Ch16 Evans BA1e Case Solution

8/10/2019 Ch16 Evans BA1e Case Solution

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PLE Case: Nonl inear Optim ization Solution

Note: Demand is based on 2012 mower sales data

Production cost ($/unit) 70.00$Inventory holding cost ($/unit) 1.40$Lost sales cost ($/unit) #NAME? #NAME?Overtime cost ($/unit) 6.50$

Undertime cost ($/unit) 3.00$Normal production rate 9,100

Month Demand Productio Inventory Lost SalesOvertime

December 9100 900January 7,080 8,867 2,687 0 0February 9,250 8,643 2,080 0 0March 10,020 8,431 491 0 0April 10,995 8,230 0 2,274 0May 11,436 8,040 102 3,499 0June 12,082 7,862 0 4,117 0

July 11,486 7,698 0 3,788 0August 9,504 7,547 200 2,157 0September 8,635 7,412 2 1,024 0October 7,451 7,295 0 154 0November 6,453 7,199 746 0 0December 5,651 7,132 2,227 0 0

Average 9,170Totals 94,356 8,535 17,014 0Cost 70.00$ 1.40$ #NAME? 6.50$

Total #NAME?

Solver Model:


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Rate Material Overtime Production

Undertime Rate Increase Rate Decreas Change Balance Undertime Rate Change

Cost ConstraintConstraint Constraint

233 0 233 $272.36 7,080 9,100 0457 0 223 $249.20 9,250 9,100 0669 0 212 $225.36 10,020 9,100 0870 0 201 $202.45 10,995 9,100 0

1,060 0 190 $180.52 11,436 9,100 01,238 0 178 $157.70 12,082 9,100 0

1,402 0 165 $135.62 11,486 9,100 01,553 0 150 $113.12 9,504 9,100 01,688 0 135 $90.91 8,635 9,100 01,805 0 117 $68.62 7,451 9,100 01,901 0 96 $46.07 6,453 9,100 01,968 0 68 $22.80 5,651 9,100 0

14,8443.00$ -$ 335,695.61$


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iven by rate-change cost = 0.005(Xt- Xt-1)2.

nth obtained using the given nonlinear function and then included in the objective function.

e-change cost is fixed.hange cost is fixed and when the rate-change cost modeled by a nonlinear function, has declined.ual to the total cost obtained with fixed rate-change cost.change costs will be zero for all the months.




0 193 0 186.856 7,080 9,100 0

0 172 0 147.87 9,250 9,100 00 147 0 107.927 10,020 9,100 00 116 0 67.7907 10,995 9,100 00 73 0 26.9308 11,436 9,100 00 0 54 14.3827 12,082 9,100 00 0 105 55.519 11,486 9,100 00 0 139 96.6451 9,504 9,100 00 0 144 103.932 8,635 9,100 00 0 123 76.2567 7,451 9,100 00 0 99 48.963 6,453 9,100 0

30 0 67 22.6094 5,651 9,100 030

$3.00 $87,278.19 $50,825.54


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0 0 0 0 7,080 9,100 00 0 0 0 9,250 9,100 00 0 0 0 10,020 9,100 00 0 0 0 10,995 9,100 00 0 0 0 11,436 9,100 00 0 0 0 12,082 9,100 00 0 0 0 11,486 9,100 00 0 0 0 9,504 9,100 00 0 0 0 8,635 9,100 00 0 0 0 7,451 9,100 00 0 0 0 6,453 9,100 00 0 0 0 5,651 9,100 00

$3.00 $- $-


7/23

Microsoft Excel 14.0 Answer Report

Worksheet: [Evans 1e Chapter 16.xlsx]Case

Result: Solver has converged to the current solution. All constraints are satisfied.

