Preemptive scheduling in a two-stage supply chain to minimize the makespan

Abstract

This paper deals with the problem of preemptive scheduling in a two-stage supply chain framework. The supply chain environment contains two stages: production and transportation. In the production stage n jobs are processed on a manufacturer's bounded serial batching machine, preemptions are allowed, and set-up time is required before a new batch is processed. In the transportation stage each batch is delivered to a customer by a single vehicle. The objective is to minimize the makespan by making decisions for both mutually coordinated stages. Specifically, two versions are studied. The first one is that all jobs are available to be processed at time zero, and the second one is that jobs have different release times. An O(n log n) time algorithm is developed for the first version, and we show that it can produce the optimal schedule for the entire problem. For the second version, based on some useful properties we have designed an O(n log n) time heuristic and a novel lower bound. The worst-case performance ratio of our algorithm is bounded by 2. Our computational study with random instances of different scales shows high-quality solutions for either small-scale or large-scale instances returned in a reasonable PC times.

A two-stage stochastic supply chain scheduling problem with production in cellular manufacturing environment: A case study

“…The objective function minimizes the total cost of production and distribution. Pei et al [39] discuss in the context of preemptive scheduling problem in a two-stage supply chain. The first stage is production stage where jobs are first divided into batches and then they process on a limited serial batching machine.…”

Preemptive scheduling with transportation delays between machines

“…Few works have addressed this concept in the literature and more specifically in the case of scheduling workshops on parallel machines. Often, one ignores the delay required for transporting the preempted jobs and assumes that the processing of the interrupted job can resume immediately on other machines (Pei et al, 2015;Liaw, 2016;Thevenin et al, 2017). Otherwise, the constraint of transportation delays has been considered in other types of scheduling workshops.…”