Developing a Cross-Docking Network Design Model Under Uncertain Environment

J Ind Eng Int DOI 10.1007/s40092-014-0088-0 ORIGINAL RESEARCH Developing a cross-docking network design model under uncertain environment S. M. Seyedhoseini • Reza Rashid • E. Teimoury Received: 5 July 2014 / Accepted: 25 August 2014 Ó The Author(s) 2014. This article is published with open access at Springerlink.com Abstract Cross-docking is a logistic concept, which M1O Highest possible Number of outdoor trucks for plays an important role in supply chain management by transportation between cross docks decreasing inventory holding, order packing, transportation M2O Highest possible Number of outdoor trucks for a costs and delivery time. Paying attention to these concerns, cross dock to transport goods for customers and importance of the congestion in cross docks, we N Number of candidate nodes for cross docks present a mixed-integer model to optimize the location and L Number of customers design of cross docks at the same time to minimize the total transportation and operating costs. The model combines Variables queuing theory for design aspects, for that matter, we xijt1 1 if there is any way from customer i to customer consider a network of cross docks and customers where j which uses cross dock t and 0 otherwise two M/M/c queues have been represented to describe ymt 1 if m indoor truck be allocated to cross dock t operations of indoor trucks and outdoor trucks in each and 0 otherwise cross dock. To prepare a perfect illustration for perfor- zmt 1 if m outdoor truck be allocated to cross dock t to mance of the model, a real case also has been examined transport goods for customers and 0 otherwise that indicated effectiveness of the proposed model. lmt 1 if m outdoor truck be allocated to cross dock t for transportation to other cross docks and 0 otherwise Keywords Cross-docking Á Network design Á Truck Nt 1 if cross dock j establish and 0 otherwise allocation Á Response time Á Queuing theory kIt Rate of indoor demand for cross dock t kO1t Rate of outdoor flows that need to be transported List of symbols from cross dock t to another cross dock flij Rate of flow goes to customer j from customer i kO2t Outdoor flows go through cross dock t and Cijtl Transportation cost between customer i and j where customers flow goes through cross docks of t and l C1mt Costs of allocating m outdoor trucks to cross dock t for transportation between cross docks Introduction C2mt Costs of allocating m indoor trucks or outdoor trucks to cross dock t for transporting for customers In the competitive environment, companies must satisfy Ft Establishing cost of cross dock t more complicated demands with less response time. Cross- MI Highest possible Number of indoor trucks docking is a relatively new warehousing strategy in logistic that involves moving products directly from the receiving dock to the shipping dock (Bellanger et al. 2013). It can be defined as a transshipment platform which receives flows & S. M. Seyedhoseini Á R. Rashid ( ) Á E. Teimoury from various suppliers and consolidates them with other Department of Industrial Engineering, Iran University of Science and Technology, Narmak, 16844 Tehran, Iran flows for a common final delivery to a destination (Kinnear e-mail: [email protected] 1997). Also the efficiency of cross-docking will influence 123 J Ind Eng Int the lead time, inventory level and response time to the were to determine the number of located distribution cen- costumer (Kuo 2013). ters, their locations, capacity level, and allocating cus- In the literature, there are some researchers who con- tomers to distribution centers. sidered cross-docking problem. For instance, Bellanger One of the most important factors in supply chain et al. (2013) dealt with the problem of finding optimal management is response time, which consists of produc- schedule in cross-docking, where the main goal was to tion, handling and waiting times (Vis and Roodbergen minimize the completion time of the latest order. In their 2011). Some researchers modeled response time in sto- paper, cross-docking was modeled as a three-stage hybrid chastic environment, and some of them used queuing the- flow shop, and for obtaining good feasible solutions, they ory to represent a mathematical model. Some researchers have developed several heuristic schemes. They also pro- believe that it makes the problem hard to solve, and some posed a branch-and-bound algorithm to evaluate the heu- suggest cutting planes for obtaining optimal solutions in ristics. Chen and Song (2009) considered two-stage hybrid small and medium-sized problem instances (Karimi-Nasab cross-docking scheduling problem, where the objective and Seyedhoseini 2013). was minimizing the make span. To do so, a mixed-integer In this area, Ha (1997) considered Poisson demand and programming and four heuristics were presented. exponential production times for a single item make-to- Kuo (2013), considered another interesting aspect in stock production system. He proposed an M/M/1/S queuing optimization of cross-docking; he