Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study

[EN] The well-known Vehicle Routing Problem (VRP) is to find proper sequence of routes in order to minimize transportation costs. In this paper, a mixed-integer programming model is presented for a food distributer company and the model outputs are to determine the optimal routes and amount of pickup and delivery. In the objective function, the costs of transportation, holding, tardiness and earliness are considered simultaneously. The proposed model with respect to real conditions is multi-period and has two different time periods: one for dispatching vehicles to customers and suppliers and the other for receiving customers’ orders. Time window and split pickup and delivery are considered for perishable products. The proposed model is nonlinear and will be linearized using exact techniques. At the end, model is solved using GAMS and the sensitivity analysis is performed. The results indicate that the trend of changes in holding and transportation costs in compared to tardiness and earliness costs are closed together and are not so sensitive to demand changes.Rashidi Komijan, A.; Delavari, D. (2017). Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study. International Journal of Production Management and Engineering. 5(2):45-53. doi:10.4995/ijpme.2017.5960SWORD455352DENG, A., MAO, C., & ZHOU, Y. (2009). Optimizing Research of an Improved Simulated Annealing Algorithm to Soft Time Windows Vehicle Routing Problem with Pick-up and Delivery. Systems Engineering - Theory & Practice, 29(5), 186-192. doi:10.1016/s1874-8651(10)60049-xAndersson, H., Hoff, A., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers & Operations Research, 37(9), 1515-1536. doi:10.1016/j.cor.2009.11.009Baldacci, R., Mingozzi, A., & Roberti, R. (2012). Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research, 218(1), 1-6. doi:10.1016/j.ejor.2011.07.037Belfiore, P., & Yoshizaki, H. T. Y. (2013). Heuristic methods for the fleet size and mix vehicle routing problem with time windows and split deliveries. Computers & Industrial Engineering, 64(2), 589-601. doi:10.1016/j.cie.2012.11.007Cacchiani, V., Hemmelmayr, V.C., Tricoire, F., (2012). A set-covering based heuristic algorithm for the periodic vehicle routing problem. Discrete Applied Mathematics, 163(1), 53-64. https://doi.org/10.1016/j.dam.2012.08.032Cattaruzza, D., Absi, N., Feillet, D., & Vidal, T. (2014). A memetic algorithm for the Multi Trip Vehicle Routing Problem. European Journal of Operational Research, 236(3), 833-848. doi:10.1016/j.ejor.2013.06.012Çetinkaya, C., Karaoglan, I., & Gökçen, H. (2013). Two-stage vehicle routing problem with arc time windows: A mixed integer programming formulation and a heuristic approach. European Journal of Operational Research, 230(3), 539-550. doi:10.1016/j.ejor.2013.05.001Eksioglu, B., Vural, A. V., & Reisman, A. (2009). The vehicle routing problem: A taxonomic review. Computers & Industrial Engineering, 57(4), 1472-1483. doi:10.1016/j.cie.2009.05.009Hasani-Goodarzi, A., & Tavakkoli-Moghaddam, R. (2012). Capacitated Vehicle Routing Problem for Multi-Product Cross- Docking with Split Deliveries and Pickups. Procedia - Social and Behavioral Sciences, 62, 1360-1365. doi:10.1016/j.sbspro.2012.09.232Rahimi-Vahed, A., Gabriel Crainic, T., Gendreau, M., & Rei, W. (2015). Fleet-sizing for multi-depot and periodic vehicle routing problems using a modular heuristic algorithm. Computers & Operations Research, 53, 9-23. doi:10.1016/j.cor.2014.07.004Shahin Moghadam, S., Fatemi Ghomi, S. M. T., & Karimi, B. (2014). Vehicle routing scheduling problem with cross docking and split deliveries. Computers & Chemical Engineering, 69, 98-107. doi:10.1016/j.compchemeng.2014.06.015Silva, M. M., Subramanian, A., & Ochi, L. S. (2015). An iterated local search heuristic for the split delivery vehicle routing problem. Computers & Operations Research, 53, 234-249. doi:10.1016/j.cor.2014.08.005Taş, D., Jabali, O., & Van Woensel, T. (2014). A Vehicle Routing Problem with Flexible Time Windows. Computers & Operations Research, 52, 39-54. doi:10.1016/j.cor.2014.07.005Yu, B., & Yang, Z. Z. (2011). An ant colony optimization model: The period vehicle routing problem with time windows. Transportation Research Part E: Logistics and Transportation Review, 47(2), 166-181. doi:10.1016/j.tre.2010.09.010Zhang, S., Lee, C. K. M., Choy, K. L., Ho, W., & Ip, W. H. (2014). Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem. Transportation Research Part D: Transport and Environment, 31, 85-99. doi:10.1016/j.trd.2014.05.01

