A manager receives a forecast for next year. Demand is projected to be 580 units

Question

A manager receives a forecast for next year. Demand is projected to be 580 units for the first half of the year and 950 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.

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 carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.)

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.)

A manager receives a forecast for next year. Demand is projected to be 580 units for the first half of the year and 950 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.

Explanation / Answer

a)

For first six months,

Ordering size = sqrt((2*D*S)/H)

D - Total Demand for period

S- Set up cost or cost per order

H - Inventory holding cost

Q= sqrt((2*580*55)/2) = 178.6 = 179(rounding off)

For next 6 months

Q= sqrt((2*950*55)/2) = 228.6 = 229( rounding off)

Therefore

b)

For period 1 - 6months

Total cost when 179 units are ordered would be = (580/179)*55+(179/2)*2 = $ 357.21

Total cost when 100 units are ordered = (580/100)*45+(100/2)*2 = $361

Total cost when 150 units are ordered = (580/150)*45 +(150/2)*2 = $324

Total cost when 200 units are ordered = (580/200)*45 +(200/2)*2 = $330.5

The cost is lowest when order size is 150 units

For period 1 , I would advise manager to take this offer with an order size of 150 units

>> For period 7 -12 months,

Total cost when 229 units are ordered = (950/229)*55+(229/2)*2 = $ 457.16

Total cost when 150 units are ordered = (950/150)*45+(150/2)*2 = $435

Total cost when 200 units are ordered =(950/200)*45+(200/2)*2 = $413.75

Total cost when 250 units are ordered = (950/250)*45 +(250/2)*2 = $ 421

The total cost is least when 200 units are ordered

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