve shifts upwards as ND increases. To investigate the value- added by UAVs, we plot the percentage value-added (PVAD) against market size under different government regulations as shown in Figure8. PVAD is calculated as the percentage increase in profits between scenarios 1(without UAVs) and 2(with UAV).

For ND = 2, PVAD is maximized when the market size is very large as shown in Figure 8a.

For λ ≤ 1.2, PVAD = 0% i.e., UAV service is not even offered due to low demand and high delivery costs. At λ = 1.3, PVAD is only 0.10%. However, as government regulations are relaxed Baloch and Gzara: UAV service with competition 37

5 Without UAV service 4 Nb. UAV facilities

3

2

1 Nb. of open facilities 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Market size, λ Market size, λ Market size, λ Market size, λ

(a) ND=2 (b) ND=5 (c) ND=10 (d) ND=30 Figure 9 Effect of government regulations on the number of UAVs facilities i.e., ND = 5, 10, 30, PVAD increases significantly for all markets as shown in Figures 8b, 8c, 8d.

PVAD is maximized when the market size is small. At λ = 0.08, PVAD = 47%, 504%, and 1094% for ND= 5, 10, and 30, respectively. To understand this phenomenon, we compare the number of

UAV facilities opened with the number of facilities without UAV service at different market sizes as shown in Figure9. Without UAV service, only one facility is open when λ ≥ 0.08. With UAV service, the number of facilities depend on ND, the number of UAVs per operator and on market size. For ND = 2, UAV service is offered only for large market size at a single facility offering other services. As ND increases to 5, 10, and 30, more facilities are open to offer UAV service for smaller market sizes. Hence, PVAD is maximized when the market size is small as UAV service allows e-retailers to enter these markets which would otherwise not have been possible due to small market size. The analysis shows that UAV service may allow e-retailers to extend same day delivery services and offer UAV service in regions with small market size when the regulations are less restrictive. On the other hand, if regulations are more restrictive, UAV service might be restricted to densely populated areas where technological limitations and high delivery charges may limit the added value of UAVs.

5.4.2. Analysis of UAV delivery charges In the base case scenario, we assume that delivery cost cijs equals service charge qs. However, service charge plays a crucial role in optimizing e- retailer’s profits and may not always be equal to delivery cost. We vary q3 between −$5 to $18, customer delivery charge sensitivity βdc from 0.05 to 1.00, and set ND = 2, 5, 10, and 30. Negative Baloch and Gzara: UAV service with competition 38

300 βdc 1.00

200 0.75

0.50

100 0.25 Profits (in millions)

0 −6 −3 0 3 6 9 12 15 18 −6 −3 0 3 6 9 12 15 18 UAV delivery charge, q3 UAV delivery charge, q3

(a) ND=2 (b) ND=5

300 βdc 1.00

200 0.75

0.50

100 0.25 Profits (in millions)

0 −6 −3 0 3 6 9 12 15 18 −6 −3 0 3 6 9 12 15 18 UAV delivery charge, q3 UAV delivery charge, q3

(c) ND=10 (d) ND=30 Figure 10 UAV delivery charge analysis under government regulations and customer delivery charge sensitivity

delivery charge, q3 < 0 may be interpreted as a discount offered by the e-retailer for using UAV service. Figure 10 plots profits against UAV delivery charge q3 at different levels of delivery charge

∗ ∗ sensitivity βdc. As βdc increases, the optimal delivery charge q3 decreases. When βdc = 0.05, q3 = $18, irrespective of government regulations. On the other hand, if customers are more sensitive, for instance when βdc = 1.00, government regulations play a crucial role in pricing decision and

UAV’s added value. Recall the profit margin per unit = απp = 0.30 × 20.0 = $6.0. When ND = 2,

∗ cij3 = $12.2. For profits to be positive, q3 > 12.2 − 6.0 = $6.2. Since customers are highly sensitive to delivery charge (βdc = 1.00), even at lowest possible q3 = $7, demand is not sufficient to cover

fixed costs and as such, e-retailers do not offer UAV service as shown in Figure 10a. Similarly, for Baloch and Gzara: UAV service with competition 39

300 ● Without UAVs With UAVs

200 ● ● ● ●

● ● ● ● 100 ● ● ● ●

● ● ● ● Profits(in millions) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 βdc βdc βdc βdc

(a) ND=2 (b) ND=5 (c) ND=10 (d) ND=30 ∗ Figure 11 Profits under optimal UAV delivery charge q3

600 ● ● 25 ● ●

20 3000 9000 400 15 2000 6000 ● ● 10 ● ● PVAD(%) 200 ● 1000 3000 5 ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● ● 0 ● ● ● ● ● ● 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 βdc βdc βdc βdc

(a) ND=2 (b) ND=5 (c) ND=10 (d) ND=30

Figure 12 Customer price sensitvity βdc and PVAD

∗ ∗ ND = 5, cij3 = $5.0, and q3 > −$1.0. In this case, q3 = $0.0 and profits equal $1.9 million as shown

∗ in Figure 10b. For ND = 10 and 30, the optimal delivery charge q3 = -$2.0 and -$3.0 respectively.

