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# Calculating optimal production batch size

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1. Jim's Knives manufactures knives for a certain retail store. His skilled workers can produce 10 knives a day of their best-selling knife (known as Bowie knife). Their retail store sells an average of 5 knives per day. Jim's workers prefer to work on only one type of knife at any given time for efficiency reasons. They have estimated that changing from one type of knife to another cost \$100. Inventory cost for this knife has been estimated at \$10 per year per knife. Jim's Knives operate both their factory and retail store 250 days a year.

a. What batch size for the production of Bowie knives would you recommend to Jim?
b. What's the total annual cost of your recommendation?
c. How many production runs a year does the manufacturing plant need to satisfy demand?
d. How long an average batch of Bowie knives will last (in days)?

2. A nursery produces its own natural organic fertilizer which it sells mostly to gardeners and homeowners. The annual demand for fertilizer is 270,000 pounds. The company is able to produce 305,000 pounds annually. The cost to transport the fertilizer from plant to the nursery is \$170 per load. The annual carrying cost of the fertilizer is \$0.12 per pound.

a. Compute the optimal production size for the fertilizer
b. Compute the maximum inventory level
c. If the company can increase production capacity to 360,000 pounds per day, will it reduce total inventory costs? Support your answer with necessary calculations.

#### Solution Preview

1.

a. What batch size for the production of Bowie knives would you recommend to Jim?
We know that EPR=[(2*Q*S)/(C*(1-d/p))]^0.5
EPR = Optimal production size
Q = estimated annual quantity to be produced in units=5*250=1250
S = estimated cost of changing=\$100
C = estimated cost to carry one unit in stock for one year=\$10
d=daily demand=5
Daily production=p=10
EPR= [(2*1250*100)/(10*(1-5/10))]^0.5 =223.6068 or 224

b. What's the total annual cost of your recommendation?
Setting up ...

#### Solution Summary

There are two problems. Solutions to these problems provide methodology to calculate optimal batch size, cost and other inventory parameters.

\$2.19