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COLUMBIA BUSINESS SCHOOL B6015: Decision Models Spring 2008 Optimization Homework 2 This assignment is to be done in groups. In your write-up, answer all the questions and provide a thorough description of your models. Each question must be answered in words and also must include a printout of the spreadsheet (as described below). Instructions on the Write-Up Try to limit your write-up to one page of text with support exhibits attached. The exhibits should include, for each problem, a printout of your optimized spreadsheet (on one page if possible). Please follow the style of the sample below: all important formulas are described, constraints are included graphically as “<=” and all important parts of the spreadsheet are labeled. Of course, the labeling can be handwritten. Another option is to use the comments feature in Excel. To write a comment: either right-click on a cell (and choose “Insert Comment”) or from the menu choose “Insert|Comment”. To get the comments to print: go to File|Page Setup and then pick the Sheet tab and pick “Comments: as displayed on sheet.” Click OK or Print. To get the file to print with row and column headings: go to File|Page Setup and pick the Sheet tab and check off “row and column headings.” Click OK or Print. A B 1 BLAND.XLS 2 3 Product: 4 Barrels to Produce: 5 Profit per Barrel: 6 7 8 9 Ingredients: 10 Corn (lbs) 11 Hops (ozs) 12 Malt (lbs) 13 14 15 C D E Bland Brewery Production Problem Ale 12 $13 Beer 28 $23 F Total Profit: $800 Product Ingredient Requirements Total Ale Beer Usage 5 15 480 4 4 160 35 20 980 =SUMPRODUCT($C$4:$D$4,C11:D11) <= <= <= G H I Decision Variables C4:D4 Objective Function =SUMPRODUCT(C4:D4,C5:D5) Quantity Available: 480 160 1190 Problem 1: CitiSavings and BankZero Merger (60 points) CitiSavings (see Problem 2 in Optimization Homework 1) intends to merge with BankZero, which has its own set of processing centers for credit card bills. BankZero’s processing centers are in Toledo, OH and Atlanta, GA. The processing capabilities of the full set of processing centers are as follows: Los Angeles Chicago New York Toledo Atlanta 60,000 105,000 100,000 135,000 155,000 Daily processing capacity By region, the daily number of bills to be processed for the two companies’ combined customer bases, and the transit times are as follows: Bills to be processed Los Angeles Chicago New York Toledo Atlanta West 100,000 2 6 8 6 8 Midwest 150,000 6 2 5 2 5 East 100,000 8 5 2 5 5 South 100,000 8 5 5 5 2 CitiSavings recognizes that the combined operations would have significant excess capacity and contemplates saving money by closing some of the processing centers. CitiSavings estimates that the cost of closing down a facility is negligibly small, while the daily fixed costs of operating the five facilities are as follows: Fixed daily operating cost Los Angeles Chicago New York Toledo Atlanta $12,000 $21,000 $20,000 $40,000 $30,000 CitiSavings would like to minimize the sum of the operating costs of the facilities, plus the float. a) (30 points) Formulate and solve this decision model. According to your analysis, which facilities should be closed down? b) (30 points) CitiSavings’ management would like to consider the expansion of the capacity at the Los Angeles processing center as another option within an overall consolidation plan. That is, in addition to either closing the center or leaving it at the current capacity, they want to consider adding the option of expanding LA’s capacity by 15,000 bills-per-day. The additional cost would be $3,000 per day. Extend the formulation of your problem in a) to B6015 Optimization Homework 2 2 include this additional option and solve the resulting model. Will this extra-capacity option be exercised? Problem 2: Profit Maximization at Campbell Motors (40 points) Campbell Motors is an auto dealership that specializes in the sales of cars, station wagons and light trucks. Due to its reputation for quality and service, Campbell has a strong position in the regional market, but demand remains somewhat sensitive to price. While evaluating the new models, Campbell’s marketing consultant has come up with the following monthly demand curves in which price are expressed in thousands of dollars: Car Demand = 600 – 25 x (Car Price) Truck Demand = 500 – 18 x (Truck Price) Wagon Demand = 400 – 11 x (Wagon Price) For example, if the car’s price is set at $20,000, the monthly demand for cars will be 600 – 25 x 20 = 100. The dealership’s unit costs are $17,000 for cars, $20,000 for trucks and $25,000 for wagons. Each car requires one hour of prep labor, while each truck requires three hours of prep labor, and each wagon requires two hours of prep labor. The current staff can supply 350 hours of labor each month. Determine prices at which Campbell Motors can maximize its monthly profit from the sales of cars, trucks and wagons (Allow for fractional demands). B6015 Optimization Homework 2 3