The Last Mile: Managing Driver Helper Dispatching for Package Delivery Services

Journal of Business Logistics, 2020, 1–16 doi: 10.1111/jbl.12242 © 2020 Council of Supply Chain Management Professionals The Last Mile: Managing Driver Helper Dispatching for Package Delivery Services Shih-Hao Lu1, Yoshinori Suzuki2, and Toyin Clottey2 1National Taiwan University of Science and Technology 2Iowa State University

iring seasonal driver helpers is one widely used approach by parcel delivery companies to deal with increased home-delivery volumes during H peak seasons. Nonetheless, driver helper-related issues have not received much attention in academic research. This study investigates how driver helpers can be utilized in the most effective way by parcel delivery companies. We show that by separating a parcel delivery route into two sub-routes, namely “no-helper” and “with-helper” routes, the utilization rates of driver helpers can be improved, and the carrier cost be reduced con- siderably. Three main contributions of this study are as follows. First, based on costtrade-off insights, we develop a new mathematical model for the last-mile distribution problem, which we call the Driver Helper Dispatching Problem. Second, using this mathematical model, we perform a series of numerical experiments to identify the conditions under which the proposed “split-route solution” works most or least effectively. Finally, we perform sensitivity analyses to investigate the impact that changes in model parameters, such as fuel cost, would have on study results. Keywords: last-mile distribution; driver helper; traveling salesman problem; transportation

