Random yield occurs if production processes are imperfect and therefore produce defective items. Examples for such imperfect production processes can be found in every industry. Consider for example the production of curved glass for Samsung's cell phones, where the company had to deal with low yield rates of 50 %, meaning that half of all products had to be scrapped. This exemplarily shows that production systems with random yield cannot be neglected and are highly relevant in increasingly complex production processes as well as under high competition and shorter product life cycles.
We consider a multi-stage production system where the input of the production system is determined by the order quantity. An order can be placed by the warehouse to replenish stock and be able to satisfy stochastic customer demands. Because the optimal ordering policy is known to be very complex, a common linear inflation policy is used. To make sure that only products meeting the quality requirements are stocked in the warehouse and afterwards sold to the customers, an error-free quality inspection is located after the production process, sorting out all defective items. Defective items are either disposed of and leave the production system or are reworked. If defective items are reworked, they have afterwards the same quality as items that were perfect when first produced. Therefore, reworked items also enter the warehouse and are sold to the customers without any price discount.
Different from most of the literature on make-to-stock production systems with random yield we consider positive production times during the production process because they are more realistic especially for highly sophisticated production systems as in the high-tech industry. Positive production times increase the complexity of the problem a lot because the decision maker in the warehouse has to place an order before knowing the exact amount of perfectly produced items leaving the production process in future periods.
We show how to set the policy parameters for such a multi-stage make-to-stock production system with random yield, positive lead times and either disposal or rework of defective items. Our approach requires low computation times even for larger production systems and leads to very good results.
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