This shows that government regulations may allow an e-retailer to either offer discounts or force it to set high UAV delivery charges.

∗ Figure 11 plots e-retailer’s profits at optimal UAV delivery charge q3 against βdc for different values of ND. It is interesting to note that when the e-retailer cannot offer discount over the retail price (i.e., negative delivery charge), its profits decrease as βdc increases as shown in Figures

11a and 11b. However, for ND = 10 and 30, the profit function is U-curved as shown in Figures

11c and 11d. In fact, e-retailer’s profits are maximized when ND = 30 and customers are most sensitive to delivery charge. Figure 12a plots PVAD against βdc for ND = 2 and shows that under strict government regulations, PVAD is maximized when customers are less sensitive to delivery charges allowing the e-retailer to charge higher prices. UAV service is therefore considered as a Baloch and Gzara: UAV service with competition 40

● ● ● ● ● ● ● 40 ● ● ● ● ● ● 120% ● 30

PVAD 115%

20 Profits (in millions)

Without UAV service 110% ● With UAV service 10 0 25 50 75 100 0 25 50 75 100 Travel time sensitivity, βtt Travel time sensitivity, βtt

(a) Profits (b) PVAD

Figure 13 Effect of Travel time sensitivity βtt premium service available to customers who are willing to pay higher delivery charges for a 30- minute delivery. On the other hand, when government regulations are relaxed, PVAD is maximized when customers are most sensitive to delivery charges as shown in Figures 12b, 12c, 12d. Relaxed regulations allow the e-retailer to set lower delivery charges or offer discounts over the retail price to maximize its profits. As such, UAV service will be accessible to a wide variety of customers.

5.5. Effects of competitive stores

We vary customer utility for in-store shopping by varying travel time sensitivity βtt between 0.0 to 100.0. Figure 13a plots the profits in function of βtt. As βtt increases, the e-retailer’s profit increases at a decreasing rate. Recall the utility function (2.1), as βtt increases, customer utility for in-store shopping decreases and the store loses market share. A proportion of the store’s lost market share is captured by the competing services offered by the e-retailer and the rest is lost due to the expenditure function (2.3) that allows market shrinkage when overall customer utility decreases. As βtt increases, the store’s lost sales increase leading to increased market share captured by the e-retailer which translates into an increase in profits. But as βtt increases, its marginal effect on the e-retailer’s profits decreases. This is further shown in Figure 13b which plots the percentage Baloch and Gzara: UAV service with competition 41

60 ● Without UAV service 1500 50 ● With UAV service

40 1000 30 ● PVAD(%) 20 ● 500

Profits (in millions) ● ● ● ● 10 ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Delivery time sensitivity, βdt Delivery time sensitivity, βdt

(a) Profits (b) PVAD

Figure 14 Effect of customer delivery time sensitivity βdt

value added by UAVs, PVAD, in function of βtt. Figure 13 suggests that the competitive advantage of UAV delivery is maximized in regions where customers do not have access to stores at a close proximity and to time sensitive customers.

5.6. Effects of customer delivery time sensitivity

Since UAVs fly over congested road networks and a single delivery per trip is made, delivery time is expected to reduce significantly. To study this attractive feature of UAVs, we vary customer sensitivity to delivery time, βdt and analyze its effects on value-added by UAVs. βdt is varied from

0.0 to 1.9 and the model is solved under scenarios 1 and 2. Figure 14a illustrates the effect of βdt on e-retailer’s profits under each scenario. As βdt increases, customer utility towards online shopping decreases exponentially which leads to reduced profits as shown in Figure 14a. Under scenario 1, when βdt > 0.4, profits equal $0. This is because delivery time sensitive customers prefer in-store shopping where there is zero delivery time and as such, the e-retailer does not have enough demand to cover its facility costs. Under scenario 2, the e-retailer is able to earn profits even when βdt = 1.8.

Due to the instant delivery feature of UAVs (30-minutes), time sensitive customers place order online and opt for UAV service. As shown in Figure 14b, PVAD is maximized when customers are most sensitive to delivery time. When βdt = 0.0, PVAD is 46% and increases to 1686% at βdt = 0.4. Baloch and Gzara: UAV service with competition 42

This shows that UAV service captures demand from time sensitive customers, which in turn leads to increased e-retailer profits. It may also allow the e-retailer to enter new markets where demand was previously low due to time sensitive customers.

