Integrated production and outbound distribution scheduling problems with job release dates and deadlines

Abstract

In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP-NSD) problem, splittable production and non-splittable delivery (SP-NSD) problem and splittable production and delivery (SP-SD) problem. We provide a polynomial-time algorithm that solves two special cases of SP-NSD and SP-SD problems. Solving these problems allows us to compute a lower bound for the NP-hard problem NSP-NSD, which we use in a branch and bound (B&B) algorithm to solve problem NSP-NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver. keywords: single machine scheduling production and delivery release dates deadlines transportation costs branch and bound.