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Part A

The Wingate Manufacturing Company experiences a mean usage of 460 motor castings during the reorder lead-time. The standard deviation of usage during this period is 160 castings.

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Part A

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  1. The Wingate Manufacturing Company experiences a mean usage of 460 motor castings during the reorder lead-time. The standard deviation of usage during this period is 160 castings. • A.) If the usage is normally distributed, what percentage of order cycles will Wingate experience stockouts if it maintains a safety stock of 240 castings? • B.) Suppose that Wingate wants to ensure that they experience a stockout during no more that 5% of the order cycles. What reorder point would be necessary to achieve this goal?

  2. Part A • Since the standard deviation of demand during the lead time period is 160 units, a safety stock of 240 units represents 240/160 = 1.5 standard deviations. From the normal table (Appendix E) 1.5 standard deviations corresponds to a 93.3% probability of not stocking out so there is a (100%-93.3%) = 6.7% probability of a stockout. Therefore we would expect this percentage of order cycles to incur a stockout.

  3. Part B • From Appendix E, 95% service probability requires 1.65 standard deviations (z). Therefore, the required reorder point is: • R = 460 + 1.65(160) = 724 units

  4. Price-Break Example 2

  5. Price-Break Example 2 – Cont’d Interval from 650 & more, the Qopt value is not feasible. Interval from 350 - 649, the Qopt value is not feasible. Interval from 50 - 349, the Qopt value is feasible. So, we only need consider 3 options: order 67 units, order 350 units, or order 650 units

  6. Total cost curves if any quantity could be ordered at each price C = 200 C = 199 C = 198 C = 197 EOQ = 67 EOQ = 67 EOQ = 68

  7. Actual total cost curve Q = 650 Q = 67 Q = 350 C = 200 C = 199 C = 198 C = 197

  8. Price-Break Example 2 – Cont’d TC(67)= (9000*199)+(9000/67)*25+(67/2)*(0.5*199) = $1,797,691 TC(350)= (9000*198) + (9000/350)*25 + (350/2)*(0.5*198) = $1,799,968 TC(650)= (9000*197) + (9000/650)*25 + (650/2)*(0.5*197) = $1,805,359 So Qopt = 67

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