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# Linear Programming BIT 3414

Virginia Tech

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## 65

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This 4 page Class Notes was uploaded by Caleb Wearmouth on Tuesday March 22, 2016. The Class Notes belongs to BIT 3414 at Virginia Polytechnic Institute and State University taught by Dr. Laura Clark in Spring 2016. Since its upload, it has received 65 views. For similar materials see Operations and Supply Chain Management in Information System at Virginia Polytechnic Institute and State University.

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Date Created: 03/22/16

Aggregate Production Planning Reading Pages with Linear Programming 622 – middle 623 The optimal solution for an aggregate production plan can be found with a linear programming model. Model Formulation Decision Variables R = units produced w/ regular production in period t t O t units produced w/overtime production in period t S t units produced w/ subcontracted production in period t It = inventory at end of period t W t workforce size for period t H t = # hired for period t Ft = # fired for period t Objective Function Minimize cost Constraints Demand, Capacity, Production, Workforce Decision Variables Consider a Trial and Error table for a mixed strategy of Level Production, Overtime, and Subcontracting: Regular Overtime Subcontract Quarter Demand Production Production Production Inventory BIT 3414 Copyright 2015 p. 1 Given the following information: Regular Prod. Capacity = 2000 units/qtr Regular Prod. Cost = $10/unit Quarter Demand 1 1200 Overtime Prod. Capacity = 500 units/qtr Overtime Prod. Cost = $20/unit 2 3100 Subcontracting Capacity = 1000 units/qtr Subcontracting Cost = $25/unit 3 2800 Inventory Capacity = 4000 units/qtr Inventory Cost = $5/unit/qtr 4 900 Beginning Inventory = 100 units Backorder Cost = $14/unit/qtr The company would like to determine the optimal mixture of the Level Production, Overtime, and Subcontracting strategies with a linear programming model. Decision Variables Objective Function Minimize Cost Z = + 25S + 25S + 25S + 25S 1 2 3 4 + 5I + 5I + 5I + 5I 1 2 3 4 Constraints Capacity Demand S: S 1 S 2 S ,3S ≤41000 3: R +3O + 3 + I 3 I 2 2803 I: I , I , I , I ≤ 4000 1 2 3 4 4: R +4O + 4 + I 4 I 3 9004 BIT 3414 Copyright 2015 p. 2 Given the following information: Hiring cost = $200 / worker Firing cost = $500 / worker Quarter Demand Regular Production Cost = $2 / unit Spring 30,000 Summer 10,000 Inventory cost = $0.50 / unit / quarter Production per employee = 1,000 units / quarter Fall 70,000 Winter 90,000 Beginning workforce = 50 workers Beginning inventory = 0 units The company would like to determine the optimal mixture of the Level Production and Chase Demand strategies with a linear programming model (assume no capacity limitations). Decision Variables Objective Function Minimize Cost Z = + 200H +1200H + 2002 + 200H 3 4 + 500F +1500F + 502F + 500F 3 4 Constraints Demand Production Workforce 3: R 3 I –2I =370,000 3: R –31000W = 0 3 3: W –3W – H2+ F =30 3 4: R 4 I –3I =490,000 4: R –41000W = 0 4 4: W –4W – H3+ F =40 4 BIT 3414 Copyright 2015 p. 3 Given the following information: Regular Prod. Capacity = 30,000 units/qtr Regular Prod. Cost = $10/unit Quarter Demand Subcontracting Capacity = 20,000 units/qtr Subcontracting Cost = $25/unit 1 30,000 2 60,000 Inventory Capacity = 10,000 units/qtr Inventory Cost = $5/unit/qtr Beginning Inventory = 4,000 units Backorder Cost = $10/unit/qtr 3 25,000 4 40,000 Production/employee = 2,000 units/qtr Hiring cost = $1000/ worker Beginning workforce = 10 workers Firing cost = $1500 / worker The company would like to determine the optimal mixture of the Level Production, Chase Demand, and Subcontracting strategies with a linear programming model. Decision Variables Objective Function Minimize Cost Z = 10R +110R + 102 + 10R 3 4 + 25S + 15S + 252 + 25S 3 4 + 5I 1 5I +25I + 3I 4 + 1000H + 1100H + 10002 + 1000H 3 4 + 1500F + 1500F + 15002 + 1500F 3 4 Constraints Capacity Production S: S 1 S 2 S 3 S 4 20,000 I: I1, 2 ,3I 4 I ≤ 10,000 2: R 2 2000W = 0 2 3: R – 2000W = 0 Demand 3 3 4: R 4 2000W = 0 4 Workforce 2: R + S + I – I = 60,000 2 2 1 2 3: R 3 S +3I – I2= 23,000 2: W –2W – H1+ F =20 2 4: R 4 S +4I – 3 = 44,000 3: W –3W – H2+ F =30 3 BIT 3414 Copyright 2015 4: W –4W – H3+ F =40 4 p. 4

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