INTRODUCTION seasons, who work with drivers to deliver packages, in order to handle the increased home-delivery volumes (Soltes, 2014). This According to the National Retail Federation (2017), the winter approach seems to be working well for parcel delivery compa- holiday shopping season from Black Friday to Christmas nies to minimize shipment delays. However, the approach that is accounts for 20%–25% of the annual retail sales in the United currently implemented in the field is not cost efficient. This paper States. E-commerce continues to grow, with many customers pre- studies the driver helper dispatching problem of large parcel ferring the ease and convenience of home delivery (Statista delivery companies in an attempt to obtain insights into how dri- 2016). Shipments during the holiday season have always been a ver helpers can be utilized in the most effective way to minimize logistical challenge, but this problem has increased in importance cost. The motivation of this study is the provision of an alterna- recently due to the growth of e-commerce. Major challenges tive approach for driver helper dispatching practices to improve include last-minute shoppers, higher than expected e-commerce the cost and operational efficiency of parcel delivery companies, volume, retailers with increasingly later delivery cutoff times, so that they can better deal with the aforementioned logistical and harsh winter weather (Soltes, 2014). challenges, especially during peak seasons. Shipment delays during peak shopping seasons have become common in the past few years, especially among international parcel delivery companies such as United Parcel Service (UPS), STATE OF THE INDUSTRY AND STUDY SCOPE Federal Express (FedEx), and Deutsche Post (DHL). For example, during the Cyber Monday shopping period in 2017, only During the holiday season, the need for drivers to work overtime is 89% of packages were delivered on time by UPS, and for pack- an industry norm (Bhattarai, 2017). Working overtime, however, ages that had been delayed, the average delay was two days has many drawbacks. First, based on the Fair Labor Standards Act (Bhattarai, 2017). Given these facts, international parcel compa- (FLSA), U.S. employees must receive overtime payment for hours nies, who service millions of customers each day, are looking for worked over 40 in a given workweek at a rate not < 150% of their better (more efficient) ways to distribute parcels across their regular rate. Thus, letting drivers work overtime increases direct logistics networks. This issue, that is, how to improve the effi- labor costs. Second, even with overtime payments, not every driver ciency of parcel delivery operations, is an important problem not is willing or able to work overtime. The unpleasant employment only for parcel delivery companies, but also for many manufac- condition, which requires overtime work, can not only put pressure turing companies. This is because last-mile logistics is known to on the drivers’ physical or mental well-being, but also increase the be one of the most expensive and least efficient segments of a turnover rate of drivers (e.g., Suzuki et al., 2009; Miller et al., supply chain (Gevaers et al., 2011; Castillo et al., 2017), so that 2017). Third, there is a physical limitation, or upper bound, on the improving the efficiency of this particular segment can eliminate drivers’ daily work time (hours of service regulation) (Miller et al., the bottlenecks and reduce costs in supply chains. 2018; Miller et al., 2019). One approach that is increasingly used by these large parcel Hiring seasonal employees is one widely used approach by delivery companies is to hire seasonal driver helpers during peak parcel delivery companies to deal with this challenge. For example, in 2015, UPS and FedEx announced a plan to hire 95,000 and 55,000 seasonal employees, respectively, to support the Corresponding author: Shih-Hao Lu, National Taiwan University of anticipated increase in package volume from November through Science and Technology, No.43, Keelung Rd., Sec.4, Da'an Dist., January (Schlangenstein 2015). In 2017, UPS again announced Taipei City 10607, Taiwan; E-mail: [email protected] plans to hire 95,000 temporary workers for November 2017 2 LU et al. through January 2018 (Bhattarai, 2017). A significant number of LITERATURE ON LAST-MILE PROBLEMS these seasonal employees work as driver helpers, who assist drivers in the delivery of packages. Driver helpers are not required The problem this paper considers, which we call the Driver to drive vehicles, and they usually meet drivers at a mutually Helper Dispatching Problem (DHDP), is a type of last-mile logis- agreed time and location (e.g., 7 am at the depot). Self-reported tics problem. Last-mile logistics refers to the last portion of tran- salary data on Glassdoor.Com (2018) and our discussions with sit in supply chains, where goods are delivered from the last industry experts (managers from UPS) revealed that the average transit point to the final drop point (Lee and Whang 2001; Esper drivers’ pay rate in the United States is about two to three times et al., 2003; Boyer et al., 2009; Wang and Odoni 2016). This higher than the average helpers’ pay rate. Therefore, the strategy part of logistics often involves routing a fleet of vehicles for of using driver helpers provides cost savings to parcel delivery physical distribution and plays a crucial role in ensuring that the companies by replacing the drivers’ work time (e.g., overtime) products are delivered to customers in correct quantities and with that of the helpers’. within time limits. To date, parcel delivery companies have primarily utilized two Although the literature on last-mile logistics can be split into types of driver helpers (Rhodes et al., 2007). Dependent driver two main bodies, namely freight and passenger logistics, our helpers, who travel with delivery trucks, are the first type. Such research focuses on the former. Readers that are interested in the helpers work together with (or sometimes separately from) the latter are referred to Wang and Odoni (2016). Issues that have drivers to deliver packages. Independent driver helpers are the been investigated in last-mile freight delivery include examining second type. These helpers do not travel with delivery trucks, fulfillment strategies (e.g., Lee and Whang 2001; Punakivi et al., but rather work at a predetermined point that typically covers a 2001); delivery options (Esper et al., 2003); effects of customer high customer density area (e.g., a small area with a large num- demand characteristics (e.g., Boyer et al., 2009; Song et al., ber of apartments or business offices). Typically, an independent 2009); crowd-sourced deliveries (e.g., Castillo et al., 2017); helper will deliver all of the packages to customers by using effects on the environment (e.g., Brown and Guiffrida 2014; Liu bicycles or other tools such as a hand truck. et al., 2019); and humanitarian aid (e.g., Balcik et al., 2008). Our There is no question that the use of driver helpers is a valu- study is geared towards optimizing the process by which parcel able cost-saving technique for parcel delivery companies. How- delivery companies use driver helpers, an issue that has received ever, based on our interviews with several practitioners scant attention. (including two UPS senior managers, namely, the Vice President To the best of our knowledge, Rhodes et al. (2007) is the only of Engineering and the Director of Engineering), we believe that previous study that has focused on driver helper decisions. They there is room for improvement in the way the parcel delivery proposed a dispatch tool for UPS’s delivery system that finds the companies are currently using driver helpers. In this paper, we optimal number of helpers based on cost–benefit analyses. In develop a new approach for parcel delivery companies that can Rhodes et al. (2007), the authors focused on answering the fol- better manage the cost of dependent driver helpers. lowing three questions: (1) how many helpers should be There are three reasons why we study dependent (rather than deployed, (2) which routes always need dependent helpers, and independent) helpers. First, while dependent helpers travel with (3) which locations always need independent helpers during the vehicles, independent helpers do not, which suggests that the holiday season. Notice that these are all strategic-level questions. problem that deals with dependent helpers is more complex, but In contrast, this study extends the scope by developing an opera- may provide higher cost-saving opportunities, than the problem tional level problem of finding the optimal vehicle routing and which deals with independent helpers. Second, independent help- scheduling decisions based on the cost of operating both drivers ers may require special equipment such as trikes (a specialized and helpers, as well as that of operating a vehicle, which can fur- tricycle with a basket in the rear) or additional trailers (for on- ther improve cost savings. site storage), which must be provided by parcel delivery firms Though the literature on driver helpers is limited, there are (Rhodes et al., 2007). This means that the use of independent several types of studies that are relevant to this study. The first is helpers may be more costly, and thereby less attractive, to parcel those that studied the vehicle routing problem with time windows delivery firms than the use of dependent helpers. Third, a driver (VRPTW). This type is relevant to our study because parcel has less oversight of an independent helper than a dependent delivery service is often considered as a time-constrained routing helper who moves with the driver. problem. Since VRPTW is difficult to solve (NP-hard), many According to our interviews with practitioners, the current studies have focused on developing efficient solution techniques. practice for using dependent helpers in industry follows a simple They include Jornsten€ et al. (1986) (Lagrangian relaxation), solution procedure; that is, the routing problem is solved by min- Kolen et al. (1987) (dynamic programming), Desrochers et al. imizing the travel distance, assuming that in each route the driver (1992) (column generation), Fisher (1994) (K-tree), and Errico helper will accompany the driver from the start to the end. This et al. (2016) (a-priori optimization). These studies, however, shortest-route approach, however, has limitations because it mostly used “hard” time window constraints. In practice, time forces driver helpers to visit locations (nodes) that have only a windows may take the form of “soft” constraints (which can single customer, which is inefficient (helpers are most useful at sometimes be violated), as Dondo and Cerda (2007) point out. nodes with multiple customers). To obtain better solutions, we This may be particularly true for package delivery services. propose an approach that (1) relaxes the shortest-route assump- Specifically, an article written by UPS executives (Holland et al. tion and (2) reduces, in addition to the truck’s travel cost, the 2017), as well as our interviews with UPS managers, confirmed cost of servicing customers (driver and helper costs combined) at that UPS is using soft, rather than hard, constraints to specify each node. time windows. In fact, our interviews suggest that, for many Driver Helper Dispatching Problem 3 vehicle routes, UPS does not even impose delivery time win- one common limitation, that is, the assistant or the drone always dows because only about 5% of all the packages are subject to travels with a truck (until both the truck and assistant or drone time windows (i.e., time-window constraints are not imposed on finally return to the depot). Such an assumption can make the many routes, as they involve no packages with time windows). solution inefficient, as it requires the assisting personnel or We propose a routing problem in which time windows are either equipment to visit those nodes for which they can provide little ignored or imposed as soft constraints. help. This study relaxes this assumption and develops a routing The second are studies that considered the routing problems model that can return a vehicle to the depot in the middle of a with heterogeneous vehicles or routes (i.e., each vehicle/route route to either pick up or drop off a driver helper. possesses a unique characteristic). Golden et al. (1984) proposed a vehicle routing case where a set of vehicles with different costs and capacities are used. Many studies have considered this prob- PROPOSED APPROACH lem (e.g., Semet and Taillard 1993; Rochat and Semet 1994; Salhi and Osman, 1996; Brandao and Mercer 1997; Taillard, In this section, we show that the current method of using driver 1999; Gendreau et al., 1999; Prins, 2002; Wu et al., 2005; helpers in practice (current approach) cannot generate optimal Tavakkoli-Moghaddam et al., 2006). A similar problem, called solutions for parcel delivery companies in every case and that in the truck and trailer routing problem (TTRP), was considered by some cases it is possible to obtain better (more efficient) solutions some studies, where customers are served by either a truck or a by using a different approach. In the paragraphs that follow, we complete vehicle (truck plus trailer). In some places, the trailer is first show, by using a simple numerical example, why the current parked first in a location with ample space near the customers, practice cannot produce optimal solutions in some cases. We then so that the truck alone can visit those customers that are less present an alternative approach that can produce, in such cases, easily accessible by a complete vehicle. Studies that dealt with better solutions than those given by current practice. this problem include Semet (1995), Gerdessen, (1996), Chao (2002), and Scheuerer (2006). Kamoun and Hall (1996) intro- Illustration duced a problem in which two types of vehicles operate in a feeder-backbone system (where each feeder vehicle performs pickup Let us consider an example problem in which there exists one and delivery from a drop-box in a given district, and the back- depot and four customer nodes (A, B, C, D). In this study, the bone vehicle performs transportation between a sorting facility term “customer node” refers to a location where a delivery vehi- and drop-boxes). Time-window constraints were later added to cle stops for service, which can contain one or more individual this problem by Mitrovic-Minic and Laporte (2006). Note that customers (e.g., an individual house or an apartment complex these studies are relevant to our study because, as we shall see where multiple individuals reside). The objective of this problem later, our approach essentially divides each vehicle route into is to minimize the labor cost (sum of driver and helper costs). two sub-routes, each having different characteristics (namely, one The parameters used in this example are shown in the top part of with a helper and one without a helper). Our study, however, dif- Figure 1 in a tabular form. The travel time between customer fers from those mentioned above because in our study the route nodes are all 5 min, and those between the depot and customer heterogeneity is captured by the service-time difference at cus- nodes are all 4 min. Assume that, if a node has more than one tomer nodes. Specifically, the time duration needed to deliver customer, the driver and the helper will equally share the service packages at a given node (stop) depends on whether the node load, so that the service time at the node will be halved (com- belongs to the “with-helper” sub-route (service time can be pared to the service time without a helper). The route shown in shorter because both driver and helper deliver packages) or to the left side of Figure 1 reflects the shortest route. The cost of the “no-helper” sub-route (service time can be long since no this solution, when no helper is used, is $73.8 (no-helper strat- helper is available). This aspect of a routing problem has not egy). If a driver accompanies a helper on this route, which been studied in the literature. reflects current practice (i.e., current-helper strategy), the cost The third are studies which considered either the assisting per- will reduce to $62.4. It can be shown, however, that the latter sonnel (e.g., foot carriers) or equipment (e.g., drones). These strategy may not be the optimal (minimal-cost) solution. types of studies are perhaps most relevant to our study. Vehicle Notice that, under the current-helper strategy, the helper does routing with foot carriers (similar to driver helpers) was consid- not actually provide any help in node C or D. Therefore, the ered by several studies, including Lin (2008a), Lin (2008b), and helper’s time spent at nodes C and D, as well as the time spent Lin (2011). These studies considered a problem that uses two for traveling to and from these nodes, are worthless. This means types of delivery resources, foot carriers and a van (which can that we may obtain a better solution by utilizing (bringing) a carry both delivery items and one or more foot couriers). Foot helper only to the subset of nodes with multiple customers. couriers can travel with a van on its outbound and/or return leg, Specifically, we can separate the route into two sub-routes, such and can pick up and deliver items independently at customer that in one sub-route the single-customer nodes are serviced by sites. Murray and Chu (2015) introduced the flying sidekick trav- the driver alone, while in the other sub-route the multiple-cus- eling salesman problem (FSTSP) which is a routing and schedul- tomer nodes are serviced by the driver and the helper together. ing problem where a truck works in collaboration with a drone. The route shown in the right side of Figure 1 reflects this alter- The objective of the FSTSP is to minimize the total time native strategy. Note that the cost of this solution is $60.2. This required to service all customers by efficiently using both a truck example shows that, in some cases, the current practice (no- and a drone. Similar problems were later considered by Agatz helper or current-helper strategy) does not produce optimal solu- et al. (2015) and Ponza (2016). These studies, however, have tions and that in such cases a better solution can be obtained by 4 LU et al.

