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This paper deals with the more realistic version of the lot sizing and scheduling problem where we have a single machine that process a number of different products and for each product we have a set of delivery dates and the quantities to deliver at each of these dates. The objective is to minimise the sum of setup costs and inventory holding costs including the holding cost of products from the finish time of each production lot to the next delivery date. In addition, a setup can be carried over from a production run to the immediately succeeding one if the same product is processed during these two runs. A mathematical formulation of this problem is given as well as two specially designed solution heuristics. As the literature does not provide any other method to solve this problem, only the results obtained by these two heuristics are compared.

Single-machine capacitated lot-sizing and scheduling with delivery dates and quantities