Distribution and operation planning at a cross-dock platform: a case of study at Renault

Distribution and operation planning at a cross-dock platform: a case of study at Renault Christian Serrano Direction de la Supply Chain Renault Guyancourt, France christian.serrano@renault.com Xavier Delorme, Alexandre Dolgui Institut Henri Fayol Ecole des Mines de Saint-Etienne Saint Etienne, France {delorme, dolgui}@emse.fr Abstract The development of international sourcing and overseas flows are at the core of Renault s supply chain strategy. In order to link distant assembly plants with suppliers, Renault relies on a worldwide network of cross-dock logistics platforms. These centers act both as information and physical consolidation point. In other words, from the point of view of an assembly plant, the logistic center performs as any other supplier. Thus, distribution and operation planning are carried out by the platform. At the shop-floor, inland deliveries are received, sorted, repacked (if needed) and loaded onto containers for overseas shipping. In this paper we present the current planning process at Renault platforms and we propose an alternative method which seeks to minimize transportation and internal resources costs, respecting storage capacity and time windows constraints. The system is modeled as an integer linear program and tested in CPLEX. Encouraging results obtained from numerical simulations led to a real-life implementation of a simplified version of the model. Our research not only responds to a specific industrial problem, but also tackles simultaneously two crossdocking research fields: distribution and operation planning. Keywords Cross-docking, Distribution planning, Integer Linear Programming, International logistics. I. INTRODUCTION Once major carmakers started to reach almost every market in the globe, all major actors in the automotive industry were pushed to internationalize their activity in order to maintain competitiveness. Economic factors such as the explosion of emerging markets and financial crisis had done nothing but back up this choice of strategy. Therefore, most car manufacturers had set up industrial facilities outside their home country and this tendency seems to grow, as many companies are currently investing all around the world [1]. In this context of globalization, overseas logistics flows have drastically increased in the automotive industry, in particular the export of individual parts. Since this activity entails a major logistic challenge in terms of lead time, quality and cost, several automotive firms use cross-dock platforms to consolidate and deliver components [2, 3]. The main idea of cross-docking strategy is to transfer incoming deliveries to outgoing vehicles, with almost no storage or treatment in between. One good example of the situation explained before is Renault group. Present in 128 countries, Renault s international development strategy has led to a rise of sales outside the EU, from 23% in 2004 to 51% in 2013, with Brazil and Russia as the second and the third market of the group. Concerning industrial facilities, by the end of 2013, 8 out of 18 Renault assembly plants were located outside Europe, accounting for 52% of finished vehicles production. However, almost 80% of engines and gearboxes were manufactured within EU countries. Moreover, many external suppliers are still implanted in this region, which means a significant amount of components must be exported to distant industrial sites. To do so, Renault relies on a set of nine multi-modal export-oriented platforms, called ILN (International Logistic Network). These centers link overseas industrial sites (which will be referred also as customers) with inland suppliers. Four of them are located in Europe and represented 87% of Renault s exported volume of individual parts in 2013 (3,5 million of m3). From Fig. 1 it can be noticed that a Renault ILN act both as information and physical consolidation point. Once customers delivery orders are received, distribution and operation planning are carried out. Based on this process, orders are generated and transmitted to suppliers. Later on, deliveries are unloaded from inbound trucks, sorted, repacked (10-20% of total volume), moved across the facility and finally loaded onto outbound containers for overseas shipping. As we can see, ILN platforms have a double purpose. On the one hand, Renault seeks economies in overseas transportation by consolidating products. On the other hand, this configuration simplifies distant supply management for industrial sites, since they ll have to deal only once with several aspects such as lead times, customs, time difference, language, cultural environment, etc. Based on the analysis of current functioning of ILN platforms, we propose an alternative method to improve the planning processes. In particular, we establish a better transportation cost assessment and a more accurate daily workload allocation. The interest of this research work is twofold. On the one hand, a specific industrial process is presented and improved, with still encouraging perspectives in the short term. On the other hand, we tackle together two research fields mostly treated individually: distribution and operation planning in a cross-dock center. This paper is organized as follows: in the next section we explain in detail Renault s ILN operation mode and we define the scope of our work. Accordingly, a literature review and the problem definition are conducted on third. Afterwards, we

