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

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.

Problem Summary 1 $5 50 2 $8 65 3 $4 100 4 $7 70 Month Cost of Production/Unit Demand 1 $5 50 2 $8 65 3 $4 100 4 $7 70

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

Constraints 1 i1 = 0 + x1 – 50 2 i2= i1 + x2 – 65 3 i3= i2 + x3 – 100 4 i4= i3 + x3 – 70 5 x1 > 0 6 x2 > 0 7 x3 > 0 8 x4 > 0 9 i1 > 0 10 i2 > 0 11 i3 > 0 12 i4 > 0

Input Values

Solution

Production Cost per Unit Units Remaining at End of Month Solution Table Month Units to Produce Production Cost per Unit Total Production Cost Demand Units Remaining at End of Month Inventory Cost Total Cost 1 115 $ 5.00 $ 575.00 50 65 $ 130.00 $ 705.00 2 $ 8.00 $ - $ - $ - 3 170 $ 4.00 $ 680.00 100 70 $ 140.00 $ 820.00 4 $ 7.00 GRAND TOTAL $ 1,525.00

Sensitivity Analysis

Sensitivity Analysis Cont.

Report to Manger The minimum cost we calculated is $1,525 Month Units to Produce Demand Units Remaining at End of Month 1 115 50 65 2 3 170 100 70 4

Unit Cost of Production Total Cost (All 4 Months) Report to Manager For month 2: Unit Cost of Production Total Cost (All 4 Months) Units to Produce $7.00 and above $1,525 $2.00 to $6.99 $1200 to $1524.35 65

Questions?