6. Analysis of solution algorithm: LAB

We conducted several experiments to study the efficiency of LAB algorithm in solving profit maxi- mization problems [NP ] by randomly generating nodes over a 1600 km2 square region. The number of customer demand points |I| = {50, 100, 150, 200, 250}. The number of candidate facility locations

|J| = {10, 20, 30, 40, 50}. To compute the maximum demand (Nip), each customer zone i ∈ I and package p ∈ P is assigned a weight from a uniform distribution [0,1]. Randomly generated weights are then used to proportion NYC grocery sales into different customer zones and packages to cal- culate Nip. We assume λ = 10.0. The facility costs are randomly generated between $1 million to $2 million. High λ and low facility costs are selected to challenge the algorithm with higher demand values and allow multiple facilities to open. Each instance is solved over two different values of the number of stores: 10 and 100. All other parameters are the same as used for the base case in

Section 5.1. For a given |I|, |J|, and stores, 10 random instances are generated resulting in a total of 500 instances.

To validate the effectiveness of the LAB algorithm, we compare its CPU time with the mixed integer linear reformulation given in AppendixB. LAB is coded in C++ Visual Studio 2013 and all optimization problems are solved using CPLEX version 12.6.1 on a 64-bit Windows 10 with Intel(R) core i7-4790 3.60GHz processors and 8.00 GB RAM. Each instance is executed to an optimality gap of 1e-09 or up to 3600 seconds in CPU time. The results are summarized in Table4 where values are reported as the average of all instances for each combination of |I| and |J|. The number X of open facilities is denoted by Wj. “Iter” denotes the number of iterations carried out by the j∈J LAB algorithm. “Gap” refers to the optimality gap: (UB − LB)/LB. CPU times are reported in seconds and the ratio of CPU time of IP model and LAB algorithm is denoted by “Time ratio”. Our algorithm performs significantly better than direct solution of the linear reformulation. On average, Baloch and Gzara: UAV service with competition 43

X LAB algorithm IP |J| |I| Wj Time ratio j∈J Iter Gap CPU time (s) Gap CPU time (s) 10 50 4 4 0.00 0.44 0.00 39.21 89 10 100 3 4 0.00 1.46 0.00 210.89 144 10 150 3 3 0.00 2.90 0.00 412.82 142 10 200 4 4 0.00 5.53 0.00 357.11 65 10 250 3 3 0.00 8.79 0.00 673.12 77 20 50 4 5 0.00 2.00 0.00 261.44 131 20 100 4 5 0.00 4.87 0.00 1174.63 241 20 150 4 6 0.00 11.55 0.06 2433.31 211 20 200 4 4 0.00 19.37 0.27 3450.15 178 20 250 4 4 0.00 27.81 0.54 3602.16 130 30 50 4 6 0.00 5.06 0.00 867.75 171 30 100 5 4 0.00 11.02 0.26 3467.26 315 30 150 4 5 0.00 20.78 0.40 3603.50 173 30 200 4 4 0.00 31.26 n/a 3600.84 115 30 250 5 4 0.00 41.07 n/a 3600.35 88 40 50 4 5 0.00 6.36 0.01 1735.12 273 40 100 4 5 0.00 13.60 0.34 3602.16 265 40 150 5 3 0.00 23.76 n/a 3600.59 152 40 200 5 4 0.00 39.49 n/a 3600.21 91 40 250 5 4 0.00 60.15 n/a 3600.20 60 50 50 5 5 0.00 8.20 0.10 3174.78 387 50 100 5 5 0.00 21.54 n/a 3603.10 167 50 150 5 6 0.00 41.23 n/a 3600.14 87 50 200 5 5 0.00 59.16 n/a 3600.21 61 50 250 5 5 0.00 85.14 n/a 3600.25 42 Average 5 5 0.00 22.10 0.12 2458.85 154

Table 4 Summary of the computational experiments

LAB is 154 times faster than Cplex. Cplex fails to close the gap in 59% of the instances while LAB solves all instances to optimality within 92 seconds. “n/a” denote instances where Cplex fails to

find a feasible solution in 3600s. Cplex fails to find a feasible solution in 28% of the instances. This signifies the need for the proposed LAB algorithm to solve large scale instances.

Nb. of services CPU time (s) Iterations [SP ] time Gap |S| total [MP] [SP] total time 3 6 50.44 50.19 0.25 0.49% 0.00% 4 4 155.33 154.93 0.40 0.25% 0.00% 5 21 805.46 802.70 2.77 0.34% 0.00% 6 102 2009.78 1990.86 18.92 0.94% 0.00% Table 5 Effect of the number of services on subproblem’s computational efficiency

To justify the use of enumeration based approach in [SP], we solve industry scale problems by varying the number of services offered |S|. Note that the world’s largest e-retail company, Amazon offers a maximum of 6 different delivery services in a single city. For |I| = 200 and |J| = 50, we vary Baloch and Gzara: UAV service with competition 44 the number of services offered |S|, by the e-retailer between 3 and 6. Ten random instances are generated and results are summarized in Table5 where average values for each |S| are reported.

