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Crawford Manufacturing: Provide the low cost production plan. Should you change your backorder policy?

Crawford Manufacturing is preparing their monthly production plan for one of their major product lines for the next year and requested assistance in determining possible plans of action.

Crawford has provided us with the following information. There are a maximum of 7500 regular time hours available per month. Overtime production can be used, but is limited to 20% of the scheduled regular time production in each month. Productivity is 1 unit / 145 minutes. Regular time production cost is $20.00/hour, overtime production cost is $30.00/hour, inventory carrying cost is $4/unit/month calculated on ending inventory each month. They will begin the year with an inventory of 100 units and they require an ending inventory of 250 units at the end of month 12. You must shut the production line down for 2 weeks (assume this is 1/2 month) for routine maintenance in either month 6 or 7. Current policy states that backorders are not allowed.

The demand for next year is presented in the table.

Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand
(units) 3250 3000 3500 3850 3500 3750 3125 3500 3100 3000 2850 2750

At a minimum address the following issues in your memo:

- Provide the low cost production plan. This plan should include the ½ month shutdown in either month 6 or 7.
- The HR and IT departments have estimated that it would cost $5.00 per item to process a backorder and you can process no more than 500 each month. Should you change your backorder policy?

Hint: Do not use integer constraints or conditional statements (if, max, etc.) in any models. Without considering the maintenance shutdown the minimum cost for the base problem is $1,964,292.

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Regular time hours available 7500 hours
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