A widget manufacturer builds widgets and sells them direct to customers online.
ID: 345032 • Letter: A
Question
A widget manufacturer builds widgets and sells them direct to customers online. The production manager wishes to optimize the inventory costs. The annual demand for widgets is 3,600 and the plant works 240 days per year. The plant can produce widgets at a rate of 20 per day. The cost to prepare the equipment to start a production run is $5 and the annual inventory carrying cost is $0.90 per year.
2. What should be the optimum quantity of widgets to produce?
3. What is the maximum inventory achieved during a production run?
4. How many production runs are needed to meet the annual demand?
5. What is the average inventory of widgets?
6. What is the total annual cost of producing and storing the company’s widgets?
Explanation / Answer
Given are following data:
Annual demand = D = 3600
Daily demand for the plant = d = 3600 / 240 = 15
Daily production capacity = p = 20
Cost of production set up = Cs = $5
Inventory carrying cost = Ch = $0.90 per unit per year
= Square root ( 2 x Cs x D / Ch x ( 1 – d/p))
= Square root ( 2 x 5 x 3600 / 0.90 x ( 1 – 15/20))
= square root ( 2 x 5 x 3600/ 0.90 x 0.25)
= 400
OPTIMUM QUANTITY OF WIDGETS ( EPQ ) TO PRODUCE = 400
= EPQ X ( 1 – d/p)
= 400 x ( 1 – 15/20)
= 400 x 0.25
= 100
MAXIMUM INVENTORY ACHIEVED DURING A PRODUCTION RUN = 100
= D/EPQ
= 3600 /400
= 9
NUMBER OF PRODUCTION RUN NEEDED TO MEET ANNUAL DEMAND = 9
AVERAGE INVENTORY OF WIDGETS = 50
Annual storage cost ( inventory carrying cost ) = Annual unit inventory carrying cost x Average inventory = $0.90 x 50 = $45
Total annual cost of producing and storing the company’s widgets = $45 + $45 = $90
TOTAL ANNUAL COST OF PRODUCING AND STORING THE COMPANY’S WIDGETS = $90
OPTIMUM QUANTITY OF WIDGETS ( EPQ ) TO PRODUCE = 400
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