[SP ]time [SP] takes less than 1% of the total CPU time as shown in total time column. Although the CPU time in [SP] increases with increasing number of services, the effect is not significant. Increasing

|S| results in higher number of iterations and as such, [SP] is solved several times. We note that it takes less than a second, to solve [SP] at each iteration. The results show that the proposed enumeration based approach in LAB algorithm works quite well for industry scale instances where the number of services are generally limited.

7. Conclusions

We used MNL market share model and optimization modelling to study the impact of UAV delivery on e-retailing. A novel logic-based Benders algorithm is proposed that not only solves the non- linear model efficiently but allows several possible extensions. We analyzed the tradeoffs between distribution costs and revenues under varying social resistance to UAVs, customer preferences, and regulatory and technological limitations. Our results show that these challenges significantly impact optimal distribution network configuration and UAV target markets. For example, under the current UAV landing capabilities, a UAV delivery service may not be possible in a densely populated area like Manhattan where demand for such a service is expected to be high. We found that under the right technological capabilities and regulations, e-retailers are able to reach smaller markets and more price sensitive customers possibly by offering discounts on UAV delivered orders.

The modelling and analysis presented in this paper may be used not only by e-retailers but by any retail business and other stakeholders including regulatory bodies. For instance, regulatory bodies may use our modelling approach to test regulations on UAV deliveries. One of the weak points of our work is that customer sensitivity parameters are not explicitly based on customer preference for UAV delivery, but rather on the literature that explores customer preference for online shopping versus in-store shopping. Estimating these parameters based on a market survey is important but is out of the scope of this work. Another extension of our work might be to incorporate charging stations to extend the range of UAVs at the expense of higher delivery times. Baloch and Gzara: UAV service with competition 45

Acknowledgments Baloch and Gzara: UAV service with competition 46

Appendix A: Proof of Lemma1

1. Recall equation (2.1) and (2.4). Equation (2.1) says that the utility Uip increases as the number of services offered increases. Taking the derivative of Disp with respect to Uip: X Nip(1 − (exp(−λUip)(λUip + 1))) × ( aspyijs) exp(β0s − βdtDTs − βdcqs) ∂Disp j∈J = − 2 < 0 (A.1) ∂Uip Uip as λ > 0, Uip > 0, and exp(−λUip) × (λUip + 1) > 1. Hence, as the number of services offered increases, utility Uip increases which results in decreasing Disp. Therefore, maximum demand that may be captured by service max 0 s ∈ S, Disp is achieved when only service s ∈ S is available i.e., yijs = 1 and yijs0 = 0 ∀ s 6= s. 2. Using equation (2.4), total demand captured TDip, by the e-retailer is expressed as:

Nip(1 − exp(−λUip))(Uip − USip) TDip = , (A.2) Uip

where USip = exp(β0,n+1 − βttTTi − βtcTCi) and (Uip − USip) ≥ 0, is the utility derived by customer zone i ∈ I for package p ∈ P given the services offered by the e-retailer. Taking the derivative of TDip with respect to total utility Uip:

−λUip λUip ∂TDip Nipe (USip(e − 1) + λUip(Uip − USip)) = 2 > 0 (A.3) ∂Uip Uip

λUip as λ > 0, Uip > 0 , (e −1) > 0, and λUip(Uip −USip) ≥ 0. Hence, as Uip increases, TDip increases. Therefore, max maximum total demand TDip , is achieved when the e-retailer offers all services in S to customer zone i ∈ I for package p ∈ P .  Appendix B: Linear formulation of model NP Three sets of binary decision variables and one set of continuous nonnegative decision variables are defined as: ( 1, if customer zone i ∈ I is offered set of services e ∈ P(S) t = ie 0, otherwise ( 1, if candidate facility j ∈ J is opened w = j 0, otherwise ( 1, if service s ∈ S is offered at facility j ∈ J x = js 0, otherwise demand captured by facility j ∈ J using service s ∈ S for package p ∈ P in d = ijspe customer zone i ∈ I when set of services offered is e ∈ P(S)

The model NP is transformed into mixed integer program [IP] as: X X X X X X X X [IP]: max (απp + qs − cijs)dijspe − Fsxjs − Lj wj (B.1) i∈I j∈J s∈S p∈P e∈P(S) j∈J s∈S j∈J X s.t. tie = 1 i ∈ I, (B.2) e∈P(S)

xjs ≤ wj j ∈ J, s ∈ S (B.3)

dijspe ≤ Mtie i ∈ I, j ∈ J, s ∈ S, p ∈ P, e ∈ P(S) (B.4)

dijspe ≤ Mrijsxijs i ∈ I, j ∈ J, s ∈ S, p ∈ P, e ∈ P(S) (B.5) X dijspe ≤ Dispe i ∈ I, s ∈ S, p ∈ P, e ∈ P(S) (B.6) j∈J

tie ∈ {0, 1} i ∈ I, e ∈ P(S) (B.7)

xjs ∈ {0, 1} j ∈ J, s ∈ S (B.8)

wj ∈ {0, 1} j ∈ J (B.9)

dijspe ≥ 0 i ∈ I, j ∈ J, s ∈ S, p ∈ P, e ∈ P(S) (B.10) Appendix C: Data used Baloch and Gzara: UAV service with competition 47

