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**No Backlogging Problem # 1(pg.104) October 20,2011**

Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan Gutierrez

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**Outline Problem Statement Problem Summary Assumptions Formulation**

Constraints Input Values Solutions Sensitivity Analysis Report to Manager

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Problem Statement A customer requires during the next four months, respectively, 50, 65, 100, and 70 units of a commodity (no backlogging is allowed). Production costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 could be sold for $6. Formulate an LP that will minimize the net cost incurred in meeting the demands of the next four months.

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**Problem Summary 1 $5 50 2 $8 65 3 $4 100 4 $7 70 Month**

Cost of Production/Unit Demand 1 $5 50 2 $8 65 3 $4 100 4 $7 70

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**Assumptions No inventory at beginning of month Unlimited capacity**

Other costs in production were ignored

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Formulation Xt = number of commodities produced each month during month t it = number of commodities on hand at the end of month t where t=1,2,3,4 for each month in the problem. O.F MINIMIZE COST Z = 5x1+8x2+4x3+7x4+2i1+2i2+2i3-6i4

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**Constraints 1 i1 = 0 + x1 – 50 2 i2= i1 + x2 – 65 3 i3= i2 + x3 – 100**

4 i4= i3 + x3 – 70 5 x1 > 0 6 x2 > 0 7 x3 > 0 8 x4 > 0 9 i1 > 0 10 i2 > 0 11 i3 > 0 12 i4 > 0

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Input Values

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Solution

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**Production Cost per Unit Units Remaining at End of Month**

Solution Table Month Units to Produce Production Cost per Unit Total Production Cost Demand Units Remaining at End of Month Inventory Cost Total Cost 1 115 $ $ 50 65 $ $ 2 $ $ $ $ 3 170 $ $ 100 70 $ $ 4 $ GRAND TOTAL $ 1,525.00

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Sensitivity Analysis

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**Sensitivity Analysis Cont.**

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**Report to Manger The minimum cost we calculated is $1,525 Month**

Units to Produce Demand Units Remaining at End of Month 1 115 50 65 2 3 170 100 70 4

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**Unit Cost of Production Total Cost (All 4 Months)**

Report to Manager For month 2: Unit Cost of Production Total Cost (All 4 Months) Units to Produce $7.00 and above $1,525 $2.00 to $6.99 $1200 to $ 65

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Questions?

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