Integrated production scheduling and batch delivery with fixed departure times and inventory holding costs. Issue 20 (18th October 2017) - Agnetis, Alessandro; Aloulou, Mohamed Ali; Kovalyov, Mikhail Y.
Abstract : In this paper, we address a model for supply chain coordination. There are m manufacturers modelled as single machines, each of which processes a specific set of jobs (products). After processing is completed, jobs are batched, and batches are shipped to a customer by means of vehicles. The problem consists in concurrently finding a production schedule of the jobs, a partition of jobs into delivery batches and an assignment of delivery batches to vehicles, so that jobs are delivered within their deadlines and total costs are minimised. We focus on a scenario characterised by fixed departure times and inventory holding costs . For each departure time there is a given number of vehicles, possibly having limited capacity. Each job incurs a cost proportional to the time from job completion to delivery departure. In this paper, we show that the problem is NP-hard even for a very restricted case, and report various polynomiality results for two scenarios, namely: (i) when the production sequence of each manufacturer is fixed in advance, and (ii) when there is a single manufacturer and processing times are all equal to 1. We also point out several open problems.