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

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

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

A Survey On Multi Trip Vehicle Routing Problem

The vehicle routing problem (VRP) and its variants are well known and greatly explored in the transportation literature. The vehicle routing problem can be considered as the scheduling of vehicles (trucks) to a set of customers under various side constraints. In most studies, a fundamental assumption is that a vehicle dispatched for service finishes its duty in that scheduling period after it returns back to the depot. Clearly, in many cases this assumption may not hold. Thus, in the last decade some studies appeared in the literature where this basic assumption is relaxed, and it is allowed for a vehicle to make multiple trips per period. We consider this new variant of the VRP an important one with direct practical impact. In this survey, we define the vehicle routing problem with multiple trips, define the current state-of-the-art, and report existing results from the current literature

Optimizing departure times in vehicle routes

Most solution methods for the vehicle routing problem with time\ud windows (VRPTW) develop routes from the earliest feasible departure time. However, in practice, temporal traffic congestions make\ud that such solutions are not optimal with respect to minimizing the\ud total duty time. Furthermore, VRPTW solutions do not account for\ud complex driving hours regulations, which severely restrict the daily\ud travel time available for a truck driver. To deal with these problems,\ud we consider the vehicle departure time optimization (VDO) problem\ud as a post-processing step of solving a VRPTW. We propose an ILP-formulation that minimizes the total duty time. The obtained solutions are feasible with respect to driving hours regulations and they\ud account for temporal traffic congestions by modeling time-dependent\ud travel times. For the latter, we assume a piecewise constant speed\ud function. Computational experiments show that problem instances\ud of realistic sizes can be solved to optimality within practical computation times. Furthermore, duty time reductions of 8 percent can\ud be achieved. Finally, the results show that ignoring time-dependent\ud travel times and driving hours regulations during the development of\ud vehicle routes leads to many infeasible vehicle routes. Therefore, vehicle routing methods should account for these real-life restrictions

Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure