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
Constraints
Input Values
Solutions
Sensitivity Analysis
Report to Manager

3. 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.

4. 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

5. Assumptions No inventory at beginning of month Unlimited capacity
Other costs in production were ignored

6. 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

7. Constraints 1 i1 = 0 + x1 – 50 2 i2= i1 + x2 – 65 3 i3= i2 + x3 – 1004
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

8. Input Values

9. Solution

10. 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 $ $ 50 65 $ $ 2 $ $ $ $ 3
170 $ $
100 70 $ $ 4 $
GRAND TOTAL
$ 1,525.00

11. Sensitivity Analysis

12. Sensitivity Analysis Cont.

13. 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

14. 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 $ 65

15. Questions?