Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Step 1 Let us assume the decision variable as E; = number of employees available in month H; = number of employees hired in month F;= number of employees fired in month R;= regular production in month 0; = overtime production in month V;= Inventory at the end of month Therefore, Regular production in each month =30 - wi Overtime production capacity =10% of ( 30 · w;) = 3w; Step 2 Objective function: Minimum total cost including employees salary, hiring and firing cost, inventory holding cost, regular and overtime production cost. Minimum z=E 110w; + 8R1 + 7R2 + 4R3 + 2R4 + 6R5 + 8R6 + 8R7 + 6R8 + 7R9 +7R10 + 5R|1 + 8R12 + 1V1 + 4V2 + 3V3 + 4V4 + 3V5 + 3V6 + 2V + 1V8 +4V9 + 5V10 + 4V11 + 1V12 + 901 + 802 + 503 + 304 + 705 + 240H +25H8 + 162H9 + 228H10 + 210H|| + 192H12 + 213F¡ + 276F2 + 342F3 +306F4 + 222F5 + 294F6 + 180F, + 190Fg + 200F9 + 200F10 + 210F11 + 240F12
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Transcribed Image Text:Step 1 Let us assume the decision variable as E; = number of employees available in month H; = number of employees hired in month F;= number of employees fired in month R;= regular production in month 0; = overtime production in month V;= Inventory at the end of month Therefore, Regular production in each month =30 - wi Overtime production capacity =10% of ( 30 · w;) = 3w; Step 2 Objective function: Minimum total cost including employees salary, hiring and firing cost, inventory holding cost, regular and overtime production cost. Minimum z=E 110w; + 8R1 + 7R2 + 4R3 + 2R4 + 6R5 + 8R6 + 8R7 + 6R8 + 7R9 +7R10 + 5R|1 + 8R12 + 1V1 + 4V2 + 3V3 + 4V4 + 3V5 + 3V6 + 2V + 1V8 +4V9 + 5V10 + 4V11 + 1V12 + 901 + 802 + 503 + 304 + 705 + 240H +25H8 + 162H9 + 228H10 + 210H|| + 192H12 + 213F¡ + 276F2 + 342F3 +306F4 + 222F5 + 294F6 + 180F, + 190Fg + 200F9 + 200F10 + 210F11 + 240F12
= bartleby Q Search for textbooks, step-by-step explanations to homework que e Q&A Library ABC company produces and sells wooden « Formulate this problem as an Lp. ABC company produces and sells wooden desks. The demand is forecasted for each month of the next year. The company currently has 20 employees and each employee can produce 30 desks in a month. The monthly salary for each employee is $110. Since raw material costs change each month, the production costs are different for each month of the year. An excessive amount produced in a month can be stored in the inventory for use in the following months. However, the storage space has a capacity of 300 desks in total. The inventory holding costs are also different each month. In order to satisfy excessive demand in a month, the company may use its inventories, may implement overtime working hours, or hire additional workers. The total overtime production for each worker each month can be at most 10% of the regular time production. Also, the overtime production cost is different than the regular time production cost. Furthermore, the maximum number of workers who can work in the company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less than 15. Hiring and firing costs differ each month. The objective function is to minimize the total cost Current Production Employe Max. Storage Number of Min Number Salary of Сараacity per es Employee Workers of Workers employees 20 30 300 25 15 110 Inventory Holding Overtime Production Production Firing Hiring Cost 192 Month Demand Cost Cost Cost Cost 1 520 9 312 2 850 4. 8. 294 276 3 670 3 5 300 342 710 4 282 306 5 520 3 7 276 222 6 660 8 3 144 294 7 300 8 2 9 240 180 400 1 252 190 470 162 200 10 760 5 8. 228 200 11 610 4. 6. 210 210 12 900 9 192 240 7. CO 8. 74 2 60 6677 558
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Transcribed Image Text:= bartleby Q Search for textbooks, step-by-step explanations to homework que e Q&A Library ABC company produces and sells wooden « Formulate this problem as an Lp. ABC company produces and sells wooden desks. The demand is forecasted for each month of the next year. The company currently has 20 employees and each employee can produce 30 desks in a month. The monthly salary for each employee is $110. Since raw material costs change each month, the production costs are different for each month of the year. An excessive amount produced in a month can be stored in the inventory for use in the following months. However, the storage space has a capacity of 300 desks in total. The inventory holding costs are also different each month. In order to satisfy excessive demand in a month, the company may use its inventories, may implement overtime working hours, or hire additional workers. The total overtime production for each worker each month can be at most 10% of the regular time production. Also, the overtime production cost is different than the regular time production cost. Furthermore, the maximum number of workers who can work in the company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less than 15. Hiring and firing costs differ each month. The objective function is to minimize the total cost Current Production Employe Max. Storage Number of Min Number Salary of Сараacity per es Employee Workers of Workers employees 20 30 300 25 15 110 Inventory Holding Overtime Production Production Firing Hiring Cost 192 Month Demand Cost Cost Cost Cost 1 520 9 312 2 850 4. 8. 294 276 3 670 3 5 300 342 710 4 282 306 5 520 3 7 276 222 6 660 8 3 144 294 7 300 8 2 9 240 180 400 1 252 190 470 162 200 10 760 5 8. 228 200 11 610 4. 6. 210 210 12 900 9 192 240 7. CO 8. 74 2 60 6677 558
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 Linear Programming is an optimization technique used to achieve the best outcome or output by taking various constraints and factors. It is a mathematical model which uses a set of variables to form linear relationships.

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