Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

Abstract In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup and configuration selection are considered simultaneously. More precisely, works under set configurations requires times to switch from one another. Also, time job is function its position configuration. The objective find sequence jobs choose process each minimize makespan. We first show that proposed can be formulated through two-stage multi-stage Stochastic Programming models, challenging computational point view. Then, by looking at as dynamic random decision process, new deterministic approximation-based formulation developed. method derives mixed-integer non-linear model based concept accessibility all possible available alternatives stage decision-making process. efficiently solve problem, measure defined convert into search shortest path throughout stages. Extensive experiments carried out various sets instances. discuss compare results found resolution plain models with those obtained approximation approach. Our shows excellent performances both terms solution accuracy time.