Showing 22 results for Routing
Yahia Zare Mehrjerdi,
Volume 24, Issue 4 (12-2013)
Abstract
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.
Mehdi Alinaghian,
Volume 25, Issue 2 (5-2014)
Abstract
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.
Ali Kourank Beheshti , Seyed Reza Hejazi,
Volume 25, Issue 4 (10-2014)
Abstract
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.
Yahia Zare Mehrjerdi, Ali Nadizadeh,
Volume 27, Issue 1 (3-2016)
Abstract
Using Greedy Clustering Method to Solve Capacitated Location-Routing Problem with Fuzzy Demands Abstract In this paper, the capacitated location routing problem with fuzzy demands (CLRP_FD) is considered. In CLRP_FD, facility location problem (FLP) and vehicle routing problem (VRP) are observed simultaneously. Indeed the vehicles and the depots have a predefined capacity to serve the customersthat have fuzzy demands. To model the CLRP_FD, a fuzzy chance constrained program is designed, based on fuzzy credibility theory. To solve the CLRP_FD, a greedy clustering method (GCM) including the stochastic simulation is proposed. Finally, to obtain the best value of the preference index of the model and analysis its influence on the final solutions of the problem, numerical experiments are carried out. Keywords: Capacitated location routing problem, Fuzzy demand, Credibility theory, Stochastic simulation, Ant colony system.
Seyed Mohammad Seyedhosseini, Mohammad Mahdavi Mazdeh, Dr. Ahmad Makui, Seyed Mohammad Ghoreyshi,
Volume 27, Issue 1 (3-2016)
Abstract
In any supply chain, distribution planning of products is of great importance to managers. With effective and flexible distribution planning, mangers can increase the efficiency of time, place, and delivery utility of whole supply chain. In this paper, inventory routing problem (IRP) is applied to distribution planning of perishable products in a supply chain. The studied supply chain is composed of two levels a supplier and customers. Customers’ locations are geographically around the supplier location and their demands are uncertain and follow an independent probability distribution functions. The product has pre-determined fixed life and is to be distributed among customers via a fleet of homogenous vehicles. The supplier uses direct routes for delivering products to customers. The objective is to determine when to deliver to each customer, how much to deliver to them, and how to assign them to vehicle and routes. The mentioned problem is formulated and solved using a stochastic dynamic programming approach. Also, a numerical example is given to illustrate the applicability of proposed approach.
Mehrdad Mirzabaghi, Alireza Rashidi Komijan, Amir H. Sarfaraz,
Volume 27, Issue 3 (9-2016)
Abstract
In the recent decade, special attention is paid to reverse logistic due to economic benefits of recovery and recycling of used products as well as environmental legislation and social concerns. On the other hand، many researches claim that separately and sequential planning of forward and reverse logistic causes sub-optimality. Effective transport activities are also one of the most important components of a logistic system and it needs an accurate planning. In this study, a mixed integer linear programming model is proposed for integrated forward / reverse supply chain as well as vehicles routing. Logistic network which is used in this paper is a multi-echelon integrated forward /reverse logistic network which is comprised capacitated facility, common facilities of production/recovery and distribution/collection, disposal facilities and customers. The proposed model is multi-period and multi-product with the ability to consider several facilities in each level. Various types of vehicle routing models are also included such as multi-period routing, multi-depot, multi-products, routing with simultaneous delivery and pick-up, flexible depot assignment and split delivery. The model results present the product flow between the various facilities in forward and reverse direction throughout the planning horizon with the objective minimization of total cost. Numerical example for solving the model using GAMS shows that the proposed model could reach the optimal solution in reasonable time for small and medium real world’s problems.
Armaghn Shadman, Ali Bozorgi-Amiri, Donya Rahmani,
Volume 28, Issue 2 (6-2017)
Abstract
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.
Adeleh Behzad, Mohammadali Pirayesh, Mohammad Ranjbar,
Volume 28, Issue 3 (9-2017)
Abstract
In last decades, mobile factories have been used due to their high production capability, carrying their equipment and covering rough and uneven routes. Nowadays, more companies use mobile factories with the aim of reducing the transportation and manufacturing costs. The mobile factory must travel between the suppliers, visit all of them in each time period and return to the initial location of the mobile factory. In this paper, we present an integer nonlinear programming model for production scheduling and routing of mobile factory with the aim of maximization of profit. This problem is similar to the well-known Traveling Salesman Problem (TSP) which is an NP-hard problem. Also at each supplier, the scheduling problem for production is NP-hard. After linearization, we proposed a heuristic greedy algorithm. The efficiency of this heuristic algorithm is analyzed using the computational studies on 540 randomly generated test instances. Finally, the sensitivity analysis of the production cost, transportation cost and relocation cost was conducted.
Ali Nadizadeh,
Volume 28, Issue 3 (9-2017)
Abstract
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.
Mosata Setak, Shabnam Izadi, Hamid Tikani,
Volume 28, Issue 4 (11-2017)
Abstract
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.
Alireza Fallah-Tafti, Mohammad Ali Vahdat Zad,
Volume 29, Issue 2 (6-2018)
Abstract
In this article, we propose a special case of two-echelon location-routing problem (2E-LRP) in cash-in-transit (CIT) sector. To tackle this realistic problem and to make the model applicable, a rich LRP considering several existing real-life variants and characteristics named BO-2E-PCLRPSD-TW including different objective functions, multiple echelons, multiple periods, capacitated vehicles, distribution centers and automated teller machines (ATMs), different type of vehicles in each echelon, single-depot with different time windows is presented. Since, routing plans in the CIT sector ought to be safe and efficient, we consider the minimization of total transportation risk and cost simultaneously as objective functions. Then, we formulate such complex problem in mathematical mixed integer linear programming (MMILP). To validate the presented model and the formulation and to solve the problem, the latest version of ε-constraint method namely AUGMECON2 is applied. This method is especially efficient for solving multi objective integer programing (MOIP) problems and provides the exact Pareto fronts. Results substantiate the suitability of the model and the formulation.