present the integer linear programming model and the results of numerical experiments. The industrial implementation based on a simplified version of the model is explained next. Finally, we address the conclusions and both industrial and research perspectives. Industrial sites Fig. 1. Logistic network of a Renault ILN platform II. RENAULT ILN OPERATION MODE AND PROBLEM DEFINITION Even if the planning process is common to all Renault ILN, physical characteristics such as lay-out, number of inbound/outbound doors, shop-floor operation, repackaging activities, etc. can be slightly different. Therefore, part A of this section explains the common planning process, but remainder information is based exclusively on a 5-month study conducted in one ILN. A. Distribution planning Fig. 2 presents the distribution planning process at Renault platforms, for a given component. The first stage is the integration of delivery orders from every customer. Then, taking into account the corresponding transportation lead time between the platform and each final destination, the outbound schedule is established. A day of transit is attributed to every package and as a result, we obtain the treatment schedule. Next, the system verifies the inbound transportation trip to which the component belongs and accordingly the delivery schedule is generated. Renault is responsible for the management of inbound transportation and so the itinerary, number of trucks, frequency and delivery hours are pre-defined for each trip. Period Delivery orders Overseas shipping Distribution and operation planning Treatment Monitoring Delivery orders Inland deliveries W1 W2 W3 W11 M T W T F M T W T F M T W T F M T W T F Due date 20 35 20 0 70 Suppliers Information flow Physical flow B. Operation planning and physical activities Daily operation planning is inferred from the delivery schedule. Based on this information, the daily workload for each shop-floor activity is calculated, which results in the estimation of the resources needed for the whole week. Once deliveries are unloaded from inbound trucks, they are placed in a first staging zone. Next, they are sorted by outbound destination and by nature of treatment. If repackaging is needed, they are moved to an intermediate work zone, if not, they go directly to their corresponding destination staging zone. From this point, components are loaded onto containers and finally, containers are transported to a nearby port for overseas shipment. The scheme of Fig. 3 resumes the physical activities in a Renault ILN. As explained before, containers are dispatched to harbor every day. However, in most cases there is only one vessel departure per week, per destination. The latter means that all containers issued from the same week, will be delivered at the same time at Renault s industrial site. C. Cost drivers We can identify three main cost drivers at Renault ILN associated to each level of the related supply chain: truck filling rate (inbound), daily workload (internal) and container filling rate (outbound). All of them are more or less impacted by the requirements planning process. Filling rate of inbound trucks and outbound containers can be deduced, respectively, from shipment schedule and delivery schedule. Since resource needs are assessed weekly, its size will be constraint by the higher workload level of the week. Finally, based on treatment schedule, storage can also be calculated. D. Improvement opportunities and work scope As seen above, customers due date is the main driver of requirements planning process at Renault ILN. This will assure a high level of service rate. However, during the planning process there is no stage in which transportation filling rates and daily workload are considered. Moreover, the fact that there is only one vessel departure per week gives, a priori, some flexibility the platform could profit to optimize its planning process and reduce costs. Staging zone Repackaging zone Staging zone per destination Shipping 20 35 20 0 70.. Treatment 20 35 20 0 70 Delivery 55 0 20 0 70 D/order X Inbound doors Outbound doors Fig. 2. Planning process at Renault ILN. In the example shown in Fig. 2, the planned days for the corresponding inbound trip are Monday, Wednesday and Friday. Hence, quantities scheduled for Monday and Tuesday will be ordered on Monday and so forth. Finally, suppliers lead time is considered and the dates of delivery orders are stablished. This process is done once a week. Fig. 3. Renault ILN s physical flow schema. In practice, outbound container loading not always corresponds to the shipment schedule originally proposed by the system. At shop-floor, much more energy is invested in container filling rate. Therefore, packages may be delayed

one or two days, on the condition that the vessel departure date is respected. As a result, container filling rate average is close to 85%. Concerning internal workload level and inbound trucks filling rate the situation is less performant. On the one hand, we observed high daily workload variability, which results in a non-optimal weekly resources assessment. On the other hand, even if the inbound transportation schedule is respected, a low truck filling rate (52% average) is observed in reality. III. LITERATURE ANALYSIS AND PROBLEM DEFINITION A. Literature review In nowadays globalized industrial environment, supply chain performance is crucial to maintain competiveness since companies must assure the delivery of products at the right time, with the desired quality level and at the minimum cost. A relatively new strategy to support this objective is crossdocking. A cross dock center is an intermediate point in a supply chain, in which products from incoming trucks are unloaded, sorted, moved