All-Star Bat Manufacturing, Inc. supplies baseball bats to major and minor leagu

Question

All-Star Bat Manufacturing, Inc. supplies baseball bats to major and minor league baseball teams. After an initial order in January, demand over the six-month baseball season is approximately constant at 1000 bats per month. Assuming that the bat production process can handle up to 4000 bats per month, the bat production setup costs are $150 per setup, the production costs is $10 per bat, and the holding costs have a monthly rate of 2%, what production lot size would you recommend to meet the demand during the baseball season? If All-Star operates 20 days per month, how often will the production process operate, and what is the length of a production run? This is a production lot size model. However, the operation is only six months rather than a full year. The basis for analysis may be for periods of one month, 6 months, or a full year. The inventory policy will be the same. In your analysis use a monthly basis.

Explanation / Answer

As proposed, the analysis is being done on monthly basis.

Given are the following data :

Monthly demand = D = 1000 bats

Daily demand of bats = d = 1000/ 20 days per month = 50 bats

Daily production of bats = p = 4000/ 20 days per month = 200 bats

Production set up cost = Cs = $150

Monthly unit holding rate = Ch = 2% of $10 per bat = $0.2

Therefore economic production lot size ( EPQ )

= Square root ( 2 x Cs x D / Ch x ( 1 – d/p) )

= Square root ( 2 x 150 x 1000 / 0.2 x ( 1 – 50/200) )

= Square root ( 2 x 150 x 1000 / 0.2 x 0.75 )

= 1414.21 ( 1414 rounded to nearest whole number )

PRODUCTION LOT SIZE = 1414 BATS

Duration of production run = EPQ/ daily production capacity = 1414/200 = 7.07 days

Total demand for 6 months = 1000 x 6 = 6000

Therefore , number of production runs = 6000/1414 = 4.243

THERE WILL BE TOTAL 4.243 NUMBER OF PRODUCTION RUNS IN 6 MONTHS

DURATION OF EACH PRODUCTION RUN = 7.07 DAYS

PRODUCTION LOT SIZE = 1414 BATS

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