Borough Minimum Maximum Manhattan 70 100 Staten Island 14 21 Brooklyn 65 75 Queens 14 25 Bronx 30 40 Table C1 Yearly Lease Rate ($) per sq. ft in Boroughs

ID Borough Name NTA code Yearly Cost ($) 1 Brooklyn BK82 5,000,000 2 Queens QN49 2,450,000 3 Queens QN01 3,000,000 4 Queens QN18 2,700,000 5 Staten Island SI11 2,750,000 6 Staten Island SI24 2,600,000 7 Brooklyn BK28 5,300,000 8 Bronx BX13 3,600,000 9 Staten Island SI45 2,650,000 10 Bronx BX06 3,550,000 11 Staten Island SI37 2,450,000 12 Manhattan MN24 5,550,000 13 Queens QN41 2,700,000 14 Brooklyn BK31 5,000,000 15 Queens QN53 3,000,000 16 Manhattan MN11 6,100,000 17 Brooklyn BK81 5,300,000 18 Brooklyn BK42 5,250,000 19 Brooklyn BK72 5,150,000 20 Queens QN70 2,650,000

Average 3,837,500 Table C2 Yearly facility Costs Baloch and Gzara: UAV service with competition 48

Parameters Estimated Value Yearly demand of delivery by UAVs YD YD Avg hourly demand, H 365×14 max YD maximum hourly demand, H = H × 2.0 365×14 × 2.0 Hmax YD 1 Nb. Of UAVs required, NbUAV s = 2 365×14 × 2 × 2 YD 1 Nb.of batteries required, NbBatteries = NbUAV s 365×14 × 2 × 2 Nb. Of UAVs per operator, ND 10 Hmax YD 1 1 Nb.of operators required per hour NbOperators = 2×ND 365×14 × 2 × 2 × 10 Nb.of hours an operator works 8 14 YD 1 1 14 Total Nb. of operators required, T otalNbOperators = NbOperators × 8 365×14 × 2 × 2 × 10 × 8

Costs calculations Cost per UAV 3000 Cost per battery 200 YD 1 Total battery cost, BC = 200 × NbBatteries 365×14 × 2 × 2 × 200 YD 1 Total UAV cost, DC = 3000 × NbUAV s 365×14 × 2 × 2 × 3000 YD 1 Total purchasing cost,PC = BC + DC (3000 + 200) × 365×14 × 2 × 2 Amortization rate, r 20% YD 1 Yearly amortized cost of UAVs & Batteries,AC = r × PC (3000 + 200) × 365×14 × 2 × 2 × 0.20 Yearly operators salary 70, 000 YD 1 1 14 Total yearly operators salary cost,OC = 70000 × NbOperators 365×14 × 2 × 2 × 10 × 8 × 70000 YD 1 YD 1 1 14 Total yearly costs, TC = AC + OC (3000 + 200) × 365×14 × 2 × 2 × 0.20 + 365×14 × 2 × 2 × 10 × 8 × 70000 Battery charging cost per delivery(in dollars) 0.10

YD 1 YD 1 1 14  (3000+200)× 365×14 ×2× 2 ×0.20+ 365×14 ×2× 2 × 10 × 8 ×70000  TC YD + 0.10 Cost per delivery, YD = 0.1252 + 2.397 + 0.10 ≈ 2.62

Table C3 Detailed calculations for UAV package delivery cost cijn Baloch and Gzara: UAV service with competition 49

References

Aboolian R, Berman O, Krass D, 2007a Competitive facility location and design problem. European Journal

of Operational Research 182(1):40–62.

Aboolian R, Berman O, Krass D, 2007b Competitive facility location model with concave demand. European

Journal of Operational Research 181(2):598–619.

Aboolian R, Sun Y, Koehler GJ, 2009 A location–allocation problem for a web services provider in a com-

petitive market. European Journal of Operational Research 194(1):64–77.

ACS, 2015 American community survey. URL https://www1.nyc.gov/site/planning/data-maps/

nyc-population/american-community-survey.page.

Adams SM, Friedland CJ, 2011 A survey of (uav) usage for imagery collection

in disaster research and management. 9th International Workshop on Remote Sensing for Disaster

Response, 8.

Agatz N, Bouman P, Schmidt M, 2018 Optimization approaches for the traveling salesman problem with

drone. Transportation Science .

Albright C, 2015 What we’ve learned from 1 year’s worth of hourly ppc data. URL https://www.ppchero.

com/what-weve-learned-from-1-years-worth-of-hourly-ppc-data/.

