artificial immune system for single machine scheduling and batching problem in supply chain

this paper addresses a production and outbound distribution scheduling problem in which a set of jobs have to be process on a single machine for delivery to customers or to other machines for further processing. we assume that there is a sufficient number of vehicles and the delivery costs is independent of batch size but it is dependent on each trip. in this paper, we present an artificial immune system (ais) for this problem. the objective is to minimize the sum of the total weighted number of tardy jobs and the batch delivery costs. a batch setup time has to be added before processing the first job in each batch. using computational test, we compare our method with an existing method for the mentioned problem in literature namely simulated annealing (sa). computational tests show the significant improvement of ais over the sa.