Question

A manager receives a forecast for next year. Demand is projected to be 530 units for the first half of the year and 1,000 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., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carry 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

1 – 6 months

7 – 12 months

Order Size

units?

units?

Answer 1

a)

1 - 6 months period

Monthly demand, D = 530/6 = 88.3

Monthly holding cost, H = $ 2

Order cost, S = $ 55

Economic Order size = SQRT(2DS/H) = SQRT(2*88.3*55/2) = 70

7 - 12 months period

Monthly demand, D = 1000/6 = 167

Monthly holding cost, H = $ 2

Order cost, S = $ 55

Economic Order size = SQRT(2DS/H) = SQRT(2*167*55/2) = 96

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b)

1 - 6 months period

Total monthly cost of EOQ policy = (D/Q)*S + (Q/2)*H = (88.3/70)*55 + (70/2)*2 = $ 139.38

Total monthly cost of Q=50 policy = (88.3/50)*(55-10) + (50/2)*2 = $ 129.47

Total monthly cost of Q=100 policy = (88.3/100)*(55-10) + (100/2)*2 = $ 139.74

Total monthly cost of Q=150 policy = (88.3/150)*(55-10) + (150/2)*2 = $ 176.49

Total cost of order size 50 is the lowest. Therefore,an order size of 50 units is recommended in the first 6 months.

7 - 12 months period

Total monthly cost of EOQ policy = (D/Q)*S + (Q/2)*H = (167/96)*55 + (96/2)*2 = $ 191.68

Total monthly cost of Q=50 policy = (167/50)*(55-10) + (50/2)*2 = $ 200.3

Total monthly cost of Q=100 policy = (167/100)*(55-10) + (100/2)*2 = $ 175.15

Total monthly cost of Q=150 policy = (167/150)*(55-10) + (150/2)*2 = $ 200.1

Total cost of order size 100 is the lowest. Therefore,an order size of 100 units is recommended in the first 6 months.

Period	Order size
1 - 6 months	50 units
7 - 12 months	100 units