Allen MJ, 2005 Autonomous soaring for improved endurance of a small uninhabited air vehicle .

Amazon, 2018 Same-day delivery rates. URL https://www.amazon.com/gp/help/customer/display.

html?nodeId=200105970.

Basuroy S, Nguyen D, 1998 Multinomial logit market share models: Equilibrium characteristics and strategic

implications. Management science 44(10):1396–1408.

Bender J, 2016 Topic: Food retail industry. URL https://www.statista.com/topics/1660/food-retail/.

Berman O, Krass D, 1998 Flow intercepting spatial interaction model: a new approach to optimal location of

competitive facilities. Location Science 6(1):41–65.

Berman O, Krass D, 2002 Locating multiple competitive facilities: spatial interaction models with variable

expenditures. Annals of Operations Research 111(1-4):197–225. Baloch and Gzara: UAV service with competition 50

Boyd T, 2014 Comparative Distribution Warehousing Operating Costs (The Boyd Company), URL http:

//www.theboydcompany.com/.

Burgess M, 2017 Dhl’s can make drops quicker than a car. URL http://www.wired.co.uk/

article/dhl-drone-delivery-germany.

Butter S, 2015 The rise of delivery drones. URL https://www.standard.co.uk/lifestyle/london-life/

the-rise-of-delivery-drones-google-and-amazon-race-to-corner-the-market-a3107496.

html.

Campbell JF, Sweeney II DC, Zhang J, 2017 Strategic design for delivery with trucks and drones Unpublished

paper.

Carlsson JG, Song S, 2017 Coordinated logistics with a truck and a drone. Management Science .

Chawla S, Rajan U, Ravi R, Sinha A, 2006 Min–max payoffs in a two-player location game. Operations

Research Letters 34(5):499–507.

Chronicle CHH, 2015 Top-selling amazon prime now products in major u.s. cities tells

us what americans need in a hurry. URL http://www.chron.com/business/article/

Top-selling-Amazon-Prime-Now-products-in-major-6688997.php#photo-9090460.

Chu Y, Xia Q, 2004 Generating benders cuts for a general class of integer programming problems. Interna-

tional Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Tech-

niques in Constraint Programming, 127–141 (Springer).

Chuang T, 2016 Amazon will pay you 18-25 per hour to make deliveries in your own car. URL http:

//www.denverpost.com/2016/08/10/amazon-pay-18-25-deliveries-own-car/.

Cook KL, 2007 The silent force multiplier: the history and role of uavs in warfare. Aerospace Conference,

2007 IEEE, 1–7 (IEEE).

Cooper LG, Nakanishi M, Eliashberg J, 1988 Market-share analysis: Evaluating competitive marketing effec-

tiveness (Kluwer Academic Publishers Boston).

D’Andrea R, 2014 Guest editorial can drones deliver? IEEE Transactions on Automation Science and Engi-

neering 11(3):647–648. Baloch and Gzara: UAV service with competition 51

Darack E, 2012 Uavs: The new frontier for weather research and prediction. Weatherwise 65(2):20–27.

Drezner T, Drezner Z, 1998 Facility location in anticipation of future competition. Location Science 6(1):155–

173.

Drezner T, Drezner Z, Salhi S, 2002 Solving the multiple competitive facilities location problem. European

Journal of Operational Research 142(1):138–151.

ECN, 2017 Chinese e-commerce market growth, statistics’ report 2016. URL https://www.

ecommerce-nation.co/chinese-ecommerce-market-growth-statistics-report-2016/.

Farahani RZ, Rezapour S, Drezner T, Fallah S, 2014 Competitive supply chain network design: An overview

of classifications, models, solution techniques and applications. Omega 45:92–118.

Fazel-Zarandi MM, Beck JC, 2012 Using logic-based benders decomposition to solve the capacity-and distance-

constrained plant location problem. INFORMS Journal on Computing 24(3):387–398.

Fazel-Zarandi MM, Berman O, Beck JC, 2013 Solving a stochastic facility location/fleet management problem

with logic-based benders’ decomposition. Iie Transactions 45(8):896–911.

Fern´andezJ, Pelegrı B, Plastria F, T´othB, et al., 2007a Solving a huff-like competitive location and design

model for profit maximization in the plane. European Journal of Operational Research 179(3):1274–

1287.

Fern´andezP, Pelegr´ınB, P´erezMDG, Peeters PH, 2007b A discrete long-term location–price problem under

the assumption of discriminatory pricing: Formulations and parametric analysis. European journal of

operational research 179(3):1050–1062.

Ferrandez SM, Harbison T, Weber T, Sturges R, Rich R, 2016 Optimization of a truck-drone in tandem deliv-

ery network using k-means and genetic algorithm. Journal of Industrial Engineering and Management

9(2):374.

