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**Unformatted text preview: **Department of Industrial Engineering & Operations Research IEOR150 Production System Analysis Sampe Final Exam Fall 2010 Name: Grade: 1. A retailer buys a product and sell it to a local market. The unit purchasing cost is $15 and the per order ordering cost is $50. Inventory holding costs are based on a 30% annual interest rate. The monthly demand for the product follows a normal distribution with mean 1800 and standard deviation 400. Order lead time is assumed to be 2 months. If a demand is not fulfilled when it realizes, it is back-ordered. The shortage cost assessed for each back-ordered demand is $40. Suppose the retailer decides to ignore demand uncertainty and use the EOQ quantity as the order quantity. Determine the optimal values of the order quantity and the reorder level to minimize the expected annual total holding, ordering, and shortage cost. Then determine the safety stock level and the expected annual shortage cost. 2. A factory produces a product at a rate of 1,000 units per day. Annual demand for the product is 120,000 units per year. The fixed setup cost for a production run is $3,000 and the variable cost of production is $16 per unit. The company uses a 25% annual interest rate to calculate the holding cost. Assume that there are 250 working days in a year and demand does not occur during off days. (a) Determine the optimal production quantity in each production run. 1 (b) Determine the proportion of uptime and downtime in a production cycle. (c) Determine the annual holding cost and the annual setup cost. 3. A factory purchases a raw material from a supplier. It uses this material to produce a product, which is demanded at a constant rate of 5000 per month. The supplier offers the following all-unit discount: $25 per unit if the order size is no greater than 2000, $23 if at least 2000 and no greater than 4000, and $22 if at least 4000. The factory pays the shipping cost, whichand no greater than 4000, and $22 if at least 4000....

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