GSB 622 Decision Support Systems
LINEAR PROGRAMMING & EXCEL SOLVER
PART B: LINEAR PROGRAMMING EXAMPLE — MINIMIZATION
The Electro-Wiley Corporation is the world’s leading manufacturer of slip rings. A slip ring is an electrical coupling device that allows current to pass through a spinning or rotating connection – such as a gun turret on a ship, aircraft or tank. The company recently received a $750,000 order for various quantities of three types of slip rings. Each slip ring requires a certain amount of time to wire and harness. The following table summarizes the requirements for the three models of slip rings.
Model 1 Model 2 Model 3
Number ordered 3000 2000 900
Hours of wiring required per unit 2 1.5 3
Hours of harnessing required per unit 1 2 1
Unfortunately, Electro-Wiley does not have enough wiring and harnessing capacity to fill the order by its due date. The company has only 10,000 hours of wiring capacity and 5,000 hours of harnessing capacity available to devote to this order. Should the company reject the business because it cannot handle the entire job? Or should the company subcontract a portion of the order to one of its competitors?
The unit costs of producing each model in-house and buying the finished products from a competitor are provided here:
Model 1 Model 2 Model 3
Cost to make $50 $83 $130
Cost to buy $61 $97 $145
Decision Variables:
X1 number of Model 1 slip rings to make in-house
X2 number of Model 2 slip rings to make in-house
X3 number of Model 3 slip rings to make in-house
X4 number of Model 1 slip rings to buy from a competitor
X5 number of Model 2 slip rings to buy from a competitor
X6 number of Model 3 slip rings to buy from a competitor
The linear programming model representation of this problem consists of:
Minimize: 50X1 + 83X2 + 130 X3 + 61 X4 + 97 X5 + 145 X6 cost
Constraints: X1 + X4 = 3000 demand for Model 1
X2 + X5 = 2000 demand for Model2
X3 + X6 = 900 demand for Model 3
2 X1 + 1.5 X2 + 3 X3 <=10000 wiring constraint
1 X1 + 2 X2 + 1 X3 <= 5000harnessing constraint
All decision variables must be nonnegative
Use Excel Solver (as explained in subsequent pages) to determine the optimal number of each
model to make and to buy in order to minimize cost.
Analyze the Answer Report that is produced and answer the following questions. Then upload the spreadsheet AND your answers to these questions as well for credit.
1. According to the Solver solution, what is the optimal number of Model 1 slip rings to make? ___________________ to buy? ________________
2. According to the Solver solution, what is the optimal number of Model 2 slip rings to make? ___________________ to buy? ________________
3. According to the Solver solution, what is the optimal number of Model 3 slip rings to make? ___________________ to buy? ________________
4. What is the total cost? __________________________________________
5. How much of the wiring will remain unused? __________________________________
6. Which slip ring Model does Solver indicate should be purchased in greatest number from a competitor? ___________________________________________________________
Why do you think that Solver is recommending a significant purchase of this particular Model over the other two? Explain your answer.
Decision Support Systems
LINEAR PROGRAMMING & EXCEL SOLVER
PART A: LINEAR PROGRAMMING EXAMPLE — MAXIMIZATION
You have been hired as a financial manager for Real Cool Hot Tubs (you cannot wait to get promoted high enough to change the company name!). The company sells two models of hot tubs: Aqua-Max and Hydro-Super. The company purchases prefabricated fiberglass hot tub shells and installs a common water pump and tubing into each hot tub. Every Aqua-Max requires 9 hours of labor and 12 feet of tubing. Every Hydro-Super requires 6 hours of labor and 16 feet of tubing. Demand for these products is such that each Aqua product can be sold to generate a profit of $350 and each sale of Hydro generates a profit of $300. The company expects to have 200 pumps, 1566 hours of labor and 2880 feet of tubing available for the next production cycle. You have been charged with determining the optimal number of each model to produce in order to maximize profits.
The linear programming model representation of this problem consists of:
Maximize: 350X1 + 300 X2 profit
Constraints: 1X1 + 1X2 <= 200 pump constraint
9X1 + 6X2 <= 1566 labor constraint
12X1 + 16X2 <= 2880 tubing constraint
1X1 >= 0 simple lower bound
1X2 >= 0 simple lower bound
Use Excel Solver (as explained on subsequent pages) to determine the optimal number of each model of hot tub to produce in order to maximize profit.
Analyze the Answer Report that is produced and answer the following questions.
Then upload the spreadsheet AND your answer to these questions for credit.
According to the Solver solution, what is the optimal number of Aqua tubs to produce given the constraints of the problem? _________________________
According to the Solver solution, what is the optimal number of Hydro tubs to produce given the constraints of the problem? _________________________
If the company does indeed produces these optimal numbers of tubs, what is the _______________________________________
If the company does indeed produces these optimal numbers of tubs, how many pumps will be left unused? __________________________________________
If the company does indeed produces these optimal numbers of tubs, how many labor hours will remain unused? ______________________________________
If the company does indeed produces these optimal numbers of tubs, how many feet of available tubing will remain unused?
