Minmizing service span with batch-position-based learning effects

We consider the learning effects in the coordination of production and outbound distribution for manufacturers. The objective is to minimize service span, which lasts from the beginning of production to the completion of delivery of products. In production, a batch-processing facility is used to process jobs which have different sizes. Batch-position-based learning effects are considered since workers become skillful gradually after processing batches one by one. In distribution, a vehicle with a fixed capacity is used to deliver products the customer and the transportation time from the manufacturer to the customer is a constant. We show the coordinated scheduling problem is NP-hard in the strong sense. We propose properties of optimal solutions and we provide an approximation algorithm for the problem. The absolute performance guarantee of the algorithm is 1.667 and the asymptotic performance guarantee is 1.223. Then we consider the problem where there are infinite vehicles and the performance guarantees are respectively 1.5 and 1.223. Finally we analyze the performance of the algorithm by the change of the problem scale, the learning index and operational factors. We propose managerial suggestions for decision makers of manufacturers according to our results.