Problem 13-7 20 A manager receives a forecast for next year. Demand is projected
ID: 3283790 • Letter: P
Question
Problem 13-7 20 A manager receives a forecast for next year. Demand is projected to be 540 units for the first half of second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order 225 points a. Assuming that monthly demand will be level during each of the six-month periods covered by the each of the first six months), determine an order month periods. (Round your answers to the nearest whole number.) size that will minimize the sum of ordering and carrying costs for each of the six- eBook 1-6months References-12 units units b. If the vendor 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 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 -6 months 7-12 months unitsExplanation / Answer
a) cumulative demand during first six months = D1 = 600 units
Cumulative demand during next six months= D2 = 900 units
Ordering cost ,Co= $55 per order
Six monthly unit holding cost, Ch= $2 *6 = $12
EOQ for first six months= sqrt(2*600*55/12)= 74.16 =74 units
EOQ for next six months= sqrt(2*900*55/12) = 90.8 =91 units
b) now, the processing cost is reduced to $45 but only if you order in multiples of 50 units. At first six months, EOQ = sqrt(2*600*45/12) = 67.02 = 67 units, but you can't actually order 67 units for $45. An order size of 100 may be worse than 67, but itsi better than 150. The optimal order size for $45 processing must be either 50 or 100, the option closest to 67.
EOQ for the next six months = sqrt(2*900*45/12)= 82.45 = 82 units.
At this point, we do not have to abandon the EOQ model. You have to actually calculate the total cost of order sizes 50 and 100 in order to find out which is better. And you have to calculate the total cost of order size 75 to find out whether the discount is worth taking or not.