Distribution of finished goods from depots to predetermined customers and collection of goods and wastes are practical and challengeable optimization and logistics problems; therefore, appropriate management of transportation system can help companies decrease their costs and consequently earn more benefits. Several kinds of vehicle routing problems (VRPs) have been studied in the literature. In this paper, we will combine multi-depot vehicle routing problem (MDVRP) and close–open mixed vehicle routing problem (COMVRP), assuming that the fleet of vehicles is heterogeneous. Also, in this problem, contractors are used to meet a part of customers’ requirements. The objective of the problem is to minimize the total cost of serving customers. To efficiently deal with the problem, a new mixed integer programming (MIP) model as well as a new hybrid metaheuristic is proposed. Moreover, analytic hierarchical process is utilized in hybridization of the genetic algorithm. The computational experiments are conducted to compare the results of HGA, GA and MIP solver, CPLEX.

Industrial systems are constantly subject to random events with inevitable uncertainties in production factors, especially in processing times. Due to this stochastic nature, selecting appropriate dispatching rules has become a major issue in practical problems. However, previous research implies that using one dispatching rule does not necessarily yield an optimal schedule. Therefore, a new algorithm is proposed based on computer simulation and artificial neural networks (ANNs) to select the optimal dispatching rule for each machine from a set of rules in order to minimise the makespan in stochastic job shop scheduling problems (SJSSPs). The algorithm contributes to the previous work on job shop scheduling in three significant ways: (1) to the best of our knowledge it is the first time that an approach based on computer simulation and ANNs is proposed to select dispatching rules; (2) non-identical dispatching rules are considered for machines under stochastic environment; and (3) the algorithm is capable of finding the optimal solution of SJSSPs since it evaluates all possible solutions. The performance of the proposed algorithm is compared with computer simulation methods by replicating comprehensive simulation experiments. Extensive computational results for job shops with five and six machines indicate the superiority of the new algorithm compared to previous studies in the literature.