Figure 1: Current-helper strategy vs. proposed strategy. Notes: Figures attached to arcs are travel times. Operating cost is the sum of driver and helper cost. In the Current-helper strategy, a helper accompanies a driver on the entire shortest route

Problem parameters Node A Node B Node C Node D All route Expected Service time without a helper (minutes) 60 30 5 5 − Expected Service time with a helper (minutes) 30 15 5 5 − Driver's wage per hour ($) −−−−36 Helper's wage per hour ($) −−−−12

Shortest route Proposed route

a. No-helper strategy c. Proposed helper strategy Trip time = 23 min Trip time = 26 min Service time = 100 min Service time = 55 min Total time = 123 min. Total time = 81 min. Opr. Cost = $73.8 Opr. Cost = $60.2

b. Current-helper strategy Trip time = 23 min Service time = 55 min Total time = 78 min. Opr. Cost = $62.4

using an alternative strategy. It is worth noting that what we Basic concept and study goals have just shown above, using a simple example, can also be shown theoretically using a well-known theory of cost-tradeoffs Based on the discussions above, we propose a new approach that in the optimization literature. This topic, however, is beyond the enables, at least in some cases, parcel delivery companies to bet- scope of this paper and is omitted (details are available upon ter utilize their helper time by splitting each vehicle route into request). two sub-routes, that is, the sub-route in which a helper Driver Helper Dispatching Problem 5 accompanies a driver (denoted “with-helper route”) and the sub- we decided to focus on enhancing the second step of the current route in which a driver travels alone (denoted “without-helper routing procedure by UPS (i.e., TSP), the step that is more rele- route”). vant to the utilization of driver helpers. Note that, although the It should be noted, however, that developing a good clustering focus of this study is to provide an operational decision tool, we method (that properly classifies nodes into “with-helper route” do not intend to develop a comprehensive decision tool that can and “without-helper route” clusters) for an actual route can be solve all decision problems of parcel delivery companies. If the difficult. This is because, in practice, both single-customer nodes results of this study turn out to be promising, future works can and multiple-customer nodes can be randomly scattered around extend our work and develop more comprehensive decision the network, so that a clustering method that merely assigns all tools, by using the VRP framework, that can incorporate the pro- single-customer nodes to a “without-helper route” and all multi- posed helper dispatching procedure. The model presented below ple-customer nodes to a “with-helper route” may not work well. will later be used to perform computational experiments that seek While it is possible to come up with an intuitive clustering to gain strategic insights into how the efficiency of driver helpers method by using one’s practical knowledge, such an approach can be improved via the use of our approach. does not guarantee that the resulting solutions are optimal. In order for the proposed “split-route” idea to work, a more scien- Model formulation tific approach must be used. In the next section, we present one such approach by introducing a mathematical model for the The notations used to describe the proposed DHDP model are DHDP that makes the best trade-off between driver and helper shown in Table 1. The model can be expressed as a mixed-inte- costs. ger linear program of the following form. It should also be noted that the solution given by the proposed Minimize “split-route” approach above cannot always be optimal. If, for example, all (or most) delivery points are multiple-customer DT DC þ HT HC þ Dis FC ð1Þ nodes, the current-helper strategy may be the optimal solution. Similarly, if all (or most) delivery points are single-customer Where nodes, the no-helper strategy may be the optimal solution. This X X X X means that the proposed solution, which takes a helper only to a DT ¼ xijðtijþsiÞþ yijðtij þ ziÞ subset of all nodes, is optimal only under certain conditions. i2V j2V i2V j2V From a practical standpoint, therefore, important questions to address would be “How often does the proposed approach out- Table 1: Notations used in mathematical model perform the current practice?” and “When and by how much does the proposed approach outperform the current practice?” We attempt to answer these questions numerically by performing Symbol Description a series of computational experiments later. N Set of all customer nodes = {1, 2, ..., n} V Set of all nodes (0 = n+1 = depot) = {0, 1, 2, ..., n, n + 1} Mathematical Model tij Travel time from node i to node j M An arbitrary large number This section presents a mathematical model that can generate the x Binary variable that equals 1 if the without-helper proposed “split-route” DHDP solution. This model can also gen- ij route includes arc from node i to node j erate the two “standard” (no-helper and current-helper) DHDP y Binary variable that equals 1 if the with-helper route solutions. Since labor and fuel costs are the two largest cost ele- ij includes arc from node i to node j ments in the trucking industry (they account for 43% and 21%, u Auxiliary integer variable that specifies the position respectively, of the average marginal cost; see, e.g., Hooper and i of node i in the without-helper route Murray, 2017), our model seeks to minimize the sum of these v Auxiliary integer variable that specifies the position two costs (we ignored the fuel cost in the example discussed ear- i of node i in the with-helper route lier, but we shall incorporate the fuel cost from now on). s Work time at node i if all the workload is handled by It should be noted that, although many studies cited in our lit- i the driver alone (s = s + = 0); erature review modeled freight delivery problems using the vehi- 0 n 1 z Work time at node i if all the workload is shared by cle routing problem (VRP) framework, this study uses the TSP i the driver and the helper (z = z + = 0) (Traveling Salesman Problem) framework for two reasons. First, 0 n 1 DT Driver’s total work time (sum of driver’s service time the article written by a team of UPS executives mentioned earlier at customer nodes and travel time) (Holland et al. 2017) reports that UPS is not using the VRP to HT Helper’s total work time (sum of helper’s service time solve their routing problems, but instead is using the TSP. at customer nodes and travel time) Specifically, they first assign packages to vehicles (step 1), and DC Driver’s pay rate (per hour) then solve the TSP for each vehicle to determine the route (step HC Helper’s pay rate (per hour) 2) (see Holland et al. 2017 for further technical details). Second, Dis Total traveled distance of the vehicle our interviews with UPS managers also confirmed that they do FC Fuel cost per distance unit of the vehicle not use the VRP, but use TSP instead because of the time and VS Vehicle speed (distance units per hour) complexity involved in solving the VRP. Given these conditions, 6 LU et al.

