A manager receives a forecast for next year. Demand is projected to be 590 units
ID: 462057 • Letter: A
Question
A manager receives a forecast for next year. Demand is projected to be 590 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., 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 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?
Period Order Size1 – 6 months units 7 – 12 months units
Explanation / Answer
1st 6 months Quantity, Q = 590
Holding cost for 6 months = Monthly holding cost x 6 = 2x6 = $ 12
Cost per order = $ 55
EOQ, Q = [(2 × Quantity × Cost Per Order )/ Holding cost]
EOQ, Q = [(2 × 590 × 55 )/ 12] = 73.54 , rounding off 74
EOQ = 74.
No.of orders = Total demand/74 = 7.9, rounding off 8
No.of orders = 8
Considering equal demand every month, = 590/6 months = 99
Total cost for 6 months = order cost+holding cost = 738.
Since the demand is equal, the ordering can also be equal, working on this scenario,
The Total cost here is only $ 330
For next 6 months,
EOQ, Q = [(2 × Quantity × Cost Per Order )/ Holding cost]
EOQ, Q = [(2 × 960 × 55 )/ 12] = , rounding off
EOQ = 94
The Total cost incurred is $ 330
1-6 months - 99 units per month
7-8 - 160 units per month
b)
Ordering in 100's for the 4 months will give discount, increasing it to 5 months will incure more holding cost.
Hence ordering in multiples od 50 is good for the 1-6 months.
But for the next 6 months, ordering in multiples of 50 is not benificial as it will increase the holding cost.
Month No.of orders Quantity Equal Demand Inventory order cost Holding cost Jan 1 148 99 49 55 98 Feb 2 74 99 24 110 48 Mar 1 74 98 0 55 0 Apr 2 148 98 50 110 100 May 1 74 98 26 55 52 Jun 1 72 98 0 55 0 590 590 440 298Related Questions
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