A particle swarm optimization approach for constraint joint single buyer-single vendor inventory problem with changeable lead time and (r,Q) policy in supply chain

In this paper, the chance-constraint joint single vendor-single buyer inventory problem is considered in which the demand is stochastic and the lead time is assumed to vary linearly with respect to the lot size. The shortage in combination of back order and lost sale is considered and the demand follows a uniform distribution. The order should be placed in multiple of packets, the service rate limitation on each product is considered a chance constraint, and there is a limited budget for the buyer to purchase the products. The goal is to determine the re-order point and the order quantity of each product such that the chain total cost is minimized. The model of this problem is shown to be an integer nonlinear programming type and in order to solve it, a particle swarm optimization (PSO) approach is used. To assess the efficiency of the proposed algorithm, the model is solved using both genetic algorithm and simulated annealing approaches as well. The results of the comparisons by a numerical example, in which a sensitivity analysis on the model parameters is also performed, show that the proposed PSO algorithm performs better than the other two methods in terms of the total supply chain costs.