The XYZ MANUFACTURING COMPANY has received an order to supply one item of a particular type. However, the customer has specified such stringent quality requirements that the manufacturer may have to produce more than one item to obtain an item that is acceptable. The number of extra items produced in a production run is called the reject allowance. Including a reject allowance is common practice when producing for a custom order and it seems advisable in this case. The manufacturer estimates that each item of this type that is produced will be acceptable with probability 1/3 and defective (without possibility for rework) with probability 2/3. Marginal production costs for this product are estimated to be $200 per item (even if defective), and excess items are worthless. In addition, a setup cost of $300 must be incurred whenever the production process is set up for this product, and a completely new setup at this same cost is required for each subsequent production run if a lengthy inspection procedure reveals that a completed lot has not yielded an acceptable item. The manufacturer has time to make no more than three production runs. If an acceptable item has not been obtained by the end of the third production run, the cost to the manufacturer in lost sales income and penalty costs will be $1,800. Use dynamic programming to determine the policy regarding the lot size (1 + reject allowance) for the required production run(s) that minimizes total expected cost for the manufacturer. The XYZ MANUFACTURING COMPANY has received an order to supply one item of a particular type. However, the customer has specified such stringent quality requirements that the manufacturer may have to produce more than one item to obtain an item that is acceptable. The number of extra items produced in a production run is called the reject allowance. Including a reject allowance is common practice when producing for a custom order and it seems advisable in this case. The manufacturer estimates that each item of this type that is produced will be acceptable with probability 1/3 and defective (without possibility for rework) with probability 2/3. Marginal production costs for this product are estimated to be $200 per item (even if defective), and excess items are worthless. In addition, a setup cost of $300 must be incurred whenever the production process is set up for this product, and a completely new setup at this same cost is required for each subsequent production run if a lengthy inspection procedure reveals that a completed lot has not yielded an acceptable item. The manufacturer has time to make no more than three production runs. If an acceptable item has not been obtained by the end of the third production run, the cost to the manufacturer in lost sales income and penalty costs will be $1,800. Use dynamic programming to determine the policy regarding the lot size (1 + reject allowance) for the required production run(s) that minimizes total expected cost for the manufacturer