X X Second, if we fix y = v = 0, the model produces an optimal TSP HT ¼ y ðt þz Þ ij i ij ij i solution with no helper at all (i.e., the optimal no-helper solution). i2V j2V Third, the model above can be used to produce an optimal “cur- X X rent-helper solution”. This can be accomplished by using a two- Dis ¼ tijðxijþyijÞVS fi i2V j2V step procedure where the shortest route is generated rst (using the no-helper solution procedure discussed above), and then a helper Subject to: is assigned to the vehicle traveling this shortest route, assuming X that the helper always stays with the vehicle. The no-helper and current-helper solutions, generated in this way, will be used as the x0j 1 ð2Þ j2Vnf0g benchmark solutions in our computational experiments to assess X the relative performance of the proposed split-route solution. Fourth, the DHDP formulation above is NP-hard (given that it is y0j 1 ð3Þ j2Vnf0g an extended version of the standard TSP, which is already NP- hard). This means that, while small instances can be solved to opti- X mality by using the conventional simplex algorithm, along with xij þ yij ¼ 18i 2 Vf0gð4Þ j2Vf0g the branch-and-bound technique, large instances must be solved to X X near-optimality by using a heuristic. xqi xij ¼ 0 8i 2 V ð5Þ q2Vnfig j2Vnfig COMPUTATIONAL EXPERIMENTS X X yqi yij ¼ 0 8i 2 V ð6Þ In the sections that follow, we perform two sets of experiments to q2Vnfig j2Vnfig examine the cost-saving potential of our approach. In the first experiment, we solve a large number of instances involving rela- u u þ 1 Mð1 x Þ8i 2 Vnf0g; 8j 2 Vnf0gð7Þ i j ij tively small numbers of nodes to optimality to contrast the performance of the proposed solution with those of benchmark solutions vi vj þ 1 Mð1 yijÞ8i 2 Vnf0g; 8j 2 Vnf0gð8Þ (no-helper and current-helper solutions) under various hypothetical settings. The goal of this first experiment is to investigate the con- xij 2 fg80; 1 i; j 2 V ð9Þ ditions under which the proposed approach works most, or least, ; ; yij 2 fg80 1 i j 2 V ð10Þ effectively. In the second experiment, we solve a limited number of instances involving large numbers of nodes and time window

1 ui n8i 2 Vnfg0 ð11Þ constraints by using a well-known metaheuristic to contrast the proposed and benchmark solutions. The goal of this second experi- 1 vi n8i 2 Vnfg0 ð12Þ ment is to assess the possible cost savings of our approach in practical settings. It is to be noted that, in these experiments, the The objective function (1) minimizes the sum of labor cost and proposed solution is defined as the optimal (or near-optimal) solu- fuel cost. The calculation of driver time (DT) includes both the tion of the DHDP given by eqns. (1)-(12), which means that it time spent in the “without-helper route” and that in the “with- needs not always be the split-route solution, but can be the no- helper route”. The calculation of helper time (HT) includes only helper or current-helper solution, depending on situations. the time spent in the latter route. The term Dis represents the total To obtain realistic results, the experiments and parameters were vehicle miles (summed travel distance of the two routes). Con- carefully designed by referring to a variety of reliable data sources. straints (2) to (4) make sure that each customer node is visited The sources include (1) inputs from a global retail firm with online once and only once on either route. Constraints (5) and (6) ensure shopping and delivery services, (2) expert opinions obtained from that, for each node, the inflow equals the outflow. Constraints (7) parcel delivery companies (UPS and others), and (3) a public postal and (8) work as the sub-tour elimination constraints. Constraints service database (U.S. Census Bureau, 2018ensus Bureau, 2018). (9) to (12) specify the domains of the decision variables. Note that We used Visual Basic.NET (2012), along with the standard.NET although the above formulation does not incorporate time window random class, to generate instances. For the first experiment, we used constraints, they can be easily included using various methods. IBM CPLEX (12.5), and for the second experiment, we used a meta- We discuss how we incorporate time window constraints into our heuristic algorithm which we wrote in Visual Basic.NET, to solve model later when performing numerical experiments. instances. The Visual Basic and CPLEX codes were run on a 2.66 GHz quad-core PC with 8GB of memory. Model properties

First, the formulation above generates solutions that can, when FIRST EXPERIMENT necessary, split a TSP route into two sub-routes; namely the one with a helper and the one without a helper. This means that the Experimental design model has a flexible form which can produce either the single route solution or the split-route solution depending on situations Similar to previous related studies (Boyer et al., 2009), and (i.e., chooses whichever gives the lower objective function value). based on our interviews with practitioners, we tested the Driver Helper Dispatching Problem 7 following four factors in our experiments: (1) number of cus- nodes with 90% of them being 24-customer nodes), although in tomer nodes, (2) size (area) of the network, (3) percentage of virtually all instances the number of customers ranged between multiple-customer nodes, and (4) driver’s pay rate. The ratio of 20 and 200, with an overall average of 88. the first two factors is similar to the customer density factor The driver’s pay rate was determined by the inputs given by tested in Boyer et al. (2009). Table 2 shows the selected parame- UPS, along with the estimates obtained from Glassdoor.Com ters used in our first experiment. (2018). Based on these inputs, we varied the driver’s pay rate at The number of customer nodes to be used was determined by three levels ($24, $30, and $36 per hour), which represent 2, 2.5, conducting a pilot test. In the pilot study, the service time for and 3 times that of a helper’s pay rate ($12 per hour). The over- each customer was set at 5 min, the percentage of multiple-cus- time pay was not considered for two reasons. First, ignoring the tomer nodes was varied between 10% and 90%, and the number overtime pay yields conservative results. Second, overtime pay of customers located at each multiple-customer node was varied schemes vary from one firm to another, so that the saving between 2 and 24. This test (not reported) revealed that when derived from overtime pay is context specific and difficult to there are 10 customer nodes (70 customers or packages on aver- generalize. age), the service time of a route (without helper assistance) is closest to a driver’s regular 8-hour work shift. Given this result, Simulation formulation and verification we used 10 nodes as the base level, and used three other levels that are obtained by adjusting the base level as follows: 50% A full factorial design (4 9 5 9 5 9 3) was employed for the decrease (5 nodes), 50% increase (15 nodes), and 100% increase four factors specified previously. Each simulation trial, which (20 nodes). generates and solves a DHDP instance, was executed using four The size of a network (i.e., service area that is covered by a steps. First, the locations of all nodes, including the depot and depot, expressed in square miles) is varied in five levels as fol- customers, were randomly generated, and the arc distance of lows: 16 mile2, 36 mile2, 64 mile2, 100 mile2, and 144 mile2. each pair of nodes is computed by using the Euclidean distance. These sizes capture a range from relatively small rural areas to Second, each customer node was randomly assigned a set of ser- large metropolitan areas (e.g., Detroit, MI, a large city, is 138.8 vice times zi and si. Third, the problem was solved three times to mile2 in land area, while Aberdeen, SD, a small rural city, is obtain three different solutions, namely, two “standard solutions” 15.6 mile2 in land area). To avoid increasing experimental com- (no-helper and current-helper solutions) and the proposed solu- plexity, we did not consider the shape of a service area in our tion. Fourth, the percentage of cost and time savings attained by experiment (a square shape was assumed in all service net- the proposed solution over the standard solutions were computed. works). This four-step trial was repeated multiple times for each cell The percentage of nodes with multiple customers (p) was set (unique combination of experimental factors). at the following five levels: p = 10%, 30%, 50%, 70%, and Note that our simulation is static (i.e., once an instance is gen- 90%. The service time at each node was determined as follows. erated for each cell, we only need to obtain three solutions for First, if a node has only one customer, both the service time by the instance). Thus, unlike the discrete-event simulation, where a driver alone (si) and that by a driver with a helper (zi) were set the result of one simulation trial is carried over to the next trial at 5 min. Second, if a node has multiple customers, si was deter- as an initial condition, each trial is an independent event in our mined randomly by a uniform distribution ranging from 10 to simulation. Important to such simulation experiments are random 120 min (representing 2 to 24 customers per node), and zi was number generation, factorial design, and replications (Law and set at half of si. The use of a uniform distribution to generate ser- Kelton, 2000; Kelton, 2016). To ensure as much comparability vice times is consistent with prior related studies (Boyer et al. as possible, the same random number seed was used for each 2009; Holland et al., 2017). Note that, given the parameter speci- experimental cell. After trial runs, ten replications per cell were fications above, the total number of customers to be serviced per found to yield relative-precision levels for the outcomes of inter- instance in our experiment can theoretically range from 6 (5 est (i.e., costs and time) which were at most 5% of the sample nodes with one of them being a 2-customer node) to 434 (20 means. This level of precision is consistent with