across and ultimately loaded onto outgoing trucks. This logistic solution may result in a reduction of lead times, a decrease of stock levels and economies in transportation [4]. Despite of several successful industrial cases in cross-docking, there is a lack of a structured body of academic literature in this field [5]. Moreover, since few authors present an implementation of their work in a crossdock center, a gap between industry practice and current research is shown [6]. Main study subjects concerning crossdocking can be classified as follow [7]: Strategical: geographical location and internal lay-out. Tactical: network flows, distribution planning and vehicle routing. Operational: truck scheduling, dock door assignment, internal operation planning and scheduling. Strategic issues are out of our scope, since the cross-dock platforms we consider are already active. Likewise, vehicle routing, truck scheduling and door assignment are not treated in this paper and they are rather considered as inputs (based on Renault defined transportation schedule). Recent work on previous subjects is available in [8-10]. Based on Renault ILN activity description, our interest resides on two fields: distribution and operation planning. Decisions related to distribution networks within crossdocking can be considered as an extension of the shipment consolidation problem, which studies a distribution network consisting of a set of supply, transshipment and demand nodes. Product flow quantities, number of facilities and number of trucks are the common decision variables. Different type of constraints can be contemplated: time windows, capacity (storage, treatment, and transportation), direct link between suppliers and customers, among others. The model presented in [11] includes fixed-schedule transportation constraints and tardiness costs in a distribution network and seeks to determine product flow quantities and allocation through cross-docks centers. The authors propose a genetic algorithm to minimize total costs (transportation, inventory holding and penalty) and compare their results with CPLEX performance. In [12], a distribution plan based on expected supplies and demands in a cross-docking network is determined. The model minimizes inventory handling costs and transportation costs, satisfying storage capacity and time windows constraints. A set of heuristics methods is proposed and tested, providing quality solutions in realistic timescales. An ant colony optimization algorithm which aims to minimize total shipping cost in a cross-docking network is presented in [13]. The number of trucks and product quantities are determined for each link of the network. Storage is not allowed and direct transportation between suppliers and customers is considered. Results from numerical experiments showed a significant cost reduction and outperformed Branch-and-Bound methods. In [14], a global optimization problem in a cross-docking network is studied. A two-stage heuristic algorithm which defines TL (truck load) and LTL (less-than-truckload) transportation planning is proposed to determine the quantity of products shipped on each arc of the distribution network. Model s objective is to minimize transportation and inventory costs. Time windows constraints and truck setup costs are included. Computational experiments showed efficiency in terms of runtimes and solution quality. A two-manufacturer distribution network with cross-docking centers is considered in [15]. Authors propose a mixed integer linear programming model, based on the uncapacitated-facility-location problem. They seek to minimize fixed facility cost, transportation cost and inventory cost. The latter is considered only at supply and demand nodes. Several numerical experiments were conducted using LINGO and CPLEX software and due to problem s complexity, they proposed to decompose it into a set of simpler sub-problems. Concerning internal operation planning, different settings and performance indicators are considered in current research [6]. We focus on outbound truck filling coordination, inventory level, daily workload and resource needs estimation. According to [16], a cross-docking system can be either schedule-driven (outbound trucks must respect a fixed schedule regardless its filling rate) or load-driven. Authors describe a case of study of a load-driven cross-dock at Ford Motor Company. Reference [17] considers a negotiation model for planning and scheduling at a shoes distribution logistic platform. They propose an integer linear programming model to smooth workload by modifying the dates of arrival (from suppliers) and departure (to costumers). Storage capacity constraints, earliness and tardiness costs and inventory holding costs are considered. The model is implemented and tested with CPLEX, using generated data based on two industrial propositions. A study case at Kodak cross-dock platform is presented in [18]. They evaluate the impact of cross-docking level loading on the overall supply chain cost. According to authors, detailed analyses based on distribution network characteristics are required, in order to evaluate the trade-offs between inventory policies, service level, transportation cost and workforce size. Reference [19] proposes a sequential approach to deal simultaneously with weekly planning and daily rostering of workforce in a logistic platform. To do so, they propose and implement in CPLEX three mixed-integer linear programming models. Industrial data is used for computational experiments and regarding the quality of solutions, the proposed decision tool was adopted by their industrial partner.

