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# No Backlogging Problem # 1(pg.104) October 20,2011 - PowerPoint PPT Presentation

Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan Gutierrez. No Backlogging Problem # 1(pg.104) October 20,2011. Outline. Problem Statement Problem Summary Assumptions Formulation Constraints Input Values Solutions Sensitivity Analysis Report to Manager . Problem Statement.

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

Outline Gutierrez

• Problem Statement

• Problem Summary

• Assumptions

• Formulation

• Constraints

• Input Values

• Solutions

• Sensitivity Analysis

• Report to Manager

Problem Statement Gutierrez

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.

Problem Summary Gutierrez

Assumptions Gutierrez

• No inventory at beginning of month

• Unlimited capacity

• Other costs in production were ignored

Formulation Gutierrez

• 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

Constraints Gutierrez

Input Values Gutierrez

Solution Gutierrez

Solution Table Gutierrez

Report to Manger Gutierrez

• The minimum cost we calculated is \$1,525

Report to Manager Gutierrez

For month 2:

Questions? Gutierrez