Integrated production scheduling and vehicle routing problem with energy efficient strategies: Mathematical formulation and metaheuristic algorithms

This paper addresses integrated production and distribution scheduling problem in which orders/jobs are undergone a single operation on any one of the identical machines in parallel and upon the completion of the production they are distributed to destined customers by limited number of vehicles. Customers located in dispersed regions place their orders with predetermined demand size and time windows. On production side, machines operate under discrete speed modes, low of which requires less energy cost or vice versa. On distribution side, energy consumed by a vehicle varies depending on the size of load on it. Therefore, objective is minimizing the sum of the weighted cost emanating from early and tardy deliveries plus production and distribution costs. Operational decisions for (i) production are to determine the allocation of jobs to the machines and sequence of jobs on any machine as well as speed mode of each machine for a particular job. As for (ii) distribution: We need to decide vehicle assignment to specific subset of consolidated jobs and the sequence of customer visitation for each vehicle. We develop a formulation for the problem at hand involving parallel machine scheduling and vehicle routing to obtain solutions to optimality. Not surprisingly, however, CPLEX only provides optimum solution for all instances with customer number up to and 6, for which reason we present two metaheuristics, namely Memetic Algorithm (MA) and Iterated Local Search (ILS) for practical sized instances. Computational results indicate that ILS yields better solutions in shorter times as compared to its counterpart.