Engine: Standard LSGRG Nonlinear

Objective Cell (Min)Cell Name Original Value Final Value

$C$30 Total Cost 6997140.392 6997106.358

Decision Variable Cells

Cell Name Original Value Final Value Type

$D$15 January Production 8,866 8,866 Normal

$E$15 January Inventory 2,686 2,686 Normal

$F$15 January Lost Sales 0 0 Normal

$G$15 January Overtime 0 0 Normal

$H$15 January Undertime 234 234 Normal

$I$15 January Rate Increase 0 0 Normal

$J$15 January Rate Decrease 234 234 Normal

$D$16 February Production 8,643 8,644 Normal

$E$16 February Inventory 2,080 2,080 Normal

$F$16 February Lost Sales 0 0 Normal

$G$16 February Overtime 0 0 Normal

$H$16 February Undertime 457 456 Normal

$I$16 February Rate Increase 0 0 Normal

$J$16 February Rate Decrease 223 223 Normal

$D$17 March Production 8,431 8,433 Normal$E$17 March Inventory 490 493 Normal

$F$17 March Lost Sales 0 0 Normal

$G$17 March Overtime 0 0 Normal

$H$17 March Undertime 669 667 Normal

$I$17 March Rate Increase 0 0 Normal

$J$17 March Rate Decrease 212 211 Normal

$D$18 April Production 8,229 8,232 Normal

$E$18 April Inventory 0 0 Normal

$F$18 April Lost Sales 2,276 2,270 Normal

$G$18 April Overtime 0 0 Normal

$H$18 April Undertime 871 868 Normal

$I$18 April Rate Increase 0 0 Normal

$J$18 April Rate Decrease 201 201 Normal

$D$19 May Production 8,039 8,043 Normal

$E$19 May Inventory 123 107 Normal

$F$19 May Lost Sales 3,520 3,501 Normal

$G$19 May Overtime 0 0 Normal

$H$19 May Undertime 1,061 1,057 Normal


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$G$26 December Overtime 0 0 Normal

$H$26 December Undertime 1,970 1,961 Normal

$I$26 December Rate Increase 0 0 Normal

$J$26 December Rate Decrease 68 68 Normal

Constraints

Cell Name Cell Value Formula Status Slack$L$15 January Constraint 7,080 $L$15=$B$15 Binding 0

$L$16 February Constraint 9,250 $L$16=$B$16 Binding 0

$L$17 March Constraint 10,020 $L$17=$B$17 Binding 0

$L$18 April Constraint 10,995 $L$18=$B$18 Binding 0

$L$19 May Constraint 11,436 $L$19=$B$19 Binding 0

$L$20 June Constraint 12,082 $L$20=$B$20 Binding 0

$L$21 July Constraint 11,486 $L$21=$B$21 Binding 0

$L$22 August Constraint 9,504 $L$22=$B$22 Binding 0

$L$23 September Constraint 8,635 $L$23=$B$23 Binding 0

$L$24 October Constraint 7,451 $L$24=$B$24 Binding 0

$L$25 November Constraint 6,453 $L$25=$B$25 Binding 0

$L$26 December Constraint 5,651 $L$26=$B$26 Binding 0

$M$15 January Constraint 9,100 $M$15=$B$9 Binding 0

$M$16 February Constraint 9,100 $M$16=$B$9 Binding 0

$M$17 March Constraint 9,100 $M$17=$B$9 Binding 0

$M$18 April Constraint 9,100 $M$18=$B$9 Binding 0

$M$19 May Constraint 9,100 $M$19=$B$9 Binding 0

$M$20 June Constraint 9,100 $M$20=$B$9 Binding 0

$M$21 July Constraint 9,100 $M$21=$B$9 Binding 0

$M$22 August Constraint 9,100 $M$22=$B$9 Binding 0

$M$23 September Constraint 9,100 $M$23=$B$9 Binding 0$M$24 October Constraint 9,100 $M$24=$B$9 Binding 0

$M$25 November Constraint 9,100 $M$25=$B$9 Binding 0

$M$26 December Constraint 9,100 $M$26=$B$9 Binding 0

$N$15 January Constraint 0 $N$15=0 Binding 0

$N$16 February Constraint 0 $N$16=0 Binding 0

$N$17 March Constraint 0 $N$17=0 Binding 0

$N$18 April Constraint 0 $N$18=0 Binding 0

$N$19 May Constraint 0 $N$19=0 Binding 0

$N$20 June Constraint 0 $N$20=0 Binding 0

$N$21 July Constraint 0 $N$21=0 Binding 0

$N$22 August Constraint 0 $N$22=0 Binding 0

$N$23 September Constraint 0 $N$23=0 Binding 0

$N$24 October Constraint 0 $N$24=0 Binding 0

$N$25 November Constraint 0 $N$25=0 Binding 0

$N$26 December Constraint 0 $N$26=0 Binding 0


10/23

Microsoft Excel 14.0 Sensitivity Report

Worksheet: [Evans 1e Chapter 16.xlsx]Case

Engine: Standard LSGRG Nonlinear

Objective Cell (Min)

