HW3 S12 [PDF]

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INDE4372 Operations Control Homework 3 - Spring 2012 (Due Thursday April 5, beginning of the class) 1. (40 pts) The Paris Paint Company is in the process of planning labor force requirements and production levels for the next four quarters. The marketing department has provided production with the following forecasts of demand for Paris Paint over the next year: Quarter 1 2 3 4



Demand Forecast (in thousands of gallons) 380 630 220 160



Assume that there are currently 280 employees with the company, Employees are hired to at least one full quarter. Hiring costs amount to $1,200 per employee and firing costs are $2,500 per employee. Inventory costs are $1 per gallon per quarter. It is estimated that one worker produces 1,000 gallons of paint each quarter. Assume that Paris currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons. Formulates this problem as a linear program. Assume that stock-outs are not allowed. 2. Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Michigan. Based on orders received and forecasts of buying habits, it is estimated that the demand for the first month is equal to 100,000× DD, the second month is equal to 30,000× MM, third month is equal to 1,000×YYYY and the fourth month is equal to the number of letters in your first name times 50,000, where MM-DD-YYYY is your date of birth. During a 30-day period when there were 200 workers, the company produced 1.5 million cookies. Assume that the number of workdays over the four months are respectively 26, 24, 20, and 16. There are currently 200 workers employed, and there are currently 500,000 cookies in the store. Assume cost of holding one unit of stock for one period is $10 and cost of firing the workers is $200. Suppose that the cost of hiring workers in each period is $100 for each worker until 20 workers are hired, $400 for each worker when between 21 and 50 workers are hired, and $700 for each worker hired beyond 50. • (30 pts) First, define your decision variables and parameter values explicitly. Then, write down the complete Linear Programming formulation to minimize the cost of Mr. Meadows Cookie Company. • (30 pts) Solve the LP formulation above using a solver (Excel solver, GAMS, Lindo/Lingo, Cplex, FICO Xpress etc.) Submit your code (via email: [email protected] with Subject: INDE4372) and your complete result. Determine the optimal value and optimal solution for your problem.



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