Presentation on theme: "No Backlogging Problem # 1(pg.104) October 20,2011"— Presentation transcript:
1 No Backlogging Problem # 1(pg.104) October 20,2011 Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan Gutierrez
2 Outline Problem Statement Problem Summary Assumptions Formulation ConstraintsInput ValuesSolutionsSensitivity AnalysisReport to Manager
3 Problem StatementA 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 1 $5 50 2 $8 65 3 $4 100 4 $7 70 Month Cost of Production/UnitDemand1$5502$8653$41004$770
5 Assumptions No inventory at beginning of month Unlimited capacity Other costs in production were ignored
6 FormulationXt = number of commodities produced each month during month tit = number of commodities on hand at the end of month twhere t=1,2,3,4 for each month in the problem.O.F MINIMIZE COSTZ = 5x1+8x2+4x3+7x4+2i1+2i2+2i3-6i4
10 Production Cost per Unit Units Remaining at End of Month Solution TableMonthUnits to ProduceProduction Cost per UnitTotal Production CostDemandUnits Remaining at End of MonthInventory CostTotal Cost1115$$5065$$2$$$$3170$$10070$$4$GRAND TOTAL$ 1,525.00