Job sequencing and inventory control for a parallel machine problem: a hybrid-GA approach

In general, scheduling and sequencing problems are very difficult to solve to optimality (i.e., most problems are NP-Complete). In some instances, machines produce batch quantities of products which are placed in inventories. Demands are allocated directly from these inventories if available. If current inventory levels can not satisfy the demands and associated due dates, outsourcing some of the product, generally at a premium price offers a way to meet all due dates. Scheduling to meet due-dates coupled with inventory control is an important and more complex problem than the general scheduling problem. One application arises in furniture manufacturing where the lumber used to make furniture must first be dried from green lumber in a series of parallel batch machines (kilns). Drying lumber in-house is less expensive than purchasing commercially kiln-dried lumber. Therefore, the objective is to minimize the sum of the costs of drying lumber in-house and purchasing kiln-dried lumber in order to meet all due-dates plus any inventory carrying costs incurred over the planning horizon. The problem is decomposed into two sub problems: (1) the sequencing of the product types (lumber) on the machines (kilns); and (2) the allocation of inventory to satisfy the demands. A hybrid genetic algorithm determines the best sequence of product types to produce and an embedded linear program determines the optimal allocation of inventory and quantity of outsourced lumber that minimizes total cost. The hybrid algorithm is shown to be effective at solving the problem.