Mahdi Bashiri, Elaheh Ghasemi,
Volume 29, Issue 2 (6-2018)
Abstract
Supplying of blood and blood products is one of the most challenging issues in the healthcare system since blood is as extremely perishable and vital good and donation of blood is a voluntary work. In this paper, we propose a two-stage stochastic selective-covering-inventory-routing (SCIR) model to supply whole blood under uncertainty. Here, set of discrete scenarios are used to display uncertainty in stochastic parameters. Both of the fixed blood center and bloodmobile facilities are considered in this study. We suppose that the number of bloodmobiles is indicated in the first stage before knowing which scenario is occurred. To verify the validation of the presented SCIR model to supply whole blood, we examine the impact of parameters variation on the model outputs and cost function using the CPLEX solver. Also the results of comparison between the stochastic approach and expected value approach are discussed.
Shadan Sadighbehzadi, Zohreh Moghaddas, Amirreza Keyghobadi, Mohsen Vaez-Ghasemi,
Volume 29, Issue 4 (12-2018)
Abstract
Natural disasters and crisis are inevitable and each year impose destructive effects on human as injuries and damage to property. In natural disasters and after the outbreak of the crisis, demand for logistical goods and services increase. Effective distribution of emergency aid could have a significant role in minimizing the damage and fatal accident. In this study, a three-level relief chain including a number of suppliers in fixed locations, candidate distribution centers and affected areas at certain points are considered. For this purpose a mixed integer nonlinear programming model is proposed for open transportation location routing problem by considering split delivery of demand. In order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed mode. The objectives of the proposed model include total cost minimization, minimization of the maximum travel time of
vehicles and minimization of unmet demands. In order to solve the problem of the proposed model, fuzzy multi-objective planning is used. For efficiency and effectiveness of the proposed model and solution approach, several numerical examples are studied. Computational results show the effectiveness and efficiency of the model and the proposed approach.
Hossein Jandaghi, Ali Divsalar, Mohammad Mahdi Paydar,
Volume 30, Issue 1 (3-2019)
Abstract
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.
Vahid Babaveisi, Farnaz Barzinpour, Ebrahim Teimoury,
Volume 31, Issue 1 (3-2020)
Abstract
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.
Seyed Mohammad Ghadirpour, Donya Rahmani, Ghorbanali Moslemipour,
Volume 31, Issue 2 (6-2020)
Abstract
It is indispensable that any manufacturing system is consistent with potential changes such as fluctuations in demand. The uncertainty also makes it more essential. Routing Flexibility (RF) is one of the necessities to any modern manufacturing system such as Flexible Manufacturing System (FMS). This paper suggests three mixed integer nonlinear programming models for the Unequal–Area Stochastic Dynamic Facility Layout Problems (UA–SDFLPs) by considering the Routing Flexibility. The models are proposed when the independent demands follow the random variable with the Poisson, Exponential, and Normal distributions. To validation of the proposed models, many small-sized test problems has solved that derived from a real case in literature. The large-sized test problems are solved by the Genetic Algorithm (GA) at a reasonable computational time. The obtained results indicate that the discussed models for the UA–SDFLPs are valid and the managers can take these models to the manufacturing floor to adapt to the potential changes in today's competitive market.
Parviz Fattahi, Mehdi Tanhatalab, Joerin Motavallian, Mehdi Karimi,
Volume 31, Issue 2 (6-2020)
Abstract
The present work addresses inventory-routing rescheduling problem (IRRP) that is needed when some minor changes happen in the time of execution of pre-planned scheduling of an inventory-routing problem (IRP). Due to the complexity of the process of departing from one pre-planned scheduling IRP to a rescheduling IRP, here a decision-support tool is devised to help the decision-maker. This complexity comes from the issue that changes in an agreed schedule including the used capacity of the vehicle, total distance and other factors that need a re-agreements negotiation which directly relates to the agreed costs especially when a carrier contractor is responsible for the distribution of goods between customers. From one side he wants to stick to the pre-planned scheduling and from the other side, changes in predicted data of problem at the time of execution need a new optimized solution. The proposed approached applies mathematical modeling for optimizing the rescheduled problem and offers a sensitivity analysis to study the influence of the different adjustment of variables (carried load, distance, …).
Mohammad Hasan Esmaili, Seyed Meysam Mousavi,
Volume 31, Issue 2 (6-2020)
Abstract
To demonstrate the importance of customer satisfaction can mention numbers of the service providers that attempt to differentiate themselves by satisfied their customers, witnessed high growth. In this paper, some factors that increase retailers and customers’ satisfaction, such as driver consistent services and delivering fresh products, are considered in a perishable inventory routing problem (PIRP) under possibility and necessity class of fuzzy uncertainty measures. In a typical inventory routing problem (IRP), a distribution center delivers products to a set of customers through a limited time horizon, and simultaneously makes a decision about inventory and routing to minimize the total cost. The proposed model is formulated as mixed-integer programming. Two types of consistent driver services are regarded for different kinds of customers, including particular and typical customers. To investigate the validity of the model, the problem is solved for two values of possibility and necessity measures.
Nima Hamta, Samira Rabiee,
Volume 32, Issue 3 (9-2021)
Abstract
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.
Elham Abutalebi, Masoud Rabbani,
Volume 33, Issue 2 (6-2022)
Abstract
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.