Franco M, 2016 Dhl uses completely autonomous system to deliver consumer goods by drone. URL https:

//newatlas.com/dhl-drone-delivery/43248/.

Gambella C, Naoum-Sawaya J, Ghaddar B, 2018 The vehicle routing problem with floating targets: Formu-

lation and solution approaches. INFORMS Journal on Computing 30(3):554–569. Baloch and Gzara: UAV service with competition 52

Garg M, Smith JC, 2008 Models and algorithms for the design of survivable multicommodity flow networks

with general failure scenarios. Omega 36(6):1057–1071.

Ha QM, Deville Y, Pham QD, H`aMH, 2015 Heuristic methods for the traveling salesman problem with

drone. arXiv preprint arXiv:1509.08764 .

Hern A, 2016 Amazon claims first successful prime air drone delivery. URL https://www.theguardian.

com/technology/2016/dec/14/amazon-claims-first-successful-prime-air-drone-delivery.

Hickey S, 2014 Humanitarian drones to deliver medical supplies to road-

less areas. URL http://www.theguardian.com/world/2014/mar/30/

humanitarian-drones-medical-supplies-no-roads-technology.

Hijmans RJ, 2017 Spherical trigonometry [r package geosphere version 1.5-5]. URL https://CRAN.

R-project.org/package=geosphere.

Hong I, Kuby M, Murray A, 2017 A deviation flow refueling location model for continuous space: A com-

mercial drone delivery system for urban areas. Advances in Geocomputation, 125–132 (Springer).

Hooker J, 2000 Logic-based methods for optimization: combining optimization and constraint satisfaction,

volume 1 (John Wiley & Sons).

Hooker JN, 2005 A hybrid method for the planning and scheduling. Constraints 10(4):385–401.

Hooker JN, 2007 Planning and scheduling by logic-based benders decomposition. Operations Research

55(3):588–602.

Hooker JN, Ottosson G, 2003 Logic-based benders decomposition. Mathematical Programming 96(1):33–60.

Hovrtek, 2018 The race for drone delivery dominance. URL https://hovrtek.com/drone-news/

the-race-for-drone-delivery-dominance/.

Hsiao MH, 2009 Shopping mode choice: Physical store shopping versus e-shopping. Transportation Research

Part E: Logistics and Transportation Review 45(1):86–95.

Hsu S, 2016 China’s e-commerce addiction has serious market potential. URL https://www.forbes.com/

sites/sarahsu/2016/07/16/chinas-growing-e-commerce-addiction/#50a151912550.

Intelligence B, 2017 National retail federation estimates 8-12e-commerce growth in 2017. URL https://www.

businessinsider.com. Baloch and Gzara: UAV service with competition 53

Jain V, Grossmann IE, 2001 Algorithms for hybrid milp/cp models for a class of optimization problems.

INFORMS Journal on computing 13(4):258–276.

Jll, 2015 New york monthly update - december 2015. URL http://www.us.jll.com/united-states/en-us/

research/6528/us-new-york-manhattan-monthly-december-2015-jll.

Kahn G, Villaflor A, Pong V, Abbeel P, Levine S, 2017 Uncertainty-aware reinforcement learning for collision

avoidance. arXiv preprint arXiv:1702.01182 .

Keeney T, 2016 Drone delivery: How can amazon charge £1 for drone delivery? URL https://ark-invest.

com/research/drone-delivery-amazon.

Krishnamoorthy K, Casbeer D, Chandler P, Pachter M, Darbha S, 2012 Uav search & capture of a mov-

ing ground target under delayed information. Decision and Control (CDC), 2012 IEEE 51st Annual

Conference on, 3092–3097 (IEEE).

Lewis C, 2014a The economics of amazon’s delivery drones. URL https://robotenomics.com/2014/06/

17/the-economics-of-amazons-delivery-drones/.

Lewis C, 2014b Is package delivery using drones feasible? URL http://robotenomics.com/2014/12/01/

is-package-delivery-using-drones-feasible/.

LoopNet, 2017 New york warehouses for lease on loopnet.com. URL http://www.loopnet.com/New-York_

Warehouses-For-Lease/.

Luci, 2017 Luci delivery scorpiox technologies homepage. URL http://lucidelivery.com/.

Mahony R, Kumar V, Corke P, 2012 Multirotor aerial vehicles: Modeling, estimation, and control of quadro-

tor. roboticsautomationmagazine, 19, 20-32. Mayhew et al. C. Mayhew, R. Sanfelice, and A. Teel. On

path-lifting mechanisms and unwinding in quaternion-based attitude control. Automatic Control, IEEE

Transactions on. PP (99) 1–1.

Maza I, Caballero F, Capitan J, Martinez-de Dios J, Ollero A, 2010 Firemen monitoring with multiple uavs

for search and rescue missions. Safety Security and Rescue Robotics (SSRR), 2010 IEEE International

Workshop on, 1–6 (IEEE).