B. Research framework based on Renault ILN configuration Previous described studies on shipment consolidation could be applied in a single cross-docking network. In order to model Renault ILN system a set of parameters and constraints must be considered jointly: number of trucks in inbound and in outbound segments, storage at the cross-dock, daily workload and internal resources utilization. To our best knowledge, no research work tackles the described system. References [11] and [12] do not include transportation units, as they considerate product shipment as flows. Modelling in [13] and [15] do not allow storage at the cross-dock. References [14] and [16] do not include operational aspects related to internal resources and workload. Model proposed in [17] only contemplate inbound transportation costs. Finally, study presented [19] focuses on workforce scheduling. Our research work seeks to stablish a link between tactical and operational decisions in crossdocking. In contrast to the vast literature in optimization problems for each level, interactions and dependency between them has not received enough attention [20]. IV. MODELLING AND NUMERICAL EXPERIMENTS A. Problem description We propose a jointly distribution and operation planning model at ILN platforms, which will seek to determine daily product flow in order to fulfill the total weekly demand for each component, as well as estimate the number of used trucks (inbound) and containers (outbound). Model s objective is to minimize the total cost, which includes the transportation cost (number of trucks and containers) and the internal activity cost (storage and resources).the pre-defined transportation schedule is considered as supply time windows constraints. We consider a limited storage capacity for the outbound staging zone and an unlimited capacity for the inbound staging zone (trucks can be delayed in the yard). Regarding operation planning, we consider an ILN as a load-driven cross-dock, since products are kept in the outbound staging zone until there is enough volume to load a full container. Knowing the workload inferred by product, global ILN daily workload can be estimated. Based on this information, the weekly resource need can be assessed. Sets The described framework uses the following notation: i in I Components. j in J Days of the week [1,5]. k in K Outbound destinations. l in L Inbound transportation trips. Parameters v i Volume (m 3 ) of component i. q i Total demand of component i. it i,l 1 if component i belongs to inbound transportation trip l, 0 otherwise. By definition, the sum of it i,l is 1. od i,k 1 if component i is demanded by customer k, 0 otherwise. By definition, the sum of od i,k is 1. pv j,l Number of contracted vehicles in day j, for trip l. ut i Unloading time of component i. rt i Repackaging time of component i. lt i Loading time of component i. ws j 1 if j is a working day, 0 otherwise. wd vit Worked hours in a day. Maximum capacity (m 3 ) of inbound vehicles. sm Maximum capacity of the outbound staging zone (m 3 ) vot Maximum capacity (m 3 ) of outbound containers. cit l Fixed cost of a contracted vehicle for inbound trip l. r a Cancellation cost (ratio) of a contracted vehicle. Extra cost (ratio) of contracting an extra vehicle. cst Storage cost per m 3 cwf Internal resource cost cot k Fixed cost of a container for outbound destination k. Decision variables X ij Incoming quantity of component i on day j. Y ij Outgoing quantity of component i on day j. OT j,k Approximation of the number of containers used for destination k on day j. IT j,l Approximation of the number of contracted vehicles used for trip l on day j. ITS j,l Approximation of the number of extra vehicles used by trip l on day j. W Number of weekly internal resources. S i,j Quantity of component i stored on day j. B. Mathematical formulation The integer linear programming model is defined as follows: Where: Min Z = IT_cost + IA_cost + OT_cost (1) IT_cost = j,l [cit l * (IT j,l + ITS j,l * a + ws j * (pv j,l IT j,l ) * r)] (2) IA_cost = W * cwf + i,j (S i,j * v i *cst) (3) OT_cost = j,k (OT j,k * cot k ) (4) Subject to: j X i,j = q i i (5) j Y i,j = q i i (6) X i,j q i * ws j i,j (7) Y i,j q i * ws j i,j (8) i X i,j * it i,l * v i (IT j,l + ITS j,l ) * vit j,l (9) i Y i,j * ot i,k * v i OT j,k * vot j,k (10)

