International Journal of Industrial Engineering & Production Research

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The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clarified then the new method based on ACCPM is proposed as a stabilization technique of column generation (lagrangian relaxation). Both approaches are tested on a benchmark instance to demonstrate the advantages of proposed method in terms of computational time and lower bounds quality.

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Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software for large scaled complex nonlinear programming problem with 0-1 type decision variables for stochastic vehicle routing problem (SVRP) is not easily available merely then the value of an approximation technique becomes imperative. In this article, theorems which build a foundation for moving toward the development of an approximate methodology for solving SVRP are stated and proved. Key Words: Vehicle Routing Problem, Chance Constrained Programming, Linear approximation, Optimization.

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periodic vehicle routing problem focuses on establishing a plan of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. This paper presents a new effective heuristic algorithm based on data mining tools for periodic vehicle routing problem (PVRP). The related results of proposed algorithm are compared with the results obtained by best Heuristics and meta-heuristics algorithms in the literature. Computational results indicate that the algorithm performs competitive in the accuracy and its small amount of solving time point of views.

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Customer service level is of prime importance in today competitive world and has various dimensions with delivery quality being one of the most important ones. Delivery quality has several parameters such as deliver time window options, time window size, etc. In this paper we focus on one of these parameters, namely time window setting. It has a direct impact upon customer satisfaction and business profit. On the other hand, delivery time windows affect routing and distribution costs. Generally, in the routing operation, time windows have been determined by customers or distributer and are considered as input parameters for the vehicle routing problem with time window (VRPTW) model. In this paper, a mathematical model is proposed for the integration of these two decisions in other words, in the present model, time window setting decisions are integrated with routing decisions. Then a column generation approach is employed to obtain the lower bounds of problems and to solve the problems, a quantum algorithm is proposed. Finally, the computational results of some instances are reported and the results of these approaches are compared. The results demonstrate the effectiveness of the quantum algorithm in solving this problem.

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Today, many companies after achieving improvements in manufacturing operations are focused on the improvement of distribution systems and have long been a strong tendency to optimize the distribution network in order to reduce logistics costs that the debate has become challenging. Improve the flow of materials, an activity considered essential to increase customer satisfaction. In this study, we benefit cross docking method for effective control of cargo flow to reduce inventory and improve customer satisfaction. Also every supply chain is faced with risks that threaten its ability to work effectively. Many of these risks are not in control but can cause great disruption and costs for the supply chain process. In this study we are looking for a model to collect and deliver the demands for the limited capacity vehicle in terms of disruption risk finally presented a compromised planning process. In fact, we propose a framework which can consider all the problems on the crisis situation for decision-making in these conditions, by preparing a mathematical model and software gams for the following situation in a case study. In the first step, the results presented in mode of a two-level planning then the problem expressed in form of a multi-objective optimization model and the results was explained.

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In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (FMDVRP-SPD) is investigated. The FMDVRP-SPD is the problem of allocating customers to several depots, so that the optimal set of routes is determined simultaneously to serve the pickup and the delivery demands of each customer within scattered depots. In the problem, both pickup and delivery demands of customers are fuzzy variables. The objective of FMDVRP-SPD is to minimize the total cost of a distribution system including vehicle traveling cost and vehicle fixed cost. To model the problem, a fuzzy chance-constrained programming model is proposed based on the fuzzy credibility theory. A heuristic algorithm combining K-means clustering algorithm and ant colony optimization is developed for solving the problem. To achieve an appropriate threshold value of parameters of the model, named “vehicle indexes”, and to analyze their influences on the final solution, numerical experiments are carried out.

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Logistics planning in disaster response phase involves dispatching commodities such as medical materials, personnel, food, etc. to affected areas as soon as possible to accelerate the relief operations. Since transportation vehicles in disaster situations can be considered as scarce resources, thus, the efficient usage of them is substantially important. In this study, we provide a dynamic vehicle routing model for emergency logistics operations in the occurrence of natural disasters. The aim of the model is to find optimal routes for a fleet of vehicles to give emergency commodities to a set of affected areas by considering the existence of more than one arc between each two nodes in the network (multi-graph network). Proposed model considers FIFO property and focused on minimization of waiting time and total number of vehicles. Various problem instances have been provided to indicate the efficiency of the model. Finally, a brief sensitivity analysis is presented to investigate the impact of different parameters on the obtained solutions.

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In this research, a new bi-objective routing problem is developed in which a conventional vehicle routing problem with time windows (VRPTW) is considered with environmental impacts and heterogeneous vehicles. In this problem, minimizing the fuel consumption (liter) as well as the length of the routes (meter) are the main objectives. Therefore, a mathematical bi-objective model is solved to create Pareto's solutions. The objectives of the proposed mathematical model are to minimize the sum of distance cost as well as fuel consumption and Co2 emission. Then, the proposed Mixed-Integer Linear Program (MILP) is solved using the ε-constraint approach Furthermore, numerical tests performed to quantify the benefits of using a comprehensive goal function with two different objectives. Managerial insights and sensitivity analysis are also performed to show how different parameters of the problem affect the computational speed and the solutions’ quality.

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In this paper, an inventory-routing problem for a network of appliance repair service is discussed including several repair depots and customers. The customer in this network makes a demand to have his/her faulty appliance repaired. Then, the repairman is assigned to the demand based on the skill needed for repairing of appliance differing for each one. The assigned repairman picks up the faulty appliance from the customer place using the vehicle for transferring faulty appliances to repair depot. The vehicle for picking up and delivering the appliances has a maximum capacity. Additionally, the repair depot needs spare parts to repair the faulty appliances that is supplied either by the supplier or lateral transshipment from the other depots. The capacitated vehicle inventory-routing problem with simultaneous pickup and delivery is NP-hard which needs special optimization procedure. Regarding the skill of repairman, it becomes more complex. Many solution approaches have been provided so far which have their pros and cons to deal with. In this study, an augmented angle-based sweep method is developed to cluster nodes for solving the problem. Finally, the heuristic is used in the main body of genetic algorithm with special representation.

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One of the challenging issues in today’s competitive world for servicing companies is uncertainty in some factors or parameters that they often derive from fluctuations of market price and other reasons. With regard to this subject, it would be essential to provide robust solutions in uncertain situations. This paper addresses an open vehicle routing problem with demand uncertainty and cost of vehicle uncertainty. Bertsimas and Sim’s method has been applied to deal with uncertainty in this paper. In addition, a deterministic model of open vehicle routing problem is developed to present a robust counterpart model. The deterministic and the robust model is solved by GAMS software. Then, the mean and standard deviations of obtained solutions were compared in different uncertainty levels in numerous numerical examples to investigate the performance of the developed robust model and deterministic model. The computational results show that the robust model has a better performance than the solutions obtained by the deterministic model.
 

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In large-scale emergency, the vehicle routing problem focuses on finding the best routes for vehicles. The equitable distribution has a vital role in this problem to decrease the number of death and save people's lives. In addition to this, air pollution is a threat to people’s life and it can be considered to omit other kinds of disasters happens because of it. So, a new MINLP model presented is going to face a real situation by considering real world assumptions such as fuzzy demands and travel time, multi depots and items, vehicle capacity and split delivery. The first objective function is to minimize the sum of unsatisfied demand which follows a piecewise function and the second one is to minimize the cost which depends on the fuel consumption. In order to solve the multi-objective problem with fuzzy parameters, nonlinear function has been linearized by convex combination and a new crisp model is presented by defusing fuzzy parameters. Finally, NSGA-П algorithm is applied to solve this problem and the numerical results gained by this procedure demonstrate its convergence and its efficiency in this problem.