Investigating replenishment policies for centralised and decentralised supply chains using stochastic programming approach

In this paper, a multiple period replenishment problem based on (s, S) policy is investigated for a supply chain (SC) comprising one retailer and one manufacturer with uncertain demand. Novel mixed-integer linear programming (MILP) models are developed for centralised and decentralised decision-making modes using two-stage stochastic programming. To compare these decision-making modes, a Monte Carlo simulation is applied to the optimization models' policies. To deal with demand uncertainty, scenarios are generated using Latin Hypercube Sampling method and their number is reduced by a scenario reduction technique. In large test problems, where CPLEX solver is not able to reach an optimal solution in the centralised model, evolutionary strategies (ES) and imperialist competitive algorithm (ICA) are applied to find near optimal solutions. Sensitivity analysis is conducted to show the performance of the proposed mathematical models. Moreover, it is demonstrated that both ES and ICA provide acceptable solutions compared to the exact solutions of the MILP model. Finally, the main parameters affecting difference between profits of centralised and decentralised SCs are investigated using the simulation method.