Cell Name Final Value

$C$30 Total Cost 6997106.358

Decision Variable Cells

Final Reduced

Cell Name Value Gradient

$D$15 January Production 8,866 0

$E$15 January Inventory 2,686 0

$F$15 January Lost Sales 0 4

$G$15 January Overtime 0 10

$H$15 January Undertime 234 0

$I$15 January Rate Increase 0 545

$J$15 January Rate Decrease 234 0

$D$16 February Production 8,644 0

$E$16 February Inventory 2,080 0

$F$16 February Lost Sales 0 3

$G$16 February Overtime 0 10

$H$16 February Undertime 456 0

$I$16 February Rate Increase 0 499

$J$16 February Rate Decrease 223 -4

$D$17 March Production 8,433 0

$E$17 March Inventory 493 0

$F$17 March Lost Sales 0 1$G$17 March Overtime 0 10

$H$17 March Undertime 667 0

$I$17 March Rate Increase 0 454

$J$17 March Rate Decrease 211 -7

$D$18 April Production 8,232 0

$E$18 April Inventory 0 1

$F$18 April Lost Sales 2,270 0

$G$18 April Overtime 0 10

$H$18 April Undertime 868 0

$I$18 April Rate Increase 0 407

$J$18 April Rate Decrease 201 -4

$D$19 May Production 8,043 0

$E$19 May Inventory 107 1

$F$19 May Lost Sales 3,501 0

$G$19 May Overtime 0 10

$H$19 May Undertime 1,057 0

$I$19 May Rate Increase 0 363

$J$19 May Rate Decrease 189 -6


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12/23

$I$26 December Rate Increase 0 46

$J$26 December Rate Decrease 68 0

Constraints

Final Lagrange

Cell Name Value Multiplier

$L$15 January Constraint 7,080 -4$L$16 February Constraint 9,250 -3

$L$17 March Constraint 10,020 -1

$L$18 April Constraint 10,995 0

$L$19 May Constraint 11,436 0

$L$20 June Constraint 12,082 0

$L$21 July Constraint 11,486 0

$L$22 August Constraint 9,504 0

$L$23 September Constraint 8,635 0

$L$24 October Constraint 7,451 -1

$L$25 November Constraint 6,453 -3

$L$26 December Constraint 5,651 -1

$M$15 January Constraint 9,100 3

$M$16 February Constraint 9,100 3

$M$17 March Constraint 9,100 3

$M$18 April Constraint 9,100 3

$M$19 May Constraint 9,100 3

$M$20 June Constraint 9,100 3

$M$21 July Constraint 9,100 3

$M$22 August Constraint 9,100 3

$M$23 September Constraint 9,100 3

$M$24 October Constraint 9,100 3$M$25 November Constraint 9,100 3

$M$26 December Constraint 9,100 3

$N$15 January Constraint 0 273

$N$16 February Constraint 0 251

$N$17 March Constraint 0 230

$N$18 April Constraint 0 206

$N$19 May Constraint 0 184

$N$20 June Constraint 0 161

$N$21 July Constraint 0 139

$N$22 August Constraint 0 116

$N$23 September Constraint 0 94

$N$24 October Constraint 0 72

$N$25 November Constraint 0 46

$N$26 December Constraint 0 23


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$C$6 $D$15 $E$15 $F$15 $G$15 $H$15 $I$15 $J$15 $D$16 $E$16 $F$16 $G$16 $H$16 $I$16 $J$16

0 8,867 2,687 0 0 233 0 233 8,643 2,080 0 0 457 0 223

20 8,895 2,715 0 0 205 0 205 8,699 2,164 0 0 401 0 196

40 8,925 2,745 0 0 175 0 175 8,756 2,251 0 0 344 0 169

60 8,963 2,783 0 0 137 0 137 8,829 2,362 0 0 271 0 134

80 9,018 2,838 0 0 82 0 82 8,932 2,520 0 0 168 0 86

100 9,134 2,954 0 34 0 34 0 9,135 2,839 0 35 0 0 0120 9,172 2,992 0 72 0 72 0 9,225 2,967 0 125 0 52 0

140 9,219 3,039 0 119 0 119 0 9,320 3,109 0 220 0 101 0

160 9,253 3,073 0 153 0 153 0 9,389 3,212 0 289 0 135 0

180 9,280 3,100 0 180 0 180 0 9,441 3,291 0 341 0 161 0

200 9,293 3,113 0 193 0 193 0 9,464 3,327 0 364 0 171 0


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$D$17 $E$17 $F$17 $G$17 $H$17 $I$17 $J$17 $D$18 $E$18 $F$18 $G$18 $H$18 $I$18 $J$18

