A metal fabrication shop has a single punch press. There are currently three partsthat the shop has agreed to produce that require the press, and it appears that theywill be supplying these parts well into the future. You may assume that the press isthe critical resource for these parts, so that we need not worry about the interactionof the press with the other machines in the shop. The relevant information here isPart Annual Contracted Cost ProductionNumber Amount (demand) Setup Cost (per unit) Rate (per year)1 2,500 $80 $16 45,0002 5,500 120 18 40,0003 1,450 60 22 26,000Holding costs are based on an 18 percent annual interest rate, and the productsare to be produced in sequence on a rotation cycle. Setup times can be considerednegligible.a. What is the optimal time between setups for part number 1?b. What percentage of the time is the punch press idle, assuming an optimalrotation cycle policy?c. What are the optimal lot sizes of each part put through the press at an optimalsolution?d. What is the total annual cost of holding and setup for these items on the punchpress, assuming an optimal rotation cycle?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
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A metal fabrication shop has a single punch press. There are currently three parts
that the shop has agreed to produce that require the press, and it appears that they
will be supplying these parts well into the future. You may assume that the press is
the critical resource for these parts, so that we need not worry about the interaction
of the press with the other machines in the shop. The relevant information here is
Part Annual Contracted Cost Production
Number Amount (demand) Setup Cost (per unit) Rate (per year)
1 2,500 $80 $16 45,000
2 5,500 120 18 40,000
3 1,450 60 22 26,000
Holding costs are based on an 18 percent annual interest rate, and the products
are to be produced in sequence on a rotation cycle. Setup times can be considered
negligible.
a. What is the optimal time between setups for part number 1?
b. What percentage of the time is the punch press idle, assuming an optimal
rotation cycle policy?
c. What are the optimal lot sizes of each part put through the press at an optimal
solution?
d. What is the total annual cost of holding and setup for these items on the punch
press, assuming an optimal rotation cycle?

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