presented a model for system for modeling the system. Later, Karimi-Nasab and optimizing both inbound and outbound truck sequencing Fatemi Ghomi (2012) argued that it is not a practical and both inbound and outbound truck dock assignment. assumption that production times are fixed input data of the Jayaraman and Ross (2003) considered supply chain design problem. They proposed that in many cases the production problem which incorporates cross-docking into a supply time of the item may be considered as either a decision chain environment. Agustina et al. (2010) provide a liter- variable or an uncertain input data other than a fixed value. ature review of mathematical models in cross-docking, Nonetheless, many operational managers believe that where the models were classified into three levels of making decisions with minimal total costs is of crucial operational, tactical and strategic. importance (Karimi-Nasab and Sabri-Laghaie 2014). In recent years, Santos et al. (2013) dealt with pickup Kerbache and Smith (2004) proposed context of supply and delivery in cross docks, and proposed an integer pro- chain and application of queue approach. They modeled gramming model and a Branch-and-price for the problem. supply chain network as a queuing system and analyzed it, Liao et al. (2012) considered problem of inbound and in particular, they used queuing network methods to eval- outbound truck sequencing for cross docks, and proposed uate the performance measures of a supply chain. In this two new hybrid differential evolution algorithms for the research, queuing theory has been used to describe stock problem. Agustina et al. (2014) considered perishable food control system of retailers and response of suppliers, where products, and proposed a mixed-integer model to minimize each retailer has been assumed to be an M/M/1 queue with earliness, tardiness, inventory holding, and transportation balk arrival, and each supplier has been assumed to be an cost. M/M/1 queue. Location analysis and network design are two major In summary, it is clear that despite of the many contri- research areas in supply chain optimization, location butions in the location problems, there is little consider- problems deal with the decisions of where to optimally ation due to cross dock location problem, which considers locate facilities whereas network design involves activating stochastic waiting time for cross docks. In this paper, cross optimal links (Contreras and Fernańdez 2012). In this area, dock location problem has been considered, where the Ross and Jayaraman (2008) studied location planning for primary goal is to develop a rich model to represent fol- the cross docks and distribution centers in supply chains. lowing key questions: Later, Babazadeh et al. (2012) proposed a new network – Where cross docks should be located? design mathematical model for an agile supply chain. – What is the optimal number of indoor trucks and Luër-Villagra and Marianov (2013) considered price outdoor trucks? and location; they proposed a competitive hub location and – How customers should be allocated to cross docks? pricing problem for the air passenger industry. Mousavi and Tavakoli-Moghaddam (2013) considered location and These questions are obviously interconnected, for routing scheduling problems with cross-docking, and example location and numbers of cross docks affect present a two-stage mixed-integer programming model. interval flows for each cross dock and consequently it Tavakkoli-moghaddam et al. (2013) considered a net- would influence number of trucks, for that matter, a mixed- work design problem for a three level supply chain, and integer model has been presented. The main contributions proposed a new mathematical model, where their aims of this paper can be summarized as follows: 123 J Ind Eng Int • Location problem of cross docks has been considered in locate cross docks and how to allocate customers to cross an uncertainty environment docks, and the secondary decision is determining the • A mathematical model has been developed which optimal truck number which needs to be allocated to each simultaneously optimizes location of cross docks, cross dock. The objective of the model consists of costs number of indoor trucks and outdoor trucks. related to transportation costs, establishing costs and • A congestion constraint has been considered in the operation costs of trucks. model which restricts waiting time of customers to not This problem entails the following assumptions: be more than t , and another constraint has been I 1. Demand size for each customer is less than size of a considered that restricts waiting time of shipments in truck, and each truck can give service to n customers. cross docks to not be more than t . I 2. Each truck gives service to exactly n customers, and if The reminder of this paper is organized as follows: number of customers be lesser than n, then truck waits section two provides a brief definition of the problem, and to service with full capacity.

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