Production lot sizing with a secondary outsourcing facility

An extended economic production quantity (EPQ) model under stochastic demand is investigated in this paper, where a fixed lot sizing policy is implemented to reduce the complexity of production planning and inventory control, and outsourcing with a secondary facility is used to supplement the lot sizing policy and to cope with the random demand. The considered cost includes: setup cost for the batch production, inventory carrying cost, backorder cost when the demand cannot be met immediately during the production period, and outsourcing cost when the total demand is greater than the lot size in one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex. Extensive computational tests have illustrated that the average cost reduction of the proposed model is significant when compared with that of the classical lot sizing policy. Significant cost savings can be achieved by deploying the production lot sizing policy with an outsourcing strategy when the mean demand rate is high.