Question

Problem 13-7 A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 930 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 (0.g.100 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 1 - 6 months 7 - 12 months Order Size units 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 6 months 7 - 12 months Order Size units units

Answer 1

Answer a= For period 1-6 months=

Demand =600/6=100 units

EOQ= (2*100*55/2)^0.5=74.16 units =74 units

For period 7-12 months=

Demand =930/6=155 units

EOQ= (2*155*55/2)^0.5=92.33 units =92 units

Answer b=

For period 1-6 months=

TC when the order is placed for 50 units = (100/50)*55+(50/2)*2 =160

TC when the order is placed for 100 units = (100/100)*55+(100/2)*2 =155

TC when the order is placed for 150 units = (100/150)*55+(150/2)*2 =186.67

So TC is less for 100 units so 100 units should be ordered.

For period 7-12 months=

TC when the order is placed for 50 units = (155/50)*55+(50/2)*2 =220.5

TC when the order is placed for 100 units = (155/100)*55+(100/2)*2 =185.25

TC when the order is placed for 150 units = (155/150)*55+(150/2)*2 =206.83

So TC is less for 100 units so 100 units should be ordered.