IT j,l pv j,l j,l (11) S i,j = X i,j - Y i,j i,j =1 (12) S i,j = S i,j-1 + X i,j - Y i,j i,j >1 (13) i (S i,j * v i ) sm j (14) W i (X i,j * (ut i + rt i ) + Y ij * lt i ) j (15) X i,j \in N, Y i,j \in N, S i,j \in N, W \in N i,j (16) IT j,l \in N, ITS j,l \in N, OT j,k \in N i,k,l (17) Fig. 4 illustrates the defined model network. The objective function in (1) seeks to minimize total cost. Equation (2) represents the inbound transportation cost, which includes the number of trucks, as well as penalty costs generated by canceled and additional trucks, (3) characterizes internal activity cost, defined by storage cost and resource utilization cost. Equation (4) represents the outbound transportation cost, based on the number of containers used. Constraints (5) and (6) guarantee total demand fulfillment, (7) and (8) ensures the respect of working calendar, (9) and (10) represent, respectively, the inbound and outbound vehicle capacity and (11) denotes the number of pre-contracted inbound vehicles. Suppliers Vehicle scheduling X i,j IT j,l ITS j,l ILN Fig. 4. Proposed model schema. Equations (12) and (13) are storage balance constraints that implies the inventory level of a component is equal to its previous inventory level in addition to the received quantity minus the shipped quantity in the current period (assuming that initial storage is zero). Equation (14) represents the outbound staging zone capacity, (15) assesses the resource needs for the week: it corresponds to the higher workload level. Finally, (16) and (17) are integer constraints. C. Numerical experiments The presented model was implemented in CPLEX and tested with 21-week real data from one Renault ILN using a 4GB RAM Intel Celeron P4600 @ 2.00GHz CPU. Table 1 summarizes the general statistics of the experiments. In order to evaluate model s approximation in terms of number of vehicles (inbound and outbound) we used a load packing optimization software from Renault and the following analysis are based on its results. Proposed model showed a total cost reduction of 13%. More accurate conclusions can be drawn by analysing individually each cost driver. Fig. 5(a) shows the inbound transportation cost comparison: the average of cost decrease S i,j W Y i,j Storage capacity Workload assessment OT j,k Customers Load-driven container filling per week is 17% with a standard deviation of 4.7. Concerning internal activity cost, storage is practically eliminated in the proposed model. Fig. 5(b) compares internal resource costs. We remind that this cost is associated to daily workload peaks, and regarding the current planning process, this effect is more strenuously marked in weeks with public holidays (e.g. weeks 6, 12, 13). In 5-worked-day weeks our model shows a cost reduction of 13% with a standard deviation of 6.3. An important consequence of internal resources optimization is daily workload smoothing for each activity (unloading, repackaging and loading), which will be traduced in a better organisation and management of the shop-floor. Finally, outbound transportation cost is alike in both original and proposed planning process. This is the consequence of the outbound load-driven configuration combined with the possibility of storage in the outbound staging zone. V. INDUSTRIAL IMPLEMENTATION Numerical simulations showed a significant potential of reducing ILN costs, especially those related to inbound transportation. Consequently, a simplified version of the model including