A manager receives a forecast for next year. Demand is projected to be 528 units
ID: 326387 • Letter: A
Question
A manager receives a forecast for next year. Demand is projected to be 528 units for the first half of the year and 960 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.
a. Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 88 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.)
Period Order Size
1 – 6 months units
7 – 12 months units
b. If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? (Round intermediate calculations to 2 decimal places.)
Period Order Size
1 – 6 months units
7 – 12 months units
Explanation / Answer
a1- 6-month demand, D = 528 units
Ordering cost, S= $55
Holding cost for a unit for 6 month= $2*6=$12
Optimal oder quantity= ? ((2*528*55)/12)=? 4840= 70
7= Annual demand, D = 528+960=1488
Ordering cost, S= $55
Holding cost for a unit for 1 year = $2*12=$24
Optimal oder quantity= ? ((2*1488*55)/24)=? 6820= 83
b- When there will be $10, discount per order, ordering cost will be $55-$10= $45
6 months optimal order= ? ((2*528*45)/12)=? 3960= 62.92
12months optimal order= ? ((2*1488*45)/24)=? 5580= 74.70
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