Table 2: Selected parameters

Parameter Symbol Value or range

Total number of customer nodes N {5, 10, 15, 20} Service area size (miles 9 miles)* L(.) {4 9 4, 6 9 6, 8 9 8, 10 9 10, 12 9 12} Percentage of nodes with multiple customers p {10%, 30%, 50%, 70%, 90%} Driver’s pay rate (dollars per hour) DC {24, 30, 36} Helper’s pay rate (dollars per hour) HC 12 Fuel cost (dollars per mile) TC 0.17 Vehicle speed (miles per hour) VS 30

Note: *During problem generation, the distance unit is set at 0.1 miles; for example, a 16-mile2 service area converts to a 40 (distance unit) 9 40 (distance unit) network. 8 LU et al. recommendations by Law and Kelton (2000). The ten replica- the current-helper solution underperformed the no-helper solutions and associated relative precision are also similar to those of tion. Note that this finding may be dependent on the relative pay prior related works (e.g., Boyer et al., 2009; Castillo et al., structure of drivers and helpers. We investigate the effect of pay 2017). Note that, with 10 replications per cell, we generate structure later. 4 9 5 9 5 9 3 9 10 = 3,000 instances and produce Results also show that, on average, the proposed solution can 3,000 9 3 = 9,000 DHDP solutions in our testing. save 13.34% in costs relative to the no-helper solution. Again, this represents a significant cost saving (see the 95% confidence Results interval). We see from Table 3 that companies may have an 82.40% chance of achieving better results by using the proposed Computational results are reported in Tables 3 and 4. In Table 3, solution versus using the no-helper solution, and that an average the “Frequency” column shows the percentage of all instances in cost reduction of 16.20% may be expected in such cases. Note which the solution in question provided better, the same, and that these figures are improvements over those attained by the worse cost, respectively, than the reference solution. Similarly, current-helper solution. This is perhaps because the proposed the “Cost saving”, “Driver time reduced”, “Helper time reduced”, solution can better utilize the helper time by splitting the route and “Distance increased” columns show the average change (% and eliminating the non-productive time of helpers. Although the gain or loss) in cost, driver time, helper time, and vehicle miles, proposed solution returns slightly higher travel distances than respectively, achieved by the solution in question over the refer- that of the current-helper solution (4.76% on average), it uses ence solution for each case (better, same, or worse cases). Where less helpers’ time than the current-helper solution (26.81% on appropriate, 95% confidence intervals and ANOVA results are average), thereby achieving lower costs than the current-helper also reported in Tables 3 and 4. solution. Results show that, on average, the current-helper solution can Table 3 suggests that a company that has already adopted the save 7.89% in costs relative to the no-helper solution. This repre- current-helper strategy still has a 46.97% chance of achieving sents a significant cost saving, as its 95% confidence interval better results by adopting the proposed strategy, and that, if contains only positive values. We see from Table 3 that compa- adopting the proposed strategy, a company may be able to nies have a 75.07% chance of achieving lower costs by using the achieve an average cost reduction of 4.42% (which is significant; current-helper solution, in lieu of the no-helper solution and that see 95% confidence interval). Moreover, the chance that the an average cost reduction of 16.82% may be expected in such company suffers from a worse result by adopting the proposed cases. This is accomplished by reducing the drivers’ time by strategy, in lieu of the current-helper strategy, is zero. That is 41.02% and replacing it with the helpers’ time. However, in because the proposed strategy provides the flexibility of creating 24.93% of instances, the current-helper solutions produced higher the current-helper solution (or even the no-helper solution) if the costs than no-helper solutions. In these cases, the total cost split-route approach turns out to be costly. Note, however, that increased by 18.98% on average, although the drivers’ time itself the saving achieved by the proposed solution over the current- was reduced by 15.24%. A careful examination indicates that in helper solution comes with the following costs: (1) driver’s time these 24.93% of instances the number of nodes with multiple increases by 4.44% on average, and (2) vehicle miles increase by customers tended to be low, which may explain the reason why 4.76% on average. This means that the performance of the

Table 3: Gains and reductions achieved

Case frequency Cost saving Driver time reduced Helper time reduced Distance increased

Current-Helper over No-Helper Better cases 75.07% 16.82% 41.02% – 0.00% Worse cases 24.93% 18.98% 15.24% – 0.00% Overall – 7.89% 34.59% – 0.00% (95% CI for overall) – (7.24%, 8.54%) (34.12%, 35.06%) –– Proposed over No-Helper Better cases 82.40% 16.20% 38.02% – 5.77% Same cases* 17.60% 0.00% 0.00% – 0.00% Overall – 13.34% 31.32% – 4.76% (95% CI for overall) – (12.69%, 13.99%) (30.85%, 31.79%) – (4.39%, 5.13%) Proposed over Current-Helper Better cases 46.97% 9.40% 9.46% 57.05% 10.13% Same cases* 53.03% 0.00% 0.00% 0.00% 0.00% Overall – 4.42% 4.44% 26.81% 4.76% (95% CI for overall) – (3.77%, 5.07%) (4.91%, 3.97%) (25.42%, 28.20%) (4.39%, 5.13%)

Note: *Note that the current-helper solution never generated a result with the same cost as that of the no-helper solution in our study, while the proposed solution never generated a worse result than that of the no-helper solution. rvrHle ipthn Problem Dispatching Helper Driver

Table 4: Impact of individual factors

Current-Helper over No-Helper Proposed over No-Helper Proposed over Current-Helper

Factor Levels Sample size Cost saving Driver time saving Cost saving Driver time saving Cost saving Driver time saving

