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: