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

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

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

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1. Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan Gutierrez No BackloggingProblem # 1(pg.104)October 20,2011

2. Outline • Problem Statement • Problem Summary • Assumptions • Formulation • Constraints • Input Values • Solutions • Sensitivity Analysis • Report to Manager

3. 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.

4. Problem Summary

5. Assumptions • No inventory at beginning of month • Unlimited capacity • Other costs in production were ignored

6. 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

7. Constraints

8. Input Values

9. Solution

10. Solution Table

11. Sensitivity Analysis

12. Sensitivity Analysis Cont.

13. Report to Manger • The minimum cost we calculated is \$1,525

14. Report to Manager For month 2:

15. Questions?