Multi-Item Lot-Sizing With Joint Set-Up Costs

In this paper, the authors consider a multi-item lot-sizing discrete time problem in which production takes place in (a possibly limited number of) mixed batches of constant capacity. Apart from the usual unit storage and production costs, there is a fixed cost per batch representing the use of limited capacity resources. An alternative interpretation involves a warehouse/retailer and decisions on the use of trucks of a given capacity to ship from the warehouse so as to (possibly) stock items and satisfy demand forecasts at the retailer.