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

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**Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan**Gutierrez No BackloggingProblem # 1(pg.104)October 20,2011**Outline**• Problem Statement • Problem Summary • Assumptions • Formulation • Constraints • Input Values • Solutions • Sensitivity Analysis • Report to Manager**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.**Assumptions**• No inventory at beginning of month • Unlimited capacity • Other costs in production were ignored**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**Report to Manger**• The minimum cost we calculated is $1,525**Report to Manager**For month 2: