Integrated production-inventory-routing problem for multi-perishable products under uncertainty by meta-heuristic algorithms

The present study aims to introduce an integrated production-inventory-routing problem (PIRP) with a mixed-integer linear programming model, remarking a multi-perishable product, multi-period, and heterogeneous fleets with time windows in a distribution network. The objective of the proposed model is to maximise the total profit, which equals the selling revenue subtract the aggregation of the holding, production, transportation, and utility preference costs. At the production level, a multi-period production system with production capacity constraints is considered, in which the inventory at each stage of production is intended to compute the related holding costs and schedule more appropriate planning. The vehicle routing problem is tackled at the distribution level regarding vehicles with various capacities in a multi-period condition. Consequently, a fuzzy chance-constrained programming model is used to deal with fuzzy parameters. Furthermore, two evolutionary algorithms, namely a hybrid imperialist competitive algorithm (HICA) and self-adaptive differential evolution (SADE), are proposed to solve the given problem. Subsequently, several numerical examples with managerial insights are solved to evaluate the performances of the proposed algorithms and show their effectiveness and efficiency. Computational results demonstrate the superiority of the proposed algorithms for this problem. Finally, the applicability of the proposed algorithms is investigated by a real-case study.