To reduce the environmental Pollution emissions caused by market activities, cold chain logistics companies also considered the emission of harmful gases for better service in satisfying customers’ demands. In the cold supply chain, goods are supplied and distributed that become corrupt and degraded over time. Therefore, to keep such goods fresh, the temperature must be constantly and continuously controlled, which in turn requires more fuel consumption. Also, in vehicle routing problem, the travel time of a route and fuel consumption does not only depend on the distance traveled, but also on the speed and time of day when that route is traveled. In this study, a new mixed-integer optimization model of the vehicle routing problem in a cold supply chain concerning congestion is presented with the aim is to minimize costs of Pollution emissions. In this model, in addition to the cost of the environmental Pollution emissions, other costs are considered, including the vehicle operating cost, transportation, loss of quality, product freshness, and penalty cost for arriving outside the customer's time window. In continuing, a solution method based on Benders decomposition is applied to solve the proposed model for large size networks. The computational results showed that the presented model provides the optimal route and travel time of the vehicle by considering the reduction of pollution and the appropriate speed. Also, the implementation of the solution algorithm on several test instances with different sizes showed the efficiency of the algorithm in reducing the solution time and obtaining a good solution.

What has initiated the idea of this research is the situation of marine, rail and road transportations in the south region of Iran, the Persian Gulf and Oman see. There are a few large Iranian ports in the region (e.g. Imam Khomeini and Shahid Rajaee) that have been equipped to serve large containerships while, most of the other ports either have not been developed or their geographical and topological restrictions do not let them to serve large ships. For instance, Abadan and Khorramshahr were two active ports and main Iranian Import/Export terminals until the Iraqi army attacked them in 1981. Although, the war finished in 1989, nowadays these are unable to serve current fleet of large container ships due to the limitation of their water way, the Arvand- River. Therefore, their rail and road transportation systems' capacity are mostly unused. On the other hand, due to the national economic development programs and the especial attention to the Iranian 20 year's economic vision, Iran needs to develop continuously new transportation capacities as well as better utilization of the existing capacities. To develop the transportation capacity, one way is to invest on the existing ports in order to serve larger ships. However, in one hand, the investment should continuously grow because, as the literature shows, mega-ships and rapidships are going to emerge until the year 2020. On the other hand, some of the ports, due to their geographical situation, are not able to catch any share of those investments. Therefore, we need to find a way to activate the small ports to use their capacities.

In this research, author reviews references related to the topic of multi-criterion (goal programming, multiple objective linear and nonlinear programming, bi-criterion programming, Multi-Attribute Decision-Making, Compromise Programming, Surrogate Worth Trade-off Method) and various versions of vehicle routing problem (VRP), Multi-Depot VRP (MDVRP), VRP with time windows (VRPWTW), Stochastic VRP (SVRP), Capacitated VRP (CVRP), Fuzzy VRP (FVRP), Location VRP (LVRP), Backhauling VRP (BHVRP), Facility Location VRP (FLVRP), and Inventory control VRP (ICVRP). Although VRP is a research area with rich research works and powerful researchers, only 81 articles are found that relate various vehicle routing type problems with various multiple objectives techniques. This author found that there is no research done in some areas of VRP (i.e., FVRP, ICVRP, LRP and CVRP). It is interesting to see that this research area was completely unattractive to master students (with zero research reported) and somewhat attractive to doctoral students (with 6 researches reported). Among the many multi-criterion programming techniques available, only three of them (goal programming, bi-criterion programming, linear and nonlinear multi-objective programming) are being employed to solve the problem.

