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Problem 1. Demand 1 2 3 4 5 6 7 8 9Total 1902302602802101701602601801940 There are 20 full time employees, each can produce 10 units per period at the cost of $6 per unit. Therefore the supply of full time workers is as follows - PowerPoint PPT Presentation
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Demand 1 2 3 4 5 6 7 8 9
Total190 230 260 280 210 170 160 260 180
1940
There are 20 full time employees, each can produce 10 units per period at the cost of $6 per unit. Therefore the supply of full time workers is as follows
1 2 3 4 5 6 7 8 9Total
200 200 200 200 200 200 200 200 2001800
Overtime cost is $13 per unit. Inventory carrying cost $5 per unit per periodBacklog cost $10 per unit per period
Maximum over time production is 20 units per period
Formulated the problem as a Linear Programming model. Using excel and solver find the optimal solution.
Problem 1
Solution to Problem 2
Changing Cells
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1Prod_Over1Prod_Reg2Prod_Over2Prod_Reg3Prod_Over3Prod_Reg4Prod_Over4Prod_Reg5Prod_Over5Prod_Reg6Prod_Over6Prod_Reg7Prod_Over7Prod_Reg8Prod_Over8Prod_Reg9Prod_Over9
RHS
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9 RHSProd_Reg1 <= 200Prod_Over1 <= 20Prod_Reg2 <= 200Prod_Over2 <= 20Prod_Reg3 <= 200Prod_Over3 <= 20Prod_Reg4 <= 200Prod_Over4 <= 20Prod_Reg5 <= 200Prod_Over5 <= 20Prod_Reg6 <= 200Prod_Over6 <= 20Prod_Reg7 <= 200Prod_Over7 <= 20Prod_Reg8 <= 200Prod_Over8 <= 20Prod_Reg9 <= 200Prod_Over9 <= 20
= = = = = = = = =RHS 190 230 260 280 210 170 160 260 180 0
LHS
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 =SUM(B25:J 25)Prod_Over1Prod_Reg2Prod_Over2Prod_Reg3Prod_Over3Prod_Reg4Prod_Over4Prod_Reg5Prod_Over5Prod_Reg6Prod_Over6Prod_Reg7Prod_Over7Prod_Reg8Prod_Over8Prod_Reg9Prod_Over9
=SUM(B25:B42)
LHS
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9 LHS RHSProd_Reg1 0 <= 200Prod_Over1 0 <= 20Prod_Reg2 0 <= 200Prod_Over2 0 <= 20Prod_Reg3 0 <= 200Prod_Over3 0 <= 20Prod_Reg4 0 <= 200Prod_Over4 0 <= 20Prod_Reg5 0 <= 200Prod_Over5 0 <= 20Prod_Reg6 0 <= 200Prod_Over6 0 <= 20Prod_Reg7 0 <= 200Prod_Over7 0 <= 20Prod_Reg8 0 <= 200Prod_Over8 0 <= 20Prod_Reg9 0 <= 200Prod_Over9 0 <= 20LHS 0 0 0 0 0 0 0 0 0
= = = = = = = = =RHS 190 230 260 280 210 170 160 260 180
Cost Table; Format
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1Prod_Over1Prod_Reg2Prod_Over2Prod_Reg3Prod_Over3Prod_Reg4Prod_Over4Prod_Reg5Prod_Over5Prod_Reg6Prod_Over6Prod_Reg7Prod_Over7Prod_Reg8Prod_Over8Prod_Reg9Prod_Over9
Production Cost; Regular, Overtime
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 6Prod_Over1 13Prod_Reg2 6Prod_Over2 13Prod_Reg3 6Prod_Over3 13Prod_Reg4 6Prod_Over4 13Prod_Reg5 6Prod_Over5 13Prod_Reg6 6Prod_Over6 13Prod_Reg7 6Prod_Over7 13Prod_Reg8 6Prod_Over8 13Prod_Reg9 6Prod_Over9 13
Inventory Cost
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 6 11 16 21 26 31 36 41 46Prod_Over1 13 18 23 28 33 38 43 48 53Prod_Reg2 6Prod_Over2 13Prod_Reg3 6Prod_Over3 13Prod_Reg4 6Prod_Over4 13Prod_Reg5 6Prod_Over5 13Prod_Reg6 6Prod_Over6 13Prod_Reg7 6Prod_Over7 13Prod_Reg8 6Prod_Over8 13Prod_Reg9 6Prod_Over9 13
Inventory Cost for All Periods
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 6 11 16 21 26 31 36 41 46Prod_Over1 13 18 23 28 33 38 43 48 53Prod_Reg2 6 11 16 21 26 31 36 41Prod_Over2 13 18 23 28 33 38 43 48Prod_Reg3 6 11 16 21 26 31 36Prod_Over3 13 18 23 28 33 38 43Prod_Reg4 6 11 16 21 26 31Prod_Over4 13 18 23 28 33 38Prod_Reg5 6 11 16 21 26Prod_Over5 13 18 23 28 33Prod_Reg6 6 11 16 21Prod_Over6 13 18 23 28Prod_Reg7 6 11 16Prod_Over7 13 18 23Prod_Reg8 6 11Prod_Over8 13 18Prod_Reg9 6Prod_Over9 13
