LO9-4 SOLVED PROBLEM 4 Consider the following data relevant to an MRP lot-sizing problem: Use the four lot-sizing rules in the chapter to propose an MRP schedule unaer each rule. Assume there is no beginning inventory. Solution Lot-for-Lot The lot-for-lot rule is very commonly used because it is so simple and intuitive. The planned-order quantities are equal to the net requirements each week. Economic Order Quantity We need D,S, and H in the EOQ formula. We will estimate annual demand based on average weekly demand over these 8 weeks. D= Annual demand = 8
105+80+130+50+0+200+125+100
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×52=5,135 H= Annual holding cost =0.208×$25.00=$5.20 S= Setup cost=$100 (given) EOQ= H
2DS
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= 5.20
2(5135)(100)
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=444 Seast. Totai Cost (LTC) Simalar to the cxample in Exhibit 9.16, we can create the following table comparing costs for oritering I through 8 weeks' demand in the first order. For the first order, the difference hetween holding and setup costs is least when ordering for weeks. I through 6 , so the first order should be for 565 units, enotgh for weeks 1−6. For the second order, We need to consider only weeks 7 and 8 . The difference between holding and setup costs is least when placing a second order to cover demand during weeks 7-8. so the second order should be for 225 units. Note that as we move through time and net requirements for weeks 9 and beyond become known, we would revisit the second order based on those new requirements. It is likely that the best second order will end up being for more than jus weeks 7 and 8 . For now, we can develop an order schedule based on the data we have available. Least Unit Cost (LUC) The LUC method uses calculations from the LTC method, dividing each option's total cost by the order quantity to determine a unit cost. Most of the following table is copicd from the LTC method, with one additional column to calculate the unit costs. first order would be for 365 units. (This example can be a bit tricky - we have to use a little common sense.) Ordering for weeks 1−4 has the same low unit cost because there is no demand for week 5 . We will say we are ordering for weeks 1-5 so that we don't place an unnecessary order in week 5 to cover demand for weeks 5-8. For the second order, the lowest unit cost comes from ordering for weeks 6-8, so we would plan for an order of 425 units. As with the LTC example, our second order might change as we learn net requirements for weeks 9 and beyond. Based on these orders, we can now davalion an order schedule based on LUC. Best Lot Size Method Based on the data we have available, the total costs for each lot-sizing method are lot-for-lot, $800.00; EOQ. $350.40; LTC, $359.00; and LUC, $281.50. The relatively high setup cost in this example makes lot-for-lot an unwise choice. LUC has the lowest total cost by a significant margin. It works so well here because it minimizes holding costs across the planning horizon.