Problem space search metaheuristics with fix and optimize approach for the integrated fleet sizing and replenishment planning problem

The aim of the current study is to put forward a new metaheuristic method for the problem of vehicle fleet dimensioning and shipment schedule planning. The problem includes making decisions on both the configuration of a fleet for serving customers with a single product and the replenishment schedules according to a set of given candidate delivery frequencies. The problem combines two significant logistical issues specifically fleet sizing and replenishment planning. The principal idea of the model is to minimize all the relevant costs which covers the costs related to vehicle ownership, inventory, and routing. We bring forward two versions of a Problem Space Search metaheuristic that apply fix and optimize heuristic repeatedly. The metaheuristics rely on both perturbing data and the sequence of subproblems generated in the fix and optimize algorithm. The novel metaheuristic techniques developed in the current study exhibit significant efficacy compared to existing studies on a group of non-small randomly generated instances. Results show that there is a noticeable decrease in the gaps from optimal/ best bounds taken from CPLEX and solution duration compared to previously employed solution technique.