Backlog Cost
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 6 11 16 21 26 31 36 41 46Prod_Over1 13 18 23 28 33 38 43 48 53Prod_Reg2 6 11 16 21 26 31 36 41Prod_Over2 13 18 23 28 33 38 43 48Prod_Reg3 6 11 16 21 26 31 36Prod_Over3 13 18 23 28 33 38 43Prod_Reg4 6 11 16 21 26 31Prod_Over4 13 18 23 28 33 38Prod_Reg5 6 11 16 21 26Prod_Over5 13 18 23 28 33Prod_Reg6 6 11 16 21Prod_Over6 13 18 23 28Prod_Reg7 6 11 16Prod_Over7 13 18 23Prod_Reg8 6 11Prod_Over8 13 18Prod_Reg9 86 76 66 56 46 36 26 16 6Prod_Over9 93 83 73 63 53 43 33 23 13
Backlog Cost for All Periods
Dem1 Dem2 Dem3 Dem4 Dem5 Dem6 Dem7 Dem8 Dem9Prod_Reg1 6 11 16 21 26 31 36 41 46Prod_Over1 13 18 23 28 33 38 43 48 53Prod_Reg2 16 6 11 16 21 26 31 36 41Prod_Over2 23 13 18 23 28 33 38 43 48Prod_Reg3 26 16 6 11 16 21 26 31 36Prod_Over3 33 23 13 18 23 28 33 38 43Prod_Reg4 36 26 16 6 11 16 21 26 31Prod_Over4 43 33 23 13 18 23 28 33 38Prod_Reg5 46 36 26 16 6 11 16 21 26Prod_Over5 53 43 33 23 13 18 23 28 33Prod_Reg6 56 46 36 26 16 6 11 16 21Prod_Over6 63 53 43 33 23 13 18 23 28Prod_Reg7 66 56 46 36 26 16 6 11 16Prod_Over7 73 63 53 43 33 23 13 18 23Prod_Reg8 76 66 56 46 36 26 16 6 11Prod_Over8 83 73 63 53 43 33 23 13 18Prod_Reg9 86 76 66 56 46 36 26 16 6Prod_Over9 93 83 73 63 53 43 33 23 13
Target Cell
Changing Cells
Constraints
Target Cell, Changing Cells, Constraints
Change to Min
Options
Solve
Objective Function Value
Problem 2
LP Formulation; Supply and Demand
Period 1 2 3 4 5 6 Production1 Regular 3001 Overtime 3001 OutSource 3002 Regular 3002 Overtime 3002 OutSource 3003 Regular 3003 Overtime 3003 OutSource 3004 Regular 3004 Overtime 3004 OutSource 3005 Regular 3005 Overtime 3005 OutSource 3006 Regular 3006 Overtime 3006 OutSource 300
200 200 300 400 500 200 0
LP Formulation; Cost Parameters
Period 1 2 3 4 5 61 Regular 2 3 4 5 6 71 Overtime 3 4 5 6 7 81 OutSource 6 7 8 9 10 112 Regular 7 2 3 4 5 62 Overtime 8 3 4 5 6 72 OutSource 11 6 7 8 9 103 Regular 12 7 2 3 4 53 Overtime 13 8 3 4 5 63 OutSource 16 11 6 7 8 94 Regular 17 12 7 2 3 44 Overtime 18 13 8 3 4 54 OutSource 21 16 11 6 7 85 Regular 22 17 12 7 2 35 Overtime 23 18 13 8 3 45 OutSource 26 21 16 11 6 76 Regular 27 22 17 12 7 26 Overtime 28 23 18 13 8 36 OutSource 31 26 21 16 11 6
Period 1 2 3 4 5 6 Production1 Regular 0 <= 3001 Overtime 0 <= 3001 OutSource 0 <= 3002 Regular 0 <= 3002 Overtime 0 <= 3002 OutSource 0 <= 3003 Regular 0 <= 3003 Overtime 0 <= 3003 OutSource 0 <= 3004 Regular 0 <= 3004 Overtime 0 <= 3004 OutSource 0 <= 3005 Regular 0 <= 3005 Overtime 0 <= 3005 OutSource 0 <= 3006 Regular 0 <= 3006 Overtime 0 <= 3006 OutSource 0 <= 300
0 0 0 0 0 0= = = = = =
200 200 300 400 500 200 0
LP Formulation; Sumproduct and Constraints
LP Formulation; Optimal Solution
Period 1 2 3 4 5 6 Production1 Regular 200 0 0 0 0 0 200 3001 Overtime 0 0 0 0 0 0 0 3001 OutSource 0 0 0 0 0 0 0 3002 Regular 0 200 0 0 0 0 200 3002 Overtime 0 0 0 0 0 0 0 3002 OutSource 0 0 0 0 0 0 0 3003 Regular 0 0 300 0 0 0 300 3003 Overtime 0 0 0 0 0 0 0 3003 OutSource 0 0 0 0 0 0 0 3004 Regular 0 0 0 300 0 0 300 3004 Overtime 0 0 0 100 0 0 100 3004 OutSource 0 0 0 0 0 0 0 3005 Regular 0 0 0 0 300 0 300 3005 Overtime 0 0 0 0 200 0 200 3005 OutSource 0 0 0 0 0 0 0 3006 Regular 0 0 0 0 0 200 200 3006 Overtime 0 0 0 0 0 0 0 3006 OutSource 0 0 0 0 0 0 0 300
200 200 300 400 500 200200 200 300 400 500 200 3900
