The bare-bones differential evolutionary for stochastic joint replenishment with random number of imperfect items

Abstract

In e-business running, not only uncertainties in customers’ demands cause great risks from the marketing side, but also imperfect qualities of multi-item induce great losses at the supplying side. Hence, in this paper a joint replenishment problem (IJRP) simultaneously considering the stochastic demands and random number of imperfect items for the first time is proposed and a meta-heuristic, namely, bare-bones differential evolutionary (BBDE) algorithm is redesigned based on the solution structure containing the continuous variable and discrete variable to solve the IJRP problem. Through intensive numerical experiments, it has been testified that BBDE is not only superior to genetic evolution algorithm (GA) and particle swarm optimization (PSO) algorithm at the best-found TC, the lowest mean value, and the smallest standard error for three small tested JRPs (GJRP, SJRP and IJRP), but also a competitive algorithm to differential evolution (DE) and bare bones PSO (BBPSO) for three small scale JRPs (GJRP, SJRP and IJRP) at the aspects of finding the best-found TC, the lowest mean value, the smallest standard error and the least of computation time. BBDE also shows great efficiency in solving some large scale IJRPs comparing to DE and BBPSO, the limitation of BBDE for large scale IJRP is also reported and analyzed.