Customer nodes 5 750 2.18% (4.27%) 30.30% (2.33%) 10.34% (0.84%) 26.13% (3.48%) 6.35% (1.00%) 4.16% (0.73%) 10 750 8.16% (3.02%) 34.81% (1.62%) 13.11% (0.80%) 31.53% (2.68%) 4.03% (0.61%) 3.28% (0.45%) 15 750 10.06% (2.86%) 36.24% (1.44%) 14.50% (0.83%) 33.41% (2.40%) 3.67% (0.53%) 2.83% (0.33%) 20 750 11.18% (2.65%) 37.03% (1.37%) 15.42% (0.81%) 34.20% (2.26%) 3.61% (0.47%) 2.83% (0.29%) ANOVA (F) 37.63* 40.19* 44.88* 36.60* 19.54* 6.61* Service area (miles2) 4 9 4 600 10.84% (3.53%) 36.72% (1.85%) 16.34% (0.88%) 34.55% (2.40%) 4.55% (0.66%) 2.18% (0.18%) 6 9 6 600 9.87% (3.24%) 36.05% (1.69%) 14.89% (0.86%) 33.23% (2.58%) 4.11% (0.61%) 2.82% (0.34%) 8 9 8 600 7.66% (3.34%) 34.43% (1.77%) 13.12% (0.83%) 31.15% (2.84%) 4.38% (0.68%) 3.27% (0.48%) 10 9 10 600 6.26% (3.13%) 33.42% (1.66%) 11.71% (0.77%) 29.23% (3.02%) 4.38% (0.66%) 4.19% (0.64%) 12 9 12 600 4.83% (3.13%) 32.34% (1.70%) 10.64% (0.74%) 28.43% (2.92%) 4.65% (0.71%) 3.91% (0.59%) ANOVA (F) 11.31* 11.37* 39.41* 14.59* 0.38 8.87* % of multiple-customer nodes 10% 600 17.63% (2.84%) 15.50% (1.57%) 2.56% (0.18%) 8.37% (1.37%) 15.81% (0.95%) 7.13% (0.70%) 30% 600 3.50% (1.90%) 31.49% (0.96%) 8.85% (0.47%) 25.60% (2.07%) 4.67% (0.46%) 5.88% (0.62%) 50% 600 13.04% (1.00%) 38.53% (0.43%) 14.45% (0.53%) 36.02% (1.26%) 1.30% (0.13%) 2.51% (0.40%) 70% 600 18.64% (0.45%) 42.56% (0.15%) 18.88% (0.38%) 41.93% (0.41%) 0.24% (0.01%) 0.63% (0.12%) 90% 600 21.92% (0.32%) 44.89% (0.08%) 21.96% (0.30%) 44.68% (0.18%) 0.05% (0.00%) 0.21% (0.04%) ANOVA (F) 1164.95* 1313.14* 978.50* 1,235.21* 848.77* 154.51* Driver pay rate (dollars/hour) 24 1,000 2.26% (3.36%) 34.54% (1.73%) 9.51% (0.52%) 29.63% (3.17%) 5.74% (0.87%) 6.81% (0.71%) 30 1,000 8.64% (3.09%) 34.65% (1.75%) 13.71% (0.80%) 31.75% (2.71%) 4.13% (0.62%) 3.89% (0.38%) 36 1,000 12.78% (2.94%) 34.59% (1.79%) 16.80% (0.98%) 32.58% (2.49%) 3.37% (0.47%) 2.63% (0.22%) ANOVA (F) 89.69* 0.017 174.241* 8.30* 22.39* 50.33*

Note: Figures in brackets are standard deviations. ANOVA results show the one-way ANOVA F value with *p < 0.01. Time saving calculations are based on the total work time of driver. 9 10 LU et al. proposed strategy (whether it outperforms other strategies) may solution (relative to that of the proposed solution) is an increas- be dependent on the values of certain parameters, such as the dri- ing function of the degree of urbanization, such that it works rel- ver’s pay and fuel costs. We look into this issue next (impacts of atively well in urban areas (gap is small), but not in suburban or fuel costs are discussed later). rural areas (gap is large). These findings jointly imply that the merit of using the proposed solution, which can be defined as Impact of experimental factors the amount by which it outperforms either the no-helper or the current-helper solution (whichever performs better), is small in Table 4 reports the results of factorial experiments. Specifically, rural and urban areas but is large in suburban areas. This is the table shows how the average savings in cost and driver time because, as discussed above, the gap between the proposed solu- achieved by each solution over a benchmark solution are affected tion and the better of the two standard solutions is small in urban by the changes in factor values. The figures shown are computed and rural areas, but it is large in suburban areas. by taking the averages of all the instances for which the condition specified in the table applies. The key findings follow. First, Table 4 indicates that the cost saving attained by both SECOND EXPERIMENT the proposed and current-helper solutions (“helper strategies”) over the no-helper solution becomes large when: (1) service area Design is small, (2) number of customer nodes is large, (3) percentage of multiple-customer nodes is high, and (4) driver wage is high. In practice, each parcel delivery vehicle can make more than 100 Since these characteristics (many nodes exist in a small area with delivery stops (nodes) per day, and some packages must be a high concentration of multiple-customer nodes and high labor delivered within certain time windows (Holland et al., 2017). To cost) typically apply to urban areas, the above finding suggests incorporate such realities, this section conducts a second experi- that “helper strategies” may work well in urban, but not neces- ment in which we solve a limited number of time-constrained sarily in rural, areas. This makes intuitive sense, because in rural DHDP instances with large numbers of nodes. This second areas, where the customer density (ratio of number of nodes to experiment also varies the fuel cost at three levels, so that we area size), concentration of multiple-customer nodes, and driver can examine the impact that the fuel price volatility may have on wage are low, the opportunities for cost savings by using helpers results (if any). Based on the expert opinions obtained from are small. This is because, in such areas, (1) the driving time is UPS, we specified the experiment such that every instance used much longer than the service time spent at customer nodes (only in our testing would have 60–150 delivery stops (nodes), deliver the latter can be reduced by using helpers), (2) the extent to 90–300 packages, and be subject to two types of time-window which the service time can be cut by helpers at each customer constraints (before 11am and anytime deliveries). Note that, node is low (as most nodes are single-customer nodes), and (3) although UPS has three delivery specifications (before 8am, the gap between the drivers’ and the helpers’ wages is small before 11am, and anytime deliveries), the UPS managers we (merit of replacing driver’s time with helper’s time is low). interviewed indicated that packages with 8 am delivery con- Second, Table 4 indicates that the cost saving achieved by the straints are rare, and that over 90% are “anytime deliveries”. proposed solution over the current-helper solution diminishes We used a 3 9 2 9 3 experimental design, where 3 network when: (1) service area is small (except for the anomaly observed densities (low, medium, and high), two customer demand levels in the 4 9 4 area), (2) number of customer nodes is large, (3) (high and low), and three fuel price levels (low, medium, and percentage of multiple-customer nodes is high, and (4) driver high) are used to formulate 18 different factor combinations wage is high. This suggests that the performance gap between (cells) (see Table 5). The network density was measured by the the two solutions becomes small (though the former always out- number of customer nodes per square mile (which was set below performs the latter) in urban areas but it can be large in rural 1.0 for low density, between 1.0 and 6.0 for medium density, areas. This finding, again, makes intuitive sense because when and above 6.0 for high density). The customer demand was mea- the degree of urbanization is high (e.g., all nodes are multiple- sured by the average number of packages delivered per node (de- customer nodes) the current-helper strategy should perform well noted d, which is set at 2 for a high demand level and 1.5 for a (as discussed earlier), but when the degree of urbanization is low low demand level). The fuel price was measured by the dollars (e.g., all nodes are single-customer nodes) the strategy that takes per mile, and its range was determined by reviewing the histori- a helper to all nodes is inefficient. cal fuel price data obtained from U.S. Energy Information From the above two findings, we can derive an interesting Administration (2019) (fuel price was varied in three levels insight into the conditions under which our approach works most between $0.085 and $0.255 per mile, which roughly mimic the effectively; that is, it may work particularly well in suburban lower and upper bounds of fuel prices observed in the last areas where the degree of urbanization is moderate (e.g., such 10 years). In each cell, we randomly generated 10 instances and areas may have an equal mix of single-customer nodes and mul- solved each instance three times by using the no-helper, current- tiple-customer nodes). Note that the first finding above suggests helper, and proposed methods (as before). This means that, in that the performance of the no-helper solution (relative to that of total, we produced 180 instances and computed 540 DHDP solu- the proposed solution) is a decreasing function of the degree of tions. urbanization, such that it works relatively well (performance gap It should be noted that we had to cap the value of d at 2 with the proposed solution is small) in rural areas, but not in because, given the large number of nodes considered in this suburban or urban areas (gap is large). Similarly, the second experiment (60 to 150), the use of a larger d (e.g., 13, as in the finding above suggests that the performance of the current-helper first experiment) would increase the total number of packages Driver Helper Dispatching Problem 11 per vehicle to an unrealistically high value (e.g., 2,000, which is simulated annealing algorithm. According to Holland et al. beyond the feasible capacity of a single vehicle). Also note that, (2017), as well as our interviews with UPS managers, the way with the upper bound of d set at 2, we cannot create urban sce- ORION specifies time window constraints differs from that used narios in the second experiment because, as discussed earlier, in standard routing problems (TSP or VRP) with time windows. one of the main characteristics of urban areas is given by the Specifically, ORION uses “soft” constraints to satisfy the deliv- large number of packages delivered per node, which cannot be ery time windows such that, for each vehicle, the customers with emulated with d ≤ 2. This means that the results of our second morning delivery packages (before 11am) must be visited within experiment should be viewed as representing the relative perfor- the first m stops, where m is an integer value much smaller than mance of the methods in rural and suburban areas, where only a the total number of nodes visited by the vehicle (e.g., m = 10% limited number of apartments or business offices exist. of the total number of nodes). When writing our simulated annealing codes, we followed this practice by adding a penalty Method function that penalizes those solutions in which the customers with morning delivery constraints are not visited within the first We solved each instance by using simulated annealing, a meta- m stops. heuristic widely used to solve routing problems (TSP or VRP). While several other metaheuristics can also be used to solve the Results proposed DHDP (e.g., tabu search, genetic algorithm, and ant- colony optimization), we chose simulated annealing over others Experimental results are reported in Table 6. The table confirms because simulated annealing is the method that is actually used that the findings obtained in the first experiment generally hold by ORION, the proprietary routing software developed and used in the second experiment too (i.e., for larger, more practical by UPS (see, e.g., Holland et al. 2017). Specifics of how the instances). Table 6 shows that: (1) the cost savings attained by simulated annealing codes were written for this study are beyond the current-helper solution over the no-helper solution are not the scope of this paper and will not be discussed here (details always positive (negative when demand per node is low and are available upon request). Readers that are interested in know- when network density is low or medium), (2) the cost savings by ing the technical details of simulated annealing, or how it is used the proposed solution over the no-helper solution are always to solve the TSP and VRP, are referred to Hillier and Lieberman non-negative (always positive in Table 6), and (3) the cost sav- (2010) and Ohlmann and Thomas (2007). ings by the proposed solution over the current-helper solution are One technical issue, however, which requires attention is the always non-negative (again, always positive in Table 6). All of way by which the time window constraints were handled in our these findings are consistent with those from the first experiment.