8,431 491 0 0 669 0 212 8,230 0 2,274 0 870 0 201

8,510 654 0 0 590 0 189 8,331 0 2,010 0 769 0 179

8,593 824 0 0 507 0 163 8,436 0 1,735 0 664 0 157

8,697 1,040 0 0 403 0 132 8,568 0 1,387 0 532 0 129

8,842 1,342 0 0 258 0 89 8,749 0 904 0 351 0 94

9,110 1,929 0 10 0 0 25 9,069 3 0 0 31 0 419,226 2,173 0 126 0 1 0 9,175 353 0 75 0 0 51

9,399 2,488 0 299 0 79 0 9,445 938 0 345 0 46 0

9,503 2,695 0 403 0 114 0 9,591 1,291 0 491 0 88 0

9,578 2,849 0 478 0 137 0 9,687 1,541 0 587 0 109 0

9,611 2,918 0 511 0 147 0 9,728 1,660 9 628 0 116 0


15/23

$D$19 $E$19 $F$19 $G$19 $H$19 $I$19 $J$19 $D$20 $E$20 $F$20 $G$20 $H$20 $I$20 $J$20

8,039 92 3,488 0 1,061 0 191 7,862 0 4,128 0 1,238 0 177

8,161 92 3,367 0 939 0 170 8,000 0 3,991 0 1,100 0 162

8,285 69 3,221 0 815 0 151 8,139 0 3,873 0 961 0 145

8,440 65 3,061 0 660 0 128 8,315 0 3,702 0 785 0 126

8,651 5 2,790 0 449 0 98 8,548 0 3,529 0 552 0 103

9,010 95 2,518 0 90 0 59 8,935 0 3,052 0 165 0 759,100 72 2,055 0 0 0 75 9,009 0 3,002 0 91 0 91

9,401 49 1,146 301 0 0 44 9,323 0 2,710 223 0 0 78

9,637 35 544 537 0 46 0 9,578 0 2,469 478 0 0 59

9,755 76 216 655 0 68 0 9,710 0 2,296 610 0 0 45

9,801 38 13 701 0 74 0 9,748 0 2,296 648 0 0 53


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$D$21 $E$21 $F$21 $G$21 $H$21 $I$21 $J$21 $D$22 $E$22 $F$22 $G$22 $H$22 $I$22 $J$22

7,698 0 3,788 0 1,402 0 165 7,548 189 2,145 0 1,552 0 150

7,847 0 3,639 0 1,253 0 152 7,706 190 1,987 0 1,394 0 141

8,001 0 3,485 0 1,099 0 139 7,868 167 1,802 0 1,232 0 132

8,191 0 3,295 0 909 0 124 8,069 163 1,598 0 1,031 0 122

8,442 0 3,044 0 658 0 107 8,331 102 1,276 0 769 0 111

8,847 0 2,639 0 253 0 88 8,746 0 758 0 354 0 1008,900 0 2,586 0 200 0 109 8,776 0 728 0 324 0 124

9,221 0 2,265 121 0 0 102 9,100 0 404 0 0 0 121

9,483 0 2,003 383 0 0 95 9,363 0 141 263 0 0 120

9,618 0 1,868 518 0 0 92 9,494 0 10 394 0 0 124

9,643 0 1,843 543 0 0 105 9,504 0 0 404 0 0 139


17/23

$D$23 $E$23 $F$23 $G$23 $H$23 $I$23 $J$23 $D$24 $E$24 $F$24 $G$24 $H$24 $I$24 $J$24

7,414 0 1,032 0 1,686 0 134 7,298 0 153 0 1,802 0 116

7,577 0 868 0 1,523 0 129 7,458 7 0 0 1,642 0 119

7,742 0 726 0 1,358 0 126 7,623 172 0 0 1,477 0 119

7,948 0 524 0 1,152 0 120 7,830 379 0 0 1,270 0 118

8,216 0 316 0 884 0 115 8,099 648 0 0 1,001 0 118

8,635 0 0 0 465 0 111 8,517 1,066 0 0 583 0 1188,638 3 0 0 462 0 138 8,520 1,072 0 0 580 0 118

8,963 328 0 0 137 0 137 8,845 1,722 0 0 255 0 118

9,221 586 0 121 0 0 142 9,100 2,235 0 0 0 0 121

9,345 710 0 245 0 0 149 9,216 2,476 0 116 0 0 129

9,360 725 0 260 0 0 144 9,237 2,511 0 137 0 0 123


18/23

$D$25 $E$25 $F$25 $G$25 $H$25 $I$25 $J$25 $D$26 $E$26 $F$26 $G$26 $H$26 $I$26 $J$26

7,202 749 0 0 1,898 0 96 7,134 2,232 0 0 1,966 0 68

7,362 917 0 0 1,738 0 96 7,295 2,560 0 0 1,805 0 68

7,528 1,247 0 0 1,572 0 96 7,460 3,056 0 0 1,640 0 68

7,734 1,660 0 0 1,366 0 96 7,667 3,676 0 0 1,433 0 68

8,003 2,197 0 0 1,097 0 96 7,935 4,481 0 0 1,165 0 68

8,421 3,034 0 0 679 0 96 8,353 5,736 0 0 747 0 688,424 3,043 0 0 676 0 96 8,357 5,749 0 0 743 0 68

