Lot-sizing and scheduling problem with earliness and tardiness penalties

Production planning and scheduling is one of the most challenging tasks facing managers today. For those companies that produce products in batches or lots (for example, plastic injection, steel making, or chemical producing companies), planning production lot-sizes for the finished products and deciding when to process them are two important problems requiring careful analysis. These can be termed the lot-sizing and scheduling problem. In traditional lot sizing and scheduling models, the production lot-sizes and their schedules should be made such that all orders (demands) are satisfied on time (no backorder) and the sum of the total setup cost and total holding cost are minimized.; Currently, several researches have studied the scheduling problem under the Just-In-Time (JIT) philosophy. With the JIT concept, customers are unwilling to receive early or tardy shipments. A well known scheduling model involving the JIT concept is the earliness/tardiness (E/T) scheduling problem. The objective is to determine the job schedule to minimize the sum of earliness and tardiness penalties. In the general E/T problem, the lot-sizing decision is not considered.; The problem considered in this dissertation is to relax the assumption of no backorder and apply the concept of the E/T problem to the lot-sizing and scheduling problem. This problem will be called the earliness tardiness lot-sizing and scheduling (ETLS) problem. In the ETLS problem, there are n orders of either the same or different products to be processed. The production is accomplished in lots, which is the manufacturing of the same product continuously. A setup is required before the production of a new lot of different products starts. Any orders finished before the due dates must be held by the manufacturer in order to be delivered on their due dates and, therefore, will incur the holding costs. On the other hand, any orders finished after the due dates will incur the tardy costs and require immediate delivery after their productions are completed. The problem objective is to determine the production lot sizes and their schedules such that the sum of the total setup cost, total holding cost and total tardy cost is minimized.