In this paper we describe the distribution problems faced by one of the largest retailers ‎in the distribution and sale of fast moving consumer goods in the U.K. The paper ‎describes an initial solution method, which is then improved by a novel form of ‎simulated annealing. A computational experiment for the improvement algorithm has ‎been also carried out in order to illustrate the flexibility of the computer programming ‎and to demonstrate how it can be used to address broader management issues‏.‏

Transportation plays a key role in economic, production and service provider systems and has a high effect in GNP scale of each country. Therefore, researchers try to omit the unnecessary paths in order to minimize the traversed links in the network. On the other hand, distribution is an important issue in production industry because it has been estimated that 20 percent of final price is spent on transportation. Improving the distribution system of each company leads the higher productivity. Vehicle Routing Problem (VRP) tries to improve the distribution system. In this paper, demand of customer is considered as a fuzzy variable and transportation time between nodes is also assumed to have a probability distribution. Due to the complexity of the model, a new multi-objective Imperialist Competitive Algorithm (MOICA) is developed for obtaining Pareto optimal solutions. The performance of the proposed solution algorithm is compared with that of two well-known meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES). Computational results show that MOICA outperforms the other meta-heuristics.

The problem of designing a set of routes with minimum cost to serve a collection of customers with a fleet of vehicles is a fundamental challenge when the number of customers to be dropped or picked up is not known during the planning horizon. The purpose of this paper is to develop a vehicle routing Problem (VRP) model that addresses stochastic simultaneous pickup and delivery in the urban public transport systems of Addis Ababa city Bus Enterprise, in Ethiopia. To this effect, a mathematical model is developed and fitted with real data collected from Anbessa City Bus Service Enterprise (ACBSE) and solved using Clark-Wright saving algorithm. The form-to-distance is computed from the data collected from Google Earth and the passenger data from the ACBSE. The findings of the study show that the model is feasible and showed an improvement as compared to the current performances of the enterprise. It showed an improvement on the current number of routes (number of buses used) and the total kilometer covered. The average performances of the model show that on average 6.48 routes are required to serve passenger demands of 271 and on average the simulation run was performed with 0.40 seconds of CPU time. During this instance, the average distance traveled by the vehicles in a single trip is 552.92kms.

Since precise assignment of vehicles to the routs in supply chain network has a great effect on the important results such as cost reduction, on time delivery of the products or services, and customer satisfaction indexes (CSI), the Vehicle Routing Problem (VRP) is one of the most important problems in the supply chain management. For the complexity of this problem in real world, researchers usually ignore some real conditions and restriction in modelling and solving this problem. In this paper, the Vehicle Routing Problem (VRP) considering real conditions, such as vehicle capacity and restriction for vehicles with their movement in some routes, is studied. At first, the literature review and past studies are presented. Then, the considered problem will be illustrated completely and its parameters and variables will be defined. After that, the mathematical model of the problem is presented considering restriction for movement of the vehicles. This mathematical model will be coded in GAMS software; because this problem is known as an NP-Hard problem, the mathematical model of the problem is solved just for the small-sized problems. A new model is also presented for the medium-and large-sized problems based on ant colony (AC). The parameters of the ant colony are adjusted well in order to increase the efficiency of the algorithm. Finally, some diversity test problems are designed considering the important and effective parameters. These test problems are solved in order to evaluate the efficiency of the proposed algorithm, and the result shows that the proposed algorithm has a good performance in solving the test problems. Performance of the proposed algorithm is also compared with two power algorithms tabou search (TA) and genetic algorithm (GA) in solving the test problems. Results show that the proposed algorithm has better performance both in optimality and running time comparison of two other algorithms.

In this paper an integrated production and outbound distribution scheduling (IPODS) with vehicle routing problem (VRP) for multi customer situation in a supply chain is addressed. There are K orders (jobs) that have to be scheduled on a single machine and delivered to K customers. Each order has its own due date. The manufacturer delivers the orders in batches which have no capacity constraint. Delivering the products in batches reduces the delivery cost but it may increase the number of tardy jobs. No other research has been conducted on this problem yet. This problem is strongly NP-Hard. The objective is to minimize the sum of the total weighted number of tardy jobs and delivery costs. Also, in this paper, an MILP model and a Heuristic Algorithm (HA) for solving this problem are presented. Full factorial Computational test is performed for evaluation of these two methods. The obtained results on 3840 problems show that the heuristic algorithm is efficient for solved problem. Also we surveyed parameter's levels effect on CPLEX and heuristic performance by analysis of variance.