Meng Q, Huang Y, Cheu RL, 2009 Competitive facility location on decentralized supply chains. European

Journal of Operational Research 196(2):487–499. Baloch and Gzara: UAV service with competition 54

Murray CC, Chu AG, 2015 The flying sidekick traveling salesman problem: Optimization of drone-assisted

parcel delivery. Transportation Research Part C: 54:86–109.

Nasiri MM, Mahmoodian V, Rahbari A, Farahmand S, 2018 A modified genetic algorithm for the capaci-

tated competitive facility location problem with the partial demand satisfaction. Computers & Industrial

Engineering 124:435–448.

NTA, 2015 Neighborhood tabulation areas. URL https://www1.nyc.gov/site/planning/data-maps/

open-data/dwn-nynta.page.

NYC, 2016 City of new york. URL http://www1.nyc.gov/.

Plastria F, Vanhaverbeke L, 2008 Discrete models for competitive location with foresight. Computers &

Operations Research 35(3):683–700.

Poikonen S, Wasil E, Golden B, 2018 A branch-and-bound approach to the traveling salesman problem with

a drone. INFORMS Journal on Computing (), to appear .

Pounds PE, Bersak DR, Dollar AM, 2012 Stability of small-scale uav helicopters and quadrotors with added

payload mass under pid control. Autonomous Robots 33(1-2):129–142.

Quinn J, 2015 Jeff bezos: five things we learned from the amazon founder. URL http://www.telegraph.

co.uk/technology/amazon/11800416/amazon-founder-jeff-bezos-what-we-learned.html.

ReVelle C, Murray AT, Serra D, 2007 Location models for ceding market share and shrinking services. Omega

35(5):533–540.

Rezapour S, Farahani RZ, 2014 Supply chain network design under oligopolistic price and service level

competition with foresight. Computers & Industrial Engineering 72:129–142.

Rhim H, Ho TH, Karmarkar US, 2003 Competitive location, production, and market selection. European

journal of operational Research 149(1):211–228.

Roshanaei V, Luong C, Aleman DM, Urbach D, 2017 Propagating logic-based benders? decomposition

approaches for distributed operating room scheduling. European Journal of Operational Research

257(2):439–455.

Schmid B, Schmutz S, Axhausen KW, 2016 Exploring the choice between in-store and online shopping. 23rd

EIRASS conference on Recent Advances in Retailing and Service Strategies, Edinburgh. Baloch and Gzara: UAV service with competition 55

Shiode S, Drezner Z, 2003 A competitive facility location problem on a tree network with stochastic weights.

European Journal of Operational Research 149(1):47–52.

Statista, 2015 U.s. peak online shopping hours 2015 — statistic. URL https://www.statista.com/

statistics/476827/usa-peak-online-shopping-hours/.

Statista, 2016 U.s. retail e-commerce sales share 2016 — statistic. URL https://www.statista.com/

statistics/187439/share-of-e-commerce-sales-in-total-us-retail-sales-in-2010/.

Statista, 2018 Amazon: annual shipping revenue and cost 2016 — statistic. URL https://www.statista.

com/statistics/236503/amazons-annual-shipping-revenue-and-outbound-shipping-costs/.

Stewart J, 2017 Ups tests the future: A drone-slinging delivery van. URL https://www.wired.com/2017/

02/drone-slinging-ups-van-delivers-future/.

Thiels CA, Aho JM, Zietlow SP, Jenkins DH, 2015 Use of unmanned aerial vehicles for medical product

transport. Air medical journal 34(2):104–108.

Ulmer MW, Thomas BW, 2017 Same-day delivery with a heterogeneous fleet of drones and vehicles .

Wang D, 2016 The economics of drone delivery. URL https://www.flexport.com/blog/

drone-delivery-economics/.

Wang X, Poikonen S, Golden B, 2016 The vehicle routing problem with drones: several worst-case results.

Optimization Letters 1–19.

Welch A, 2015 A cost-benefit analysis of . Master’s thesis, University of Tennessee at

Chattanooga, Chattanooga (Tenn.).

Wheatley D, Gzara F, Jewkes E, 2015 Logic-based benders decomposition for an inventory-location problem

with service constraints. Omega 55:10–23.

Wohlsen M, 2013 The astronomical math behind ups? new tool to deliver packages faster. URL https:

//www.wired.com/2013/06/ups-astronomical-math/.

Wu TH, Lin JN, 2003 Solving the competitive discretionary service facility location problem. European Journal

of Operational Research 144(2):366–378.

Xinhua, 2017 Alibaba’s drones deliver packages to islands. URL http://www.chinadaily.com.cn/

bizchina/2017-11/07/content_34230012.htm. Baloch and Gzara: UAV service with competition 56

Zhang L, Rushton G, 2008 Optimizing the size and locations of facilities in competitive multi-site service

systems. Computers & Operations Research 35(2):327–338.