A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

[EN] This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the vehicles are not required to return to the depot after completing a service. In this new problem, the demands of customers are fulfilled by a heterogeneous fixed fleet of vehicles having various capacities, fixed costs and variable costs. This problem is an important variant of the open vehicle routing problem (OVRP) and can cover more practical situations in transportation and logistics. Since this problem belongs to NP-hard Problems, An approach based on column generation (CG) is applied to solve the HFFOVRP. A tight integer programming model is presented and the linear programming relaxation of which is solved by the CG technique. Since there have been no existing benchmarks, this study generated 19 test problems and the results of the proposed CG algorithm is compared to the results of exact algorithm. Computational experience confirms that the proposed algorithm can provide better solutions within a comparatively shorter period of time.Yousefikhoshbakht, M.; Dolatnejad, A. (2017). A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem. International Journal of Production Management and Engineering. 5(2):55-71. doi:10.4995/ijpme.2017.5916SWORD557152Aleman, R. E., & Hill, R. R. (2010). A tabu search with vocabulary building approach for the vehicle routing problem with split demands. International Journal of Metaheuristics, 1(1), 55. doi:10.1504/ijmheur.2010.033123Anbuudayasankar, S. P., Ganesh, K., Lenny Koh, S. C., & Ducq, Y. (2012). Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Systems with Applications, 39(3), 2296-2305. doi:10.1016/j.eswa.2011.08.009Brandão, J. (2009). A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. European Journal of Operational Research, 195(3), 716-728. doi:10.1016/j.ejor.2007.05.059Çatay, B. (2010). A new saving-based ant algorithm for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. Expert Systems with Applications, 37(10), 6809-6817. doi:10.1016/j.eswa.2010.03.045Dantzig, G. B., & Ramser, J. H. (1959). The Truck Dispatching Problem. Management Science, 6(1), 80-91. doi:10.1287/mnsc.6.1.80Gendreau, M., Guertin, F., Potvin, J.-Y., & Séguin, R. (2006). Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transportation Research Part C: Emerging Technologies, 14(3), 157-174. doi:10.1016/j.trc.2006.03.002Gendreau, M., Laporte, G., Musaraganyi, C., & Taillard, É. D. (1999). A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 26(12), 1153-1173. doi:10.1016/s0305-0548(98)00100-2Lei, H., Laporte, G., & Guo, B. (2011). The capacitated vehicle routing problem with stochastic demands and time windows. Computers & Operations Research, 38(12), 1775-1783. doi:10.1016/j.cor.2011.02.007Li, X., Leung, S. C. H., & Tian, P. (2012). A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39(1), 365-374. doi:10.1016/j.eswa.2011.07.025Li, X., Tian, P., & Aneja, Y. P. (2010). An adaptive memory programming metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 46(6), 1111-1127. doi:10.1016/j.tre.2010.02.004Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2011). An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem. Journal of Heuristics, 19(2), 201-232. doi:10.1007/s10732-011-9186-ySaadati Eskandari, Z., YousefiKhoshbakht, M. (2012). Solving the Vehicle Routing Problem by an Effective Reactive Bone Route Algorithm, Transportation Research Journal, 1(2), 51-69.Subramanian, A., Drummond, L. M. A., Bentes, C., Ochi, L. S., & Farias, R. (2010). A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. Computers & Operations Research, 37(11), 1899-1911. doi:10.1016/j.cor.2009.10.011Syslo, M., Deo, N., Kowalik, J. (1983). Discrete Optimization Algorithms with Pascal Programs, Prentice Hall.Taillard, E. D. (1999). A heuristic column generation method for the heterogeneous fleet VRP, RAIRO Operations Research, 33, 1-14. https://doi.org/10.1051/ro:1999101Tarantilis, C. D., & Kiranoudis, C. T. (2007). A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector. European Journal of Operational Research, 179(3), 806-822. doi:10.1016/j.ejor.2005.03.059Wang, H.-F., & Chen, Y.-Y. (2012). A genetic algorithm for the simultaneous delivery and pickup problems with time window. Computers & Industrial Engineering, 62(1), 84-95. doi:10.1016/j.cie.2011.08.018Yousefikhoshbakht, M., Didehvar, F., & Rahmati, F. (2013). Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm. International Journal of Production Research, 52(9), 2565-2575. doi:10.1080/00207543.2013.855337Yousefikhoshbakht, M., & Khorram, E. (2012). Solving the vehicle routing problem by a hybrid meta-heuristic algorithm. Journal of Industrial Engineering International, 8(1). doi:10.1186/2251-712x-8-1

Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times and costs, time windows, and incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. To face this challenge, we propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 existing instances within one hour. Scalability experiments on even larger problems demonstrate that it can optimally solve problems with around 60 ships and 200 cargoes (i.e., 400 pickup and delivery services) and find optimality gaps below 1.04% on the largest cases with up to 260 cargoes. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since these instances are comparable in size with the largest problems routinely solved by shipping companies

On the use of reference points for the biobjective Inventory Routing Problem

The article presents a study on the biobjective inventory routing problem. Contrary to most previous research, the problem is treated as a true multi-objective optimization problem, with the goal of identifying Pareto-optimal solutions. Due to the hardness of the problem at hand, a reference point based optimization approach is presented and implemented into an optimization and decision support system, which allows for the computation of a true subset of the optimal outcomes. Experimental investigation involving local search metaheuristics are conducted on benchmark data, and numerical results are reported and analyzed

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Ant colony optimization and its application to the vehicle routing problem with pickups and deliveries

Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickup and Delivery (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of ACO approach and presents several implementations to various combinatorial optimization problems. Next, VRPPD is described and the related literature is reviewed, Then, an ACO approach for VRPPD is discussed. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature

Modeling and solving the multi-period inventory routing problem with constant demand rates

The inventory routing problem (IRP) is one of the challenging optimization problems in supply chain logistics. It combines inventory control and vehicle routing optimization. The main purpose of the IRP is to determine optimal delivery times and quantities to be delivered to customers, as well as optimal vehicle routes to distribute these quantities. The IRP is an underlying logistical optimization problem for supply chains implementing vendor-managed inventory (VMI) policies, in which the supplier takes responsibility for the management of the customers' inventory. In this paper, we consider a multi-period inventory routing problem assuming constant demand rates (MP-CIRP). The proposed model is formulated as a linear mixed-integer program and solved with a Lagrangian relaxation method. The solution obtained by the Lagrangian relaxation method is then used to generate a close to optimal feasible solution of the MP-CIRP by solving a series of assignment problems. The numerical experiments carried out so far show that the proposed Lagrangian relaxation approach nds quite good solutions for the MP-CIRP and in reasonable computation times