Minimizing the sum of flow times with batching and delivery in a supply chain

Abstract

The aim of this thesis is to study one of the classical scheduling objectives that is of minimizing the sum of flow times, in the context of a supply chain network. We consider the situation that a supplier schedules a set of jobs for delivery in batches to several manufacturers, who in tum have to schedule and deliver jobs in batches to several customers. The individual problem from the viewpoint of supplier and manufacturers will be considered separately. The decision problem faced by the supplier is that of minimizing the sum of flow time and delivery cost of a set of jobs to be processed on a single machine for delivery in batches to manufacturers. The problem from the viewpoint of manufacturer is similar to the supplier's problem and the only difference is that the scheduling, batching and delivery decisions made by the supplier define a release date for each job, before which the manufacturer cannot start the processing of that job. Also a combined problem in the light of cooperation between the supplier and manufacturer will be considered. The objective of the combined problem is to find the best scheduling, batching, and delivery decisions that benefit the entire system including the supplier and manufacturer. Structural properties of each problem are investigated and used to devise a branch and bound solution scheme. Computational experience shows significant improvements over existing algorithms and also shows that cooperation between a supplier and a manufacturer reduces the total system cost of up to 12.35%, while theoretically the reduction of up to 20% can be achieved for special cases.