Table 5: Parameters used in second experiment

Parameters

Instance Network Demand Fuel cost Service area Customer nodes Total packages Fuel cost ID Density Level Level (miles2) ($ per mile)*

1 Low Low Low 12 9 12 60 90 0.085 2 Low Low Normal 12 9 12 60 90 0.170 3 Low Low High 12 9 12 60 90 0.255 4 Low High Low 12 9 12 90 180 0.085 5 Low High Normal 12 9 12 90 180 0.170 6 Low High High 12 9 12 90 180 0.255 7 Medium Low Low 8 9 8 80 120 0.085 8 Medium Low Normal 8 9 8 80 120 0.170 9 Medium Low High 8 9 8 80 120 0.255 10 Medium High Low 8 9 8 120 240 0.085 11 Medium High Normal 8 9 8 120 240 0.170 12 Medium High High 8 9 8 120 240 0.255 13 High Low Low 4 9 4 100 150 0.085 14 High Low Normal 4 9 4 100 150 0.170 15 High Low High 4 9 4 100 150 0.255 16 High High Low 4 9 4 150 300 0.085 17 High High Normal 4 9 4 150 300 0.170 18 High High High 4 9 4 150 300 0.255

Note: *Fuel consumption rate of 15 miles per gallon is assumed (based on practitioner input). 12 LU et al.

Table 6 also shows that the impact of experimental factors is approach outperforms the current-helper approach in 46.97% of similar between the first and second experiments. We see from all the instances, and matches the current-helper approach in the Table 6 that: (1) the performance of the helper strategies (current remaining instances (53.03%). Results also showed that the pro- or proposed) improves as the customer demand increases, (2) the posed approach outperforms the no-helper approach in 82.4% of performance of the helper strategies is better when the network all the instances and matches the no-helper approach in the density is high than when it is low, and (3) the cost saving given remaining instances (17.6%). When we presented these results to by the proposed strategy over the current-helper strategy dimin- UPS, they showed interest in implementing the proposed strategy ishes as the customer demand increases. Again, these findings in the foreseeable future. This serves as a professional endorse- are consistent with those from the first experiment. It seems that ment of the practical value of this study. our results are robust to the changes in problem size and time This study gives two implications. First, the proposed window specifications. approach may work best in suburban areas. Our results showed Interestingly, Table 6 shows that the fuel price has no signifi- that the performance gap between our approach and existing cant effect on the performance of the three methods (as evi- approaches diminishes in urban and rural areas, where the “cur- denced by the non-significant F statistics). Given that the range rent-helper” and “no-helper” solutions, respectively, work rela- of fuel price used in our testing is wide (covers the entire range tively well (though never outperformed our approach). Results observed in the last decade), this finding suggests that fuel price also showed that, in suburban areas (which may have an equal volatility has little impact on the effectiveness of the proposed mix of single-customer and multiple-customer nodes), neither the method. This finding may seem counterintuitive to some readers, no-helper nor current-helper strategy works well, so that the gap because the proposed solution tends to increase the travel dis- between the proposed and existing approaches is maximized in tance when compared to the no-helper or current-helper solutions such areas. This means that, while in suburban areas our (it can be shown that the distance of a split-route solution cannot approach should always be chosen, in rural and urban areas the be less than that of the shortest TSP route), so that it would seem no-helper and current-helper approaches, respectively, may also intuitive that the method’s performance should be negatively be chosen. Note that the definition of a suburban area may impacted by an increase in fuel price. From a conceptual per- include “temp towns”, where the percentage of multiple-customer spective, however, our finding makes sense because, when the nodes varies notably from one week to another, because of the fuel price becomes high, the proposed method will likely pro- high concentration of temporary workers (see Grabell, 2013). duce either the no-helper or current-helper solution, given its Second, our approach may give considerable cost savings to structural flexibility (recall that the method can generate “stan- parcel delivery companies. At UPS, for example, there are dard” solutions when they work better than the split-route solu- 55,000 delivery drivers in the United States, each of whom earns tion). As such, the proposed method will always match or $30 per hour on average, and about the same number of depen- outperform the other two methods regardless of the fuel price, dent helpers during the peak season, each of whom earns $15 on meaning that fuel price volatilities cannot reduce the effective- average (according to UPS managers). This means that, assuming ness of the method. 8 hr of work time for both drivers and helpers, 60 days of peak Another interesting finding from Table 6 is that the overall period, and an expected cost saving of 9.40% by the proposed performance of the current-helper strategy is worse than that of approach in 47% of occasions (0% saving in the remaining occa- the no-helper strategy (in the first experiment this was not the sions; see Table 3), UPS may save $52.5 million during the peak case). This is because the instances used in the second experi- season every year in the United States by using our approach. ment do not include urban cases, where the current-helper strat- Similar cost savings may be expected for other large parcel egy is expected to perform well. As a result of this unbalanced delivery companies too. (non-urban) experimental design, the current-helper strategy This study has its limitations. First, this study assumed that a underperforms the no-helper strategy in the majority of instances driver helper is unable to reduce the service time at single-cus- in our second experiment (note that the current-helper strategy tomer nodes. Although the validity of this assumption was not outperforms the no-helper strategy only in a limited number of questioned by practitioners when we described it to them, it is cells where the network density or the demand level is high). possible that helpers can reduce the service time at single-cus- Nonetheless, this result confirms the validity of the two implica- tomer nodes slightly if, for example, a helper delivers a package tions obtained in the first experiment. First, the current-helper while a driver is working on another task (e.g., communicating strategy cannot give cost savings in rural areas where the cus- with the depot) in the vehicle (parallel task processing). Future tomer density and/or the number of packages delivered per stop works may wish to look into this issue by collecting the delivery are low. Second, the use of the current-helper strategy in such time statistics separately for drivers and helpers (to our knowl- areas can be detrimental. edge, UPS does not collect such data). Second, if implemented “as is”, our approach may require driver helpers to spend less time accompanying drivers, than they CONCLUSIONS AND FUTURE RESEARCH currently do (because helpers visit reduced number of nodes per route). This could result in helpers working fewer hours per day, In this paper, we proposed a new approach (model) that allows which may require the parcel delivery companies to offer higher parcel delivery companies to better utilize the driver helper time, hourly wages in exchange for reduced guaranteed hours. Thus, and conducted numerical experiments with this model to gain with the use of our approach, companies may need to think managerial insights into how the efficiency of driver helpers can about how to utilize the saved helper time elsewhere. This, how- be improved. Simulation results showed that the proposed ever, may not be a difficult task because, during the peak season, rvrHle ipthn Problem Dispatching Helper Driver

