Tabu search and lower bounds for a combined production–transportation problem

In this paper we consider a combined production–transportation problem, where n jobs have to be processed on a single machine at a production site before they are delivered to a customer. At the production stage, for each job a release date is given; at the transportation stage, job delivery should be completed not later than a given due date. The transportation is done by m identical vehicles with limited capacity. It takes a constant time to deliver a batch of jobs to the customer. The objective is to find a feasible schedule minimizing the maximum lateness.After formulating the considered problem as a mixed integer linear program, we propose different methods to calculate lower bounds. Then we describe a tabu search algorithm which enumerates promising partial solutions for the production stage. Each partial solution is complemented with an optimal transportation schedule (calculated in polynomial time) achieving a coordinated solution to the combined production–transportation problem. Finally, we present results of computational experiments on randomly generated data.