8,749 4,017 0 0 351 0 96 8,681 7,048 0 0 419 0 68

9,004 4,786 0 0 96 0 96 8,936 8,071 0 0 164 0 68

9,117 5,139 0 17 0 0 100 9,048 8,536 0 0 52 0 68

9,138 5,195 0 38 0 0 99 9,070 8,614 0 0 30 0 68


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$C$30

6,997,056.03$

7,324,794.45$

7,632,809.81$

7,917,455.27$

8,172,601.53$

8,379,239.80$8,550,988.73$

8,696,582.53$

8,811,353.41$

8,904,882.78$

8,989,598.10$


20/23

PLE Case: Optim al Solution


Production cost ($/unit) 70.00$Inventory holding cost ($/unit) 1.40$Lost sales cost ($/unit) 200.00$Overtime cost ($/unit) 6.50$


Month Demand Productio Inventory Lost SalesOvertime

December 9100 900January 7,080 9,293 3,113 0 193February 9,250 9,465 3,329 0 365March 10,020 9,612 2,921 0 512April 10,995 9,729 1,654 0 629May 11,436 9,802 80 60 702June 12,082 9,748 0 2,253 648

July 11,486 9,643 0 1,843 543August 9,504 9,504 0 0 404September 8,635 9,360 725 0 260October 7,451 9,236 2,510 0 136November 6,453 9,137 5,195 0 37December 5,651 9,070 8,614 0 0

Average 9,170Totals 113,601 28,141 4,156 4,430Cost 70.00$ 1.40$ 200$ 6.50$

Total 8,989,643.47$


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Undertime Rate Increase Rate Decrease Change Balance Undertime Rate Change

Cost Constraint Constraint Constraint

0 193 0 186.8560415 7,080 9,100 00 172 0 147.8700942 9,250 9,100 00 147 0 107.9266563 10,020 9,100 00 116 0 67.79068859 10,995 9,100 00 73 0 26.93081587 11,436 9,100 00 0 54 14.38267773 12,082 9,100 0

0 0 105 55.51895827 11,486 9,100 00 0 139 96.64506938 9,504 9,100 00 0 144 103.9318902 8,635 9,100 00 0 123 76.25669255 7,451 9,100 00 0 99 48.96302103 6,453 9,100 0

30 0 67 22.60943821 5,651 9,100 0

303.00$ 87,278.19$ 50,825.54$


22/23

PLE Case: Level product ion strategy


Production cost ($/unit) 70.00$Inventory holding cost ($/unit) 1.40$Lost sales cost ($/unit) 200.00$Overtime cost ($/unit) 6.50$


Month Demand Production Inventory Lost SalesOvertime

December 9100 900January 7,080 9,100 2,920 0 0February 9,250 9,100 2,770 0 0March 10,020 9,100 1,850 0 0April 10,995 9,100 0 45 0May 11,436 9,100 0 2,336 0June 12,082 9,100 0 2,982 0

July 11,486 9,100 0 2,386 0August 9,504 9,100 0 404 0September 8,635 9,100 465 0 0October 7,451 9,100 2,114 0 0November 6,453 9,100 4,761 0 0December 5,651 9,100 8,210 0 0

Average 9,170Totals 109,200 23,090 8,153 0Cost 70.00$ 1.40$ 200$ 6.50$

Total 9,306,926.00$


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Undertime Rate Increase Rate Decrease Change Balance Undertime Rate Change

Cost Constraint Constraint Constraint

0 0 0 0 7,080 9,100 00 0 0 0 9,250 9,100 00 0 0 0 10,020 9,100 00 0 0 0 10,995 9,100 00 0 0 0 11,436 9,100 00 0 0 0 12,082 9,100 0

0 0 0 0 11,486 9,100 00 0 0 0 9,504 9,100 00 0 0 0 8,635 9,100 00 0 0 0 7,451 9,100 00 0 0 0 6,453 9,100 00 0 0 0 5,651 9,100 0

03.00$ -$ -$

Ch16 Evans BA1e Case Solution

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