Table 6: Results of second experiment

Current-Helper over No-Helper over No-Helper Proposed over No-Helper Proposed over Current-Helper Sample Factor size Cost saving Driver time saving Cost saving Driver time saving Cost saving Driver time saving

Customer demand Low (1.5 pkgs) 90 8.30% (0.09%) 22.37% (0.05%) 2.03% (0.19%) 5.84% (0.81%) 9.52% (0.13%) 21.18% (1.00%) High (2.0 pkgs) 90 6.40% (0.10%) 33.27% (0.05%) 11.42% (0.50%) 30.69% (0.54%) 5.47% (0.26%) 3.66% (0.62%) ANOVA (F) 1,031.17* 1,019.59* 115.017* 413.10* 37.52* 170.75* Fuel cost Low ($0.085) 60 1.30% (0.68%) 27.60% (0.36%) 6.28% (0.54%) 17.59% (2.38%) 7.35% (0.23%) 12.94% (1.68%) Normal ($0.170) 60 0.77% (0.63%) 27.95% (0.35%) 6.59% (0.60%) 17.95% (2.28%) 7.22% (0.23%) 13.06% (1.67%) High ($0.255) 60 0.78% (0.62%) 27.91% (0.36%) 7.31% (0.57%) 19.26% (2.06%) 7.92% (0.26%) 11.26% (1.41%) ANOVA (F) 0.09 0.94 0.29 0.21 0.34 0.38 Network density Low density 60 4.66% (0.54%) 25.04% (0.31%) 2.15% (0.05%) 11.55% (1.40%) 6.19% (0.22%) 17.50% (0.59%) Medium density 60 0.53% (0.58%) 28.15% (0.32%) 4.79% (0.24%) 16.53% (2.19%) 5.09% (0.11%) 15.37% (1.52%) High density 60 2.34% (0.55%) 30.27% (0.30%) 13.24% (0.74%) 26.71% (1.93%) 11.22% (0.18%) 4.40% (1.67%) ANOVA (F) 13.26* 13.50* 58.73* 19.45* 38.41* 23.53* Overall average 180 0.95% 27.82% 6.72% 18.26% 7.50% 12.42% (95% CI overall) (1.04%, 0.86%) (27.77%, 27.87%) (6.64%, 6.81%) (17.94%, 18.59%) (7.46%, 7.53%) (12.65%, 12.19%)

Note: Figures in brackets are standard deviations except where indicated otherwise. ANOVA results show the one-way ANOVA F value with *p < .01. 13 14 LU et al. there would be many other tasks that could make use of a help- Desrochers, M., Desrosiers, J., and Solomon, M. 1992. “A New er’s time. One interesting direction which we are looking into is Optimization Algorithm for the Vehicle Routing Problem the coordination of helper assistance between different vehicles with Time Windows.” Operations Research 40(2):342–354. (routes), such that, for example, a helper would first accompany Dondo, R., and Cerda, J. 2007. “A Cluster-Based Optimization driver A in the morning, and then accompany driver B in the Approach for the Multi-depot Heterogeneous Fleet Vehicle afternoon. This way, helpers can be fully utilized, even though Routing Problem with Time Windows.” European Journal of they only visit a reduced number of nodes in each route. Future Operational Research 176:1478–1507. studies may consider this extension. Errico, F., Desaulniers, G., Gendreau, M., Wei, W., and In closing, we suggest that future works design more advanced Rousseau, L.-M. 2016. “A Priori Optimization with Recourse DHDP models, along with the effective solution techniques for for the Vehicle Routing Problem with Hard Time Windows such models, to expand the cost-saving potential. While we have and Stochastic Service Times.” European Journal of shown that a simple idea of separating a route into two sub- Operational Research 249:55–66. routes can reduce the total costs of last-mile delivery noticeably, Esper, T.L., Jensen, T.D., Turnipseed, F.L., and Burton, S. 2003. there may be other, more sophisticated, ways to coordinate dri- “The Last Mile: An Examination of Effects of Online Retail vers and helpers to boost the utilization rates of helpers. Specifi- Delivery Strategies on Consumers.” Journal of Business cally, there may be two ways to expand this study. First, future Logistics 24(2):177–203. studies can use the VRP framework, with multiple vehicles, to Fisher, M.L. 1994. “Optimal Solution of Vehicle Routing gain additional benefits. As mentioned earlier, using VRP is not Problems Using Minimum K-trees.” Operations Research 42 currently a feasible option for some companies like UPS, but it (4):626–642. may be a feasible option for other (e.g., smaller) firms. Second, Gendreau, M., Laporte, M., Musaraganyi, C., and Taillard, E.D. as discussed earlier, future works may consider sharing helpers 1999. “A Tabu Search Heuristics for the Heterogeneous Fleet among different routes or vehicles. This may be done, for exam- Vehicle Routing Problem.” Computers & Operations ple, by transferring a helper from one truck to another at a given Research 26:1153–1173. customer node. 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UPS Helper Dispatch Analysis.InSystems and Information Shih-Hao Lu (Ph.D. Iowa State University) is Assistant Pro- Engineering Design Symposium, 2007. SIEDS 2007. IEEE. 1-6. fessor of Business Administration at National Taiwan University Rochat, Y., and Semet, F. 1994. “A Tabu Search Approach for of Science and Technology. His primary research interests are in Delivering Pet Food and Flour in Switzerland.” Journal of the the areas of logistics optimization, operations research, and green Operational Research Society 45(11):1233–1246. supply chain management. His work has been published in 16 LU et al.

Decision Support Systems, Journal of Business Logistics, The Transportation: A Global Supply Chain Perspective (9th edi- International Journal of Logistics Management, Computers in tion). Human Behavior, and other journals. Toyin Clottey (Ph.D. The Ohio State University) is Associate Yoshinori Suzuki (Ph.D. Pennsylvania State University) is Professor of Supply Chain Management at the Ivy College of Busi- Land O’Lakes Endowed Professor of Supply Chain Management ness, Iowa State University. His research interests are in sustain- at the Ivy College of Business, Iowa State University. He has able operations, supply forecasting, and survey research methods. participated in many publicly and privately funded research pro- His publications have appeared in Production and Operations jects and has published over 45 research papers in academic Management, IIE Transactions, Decision Sciences, and others. He journals. He is currently serving as the Co-Editor-in-Chief of is a member of the Decision Sciences Institute, INFORMS, and the Transportation Journal. He is the co-author of the textbook Production and Operations Management Society.