only inbound parameters was implemented and tested in real-life. To do so, we chose a group of components (between 10 to 20% of total volume) for which the proposed planning process was applied. Fig. 6 shows the obtained results during 8 weeks of operation. First set of bars represent the number of trucks needed to satisfy the original inbound delivery schedule. Likewise, second group of bars represent the alternative inbound delivery schedule, which was the one in fact transmitted to suppliers. Finally, the number of trucks really used is shown in the last set of bars. For the concerned suppliers, the inbound transportation cost was reduced by 20%. The difference between the number of planned trucks and the number of trucks that actually arrived at the platform can be explained on the one hand, by a non-accurate approximation of the model and on the other hand, by external factors such as transportation delay, supplier s capacity, etc. Further analysis is needed in order to cope with the described issues. VI. CONCLUSIONS AND PERSPECTIVES Renault ILN cross-dock platforms connect overseas industrial sites with inland suppliers. Other than physical consolidation of components, they must carry out the distribution and operation planning processes. Both are key activities in terms of ensuring a high service rate at the minimum cost. Based on ILN current processes, a set of improvement opportunities were identified and accordingly an alternative planning method is proposed. An integer linear programming model was implemented and tested in CPLEX. Numerical simulations were conducted from industrial data of 21 weeks. Results showed a significant reduction on inbound transportation and internal resources costs and therefore a simplified version of the model was implemented and tested for a group of components at one Renault ILN, with likewise outcomes. We associated described industrial situation with current literature in cross-docking distribution and operation planning. Our contribution lies on tackling these two fields together, as we considerate both inbound and outbound transportation costs, storage capacity and internal resources optimization.

This is the first stage of an extended optimization work concerning the planning process at Renault cross-dock platforms. In the next phase, numerical experiments must be extended using different data and parameters (for instance, those from a different Renault ILN) in order to better assess its performance. Industrial implementation analysis suggests two perspectives of study: first, the model s approximation regarding the number of trucks and second, the impact of the uncertain environment in model s performance. TABLE I. NUMERICAL EXPERIMENTS STATISTICS Week Components Inbound Out GAP Variables Constraints trips destinations (after 3') 1 1032 27 10 17305 35189 1,18 2 1092 27 9 18282 37181 0,34 3 1344 28 14 22350 45568 1,47 4 1303 27 12 21649 44150 2,07 5 1096 26 15 18307 37294 1,23 6 915 28 15 15435 31365 0,87 7 668 26 12 11377 23073 0,11 8 693 25 18 11783 23924 0,80 9 813 25 12 13701 27852 0,18 10 1354 28 16 22527 45925 1,15 11 1278 28 15 21303 43404 1,30 12 1229 28 15 20525 41793 1,27 13 1298 28 15 21572 44013 0,37 14 1397 28 14 23179 47298 1,44 15 1437 28 16 23830 48639 0,67 16 1469 28 16 24356 49709 1,51 17 1507 28 17 24982 50986 2,98 18 1325 27 17 22014 44914 1,88 19 1402 28 16 23257 47471 2,88 20 1396 28 15 23167 47274 1,47 21 1422 28 15 23599 48148 1,75 Cost Cost Trucks (a) Inbound transportation performance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Weeks (b) Internal resources performance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Weeks Current planning Fig. 5. Numerical experiments results. Proposed planning Inbound transportation performance 1 2 3 4 5 6 7 8 Weeks Current planning Proposed planning Real performance Fig. 6. Industrial test results at one Renault ILN. REFERENCES [1] V. Cârstea, Delocalization - the automotive industry's answer to cost reduction, Romanian Economic Business Review, vol. 8, issue 3.1, pp. 180-183, 2013. [2] V. Frigant and Z. Martin, Are automotive global production networks becoming more global? Comparison of regional and global integration processes based on auto parts trade data, 4th AFEP congress, ENS- Cachan, 2014. [3] V. Carbone and M. De Martino, The changing role of ports in supplychain management: an empirical analysis, Maritime Policy & Management, vol. 30, issue 4, pp 305-320, 2003. [4] Saddle Creek Logistics Services, 2011 Cross-docking trends report, 2011. [Available at: http://www.sclogistics.com/news-resources/whitepapers/41-cross-docking-trends-report-1/file]. [5] N. Boysen and M. Fliedner Cross dock scheduling: Classification, literature review and research agenda, Omega, vol. 38, issue 6, pp. 413-422, 2010. [6] A-L Ladier, Scheduling cross-docking operations: Integration of operational uncertainties and resource capacities, Chapter 1, Ph.D. thesis, Université de Grenoble, 2014. [Available at: http://pagesperso.gscop.grenoble-inp.fr/~ladiera/publi/ladier_manuscrit_web]. [7] J. Van Belle, P. Valckenaers and D. Cattrysse, Cross-docking: State of the art, Omega, vol. 40, issue 6, pp. 827-846, 2012. [8] Z. Li, W. He, C. H. Sim and C. C. Chen, A solution for cross-docking operations planning, scheduling and coordination, IEEE International Conference on Service Operations and Logistics, and Informatics, vol. 2, pp. 2957-2962, 2008. [9] A-L, Ladier and G. Alpan, Scheduling truck arrivals and departures in a crossdock: Earliness, tardiness and storage policies, International Conference on Industrial Engineering and Systems Management (IESM), pp. 1-7, 2013. [10] D. Agustina, C. K. M. Lee and R. Piplani, Vehicle scheduling and routing at a cross docking center for food supply chains, International Journal of Production Economics, vol. 152, issue 0, pp. 29-41, 2014. [11] Z. Miao, F. Yang and K. Fu, Transshipment problem with penalty in crossdocking distribution networks, 6th International Conference on Service Systems and Service Management, pp. 280-285, 2009. [12] P. Chen, Y. Guo, A. Lim and B. Rodrigues, Multiple crossdocks with inventory and time windows, Computers & Operations Research, vol. 33, issue 1, pp.43-63, 2006. [13] R. Musa, J-P. Arnaout and H. Jung, Ant colony optimization algorithm to solve for the transportation problem of cross-docking network, Computers & Industrial Engineering, vol. 59, issue 1, pp. 85-92, 2010. [14] H. Ma, Z. Miao, A. Lim and B. Rodrigues, Crossdocking distribution networks with setup cost and time window constraint, Omega, vol. 39, issue 1, pp. 64-72, 2011. [15] M. Gümüa and J. H. Bookbinder, Cross-docking and its implications in location-distribution systems, Journal of Business Logistics, vol. 25, issue 2, pp. 199-228, 2004. [16] H. D. Ratliff, J. V. Vate and M. Zhang, Network design for loaddriven cross-docking system, Technical Report, Georgia Institute of Technology, Industrial and Systems Engineering, 1999. [17] S. Carrera, K. Chami, R. Guimaraes, M-C. Portmann and W. Ramdane- Cherif, Negotiation models for logistic plarform planning and scheduling, 11th International Workshop on Project Management and Scheduling, pp. 43-46, 2008. [18] J. M. Palmer, Level loading and cross-docking in a global logistics network, Master thesis, Sloan School of Management, 2005. [Available at: http://dspace.mit.edu/handle/1721.1/34849]. [19] A-L. Ladier, G. Alpan and P. Bernard, Joint employee weekly timetabling and daily rostering: A decision-support tool for a logistics platform, European Journal of Operational Research, vol. 234, issue 1, pp. 278-291, 2014. [20] S. Dauzère Pérès and J-B. Lasserre, On the importance of sequencing decisions in production planning and scheduling, International Transactions in Operational Research, vol. 9, issue 6, pp. 779-793, 2002.