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https://ceprofs.civil.tamu.edu/ezechman/CVEN665/winston_ch9_Part2.pdf INSY 3410-Midterm Exam 2 November 13, 2002 3-hours and total 127 points: Q1-20, Q2-20, Q3-10, Q4-10, Q5-25, Q6-20, Q7-12, Q8-10 1 ) A company is considering opening warehouses in four cities: New York, Los Angles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse open is $400 for New York, $500 for Los Angles, $300 for Chicago, and $150 for Atlanta. Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs of sending one unit from a plant to a region are shown in the following table. To From Region 1 Region 2 Region 3 New York (NY) $20 $40 $50 Los Angles (LA) $48 $15 $26 Chicago (CH) $26 $35 $18 Atlanta (AT) $24 $50 $35 We want to meet weekly demands at minimum cost, subject to following restrictions If the New York warehouse is opened, the Los Angeles warehouse must be opened. At most two warehouses can be opened. Either the Atlanta or the Los Angles warehouses must be opened. Formulate a MIP model for the problem. Briefly define decision variables and constraints. Solution: Xij= units shipped from city i to region j, i=1,2,3,4 and j=1,2,3. Yi= 1 if a warehouse is opened in city i, 0 otherwise. Min z= 20X11+40X12+50X13+…+35X43+400Y1+500Y2+300Y3+150Y4 st. CAPACITY AND FIXED CHARGE CONSTRAINTS X11+X12+X13 <= 100Y1 X21+X22+X23<=100Y2 X31+X32+X33 <=100Y3 X41+X42+X43<=100Y4 DEMAND CONSTRAINTS X11+X21+X31+X41 >=80 X12+X22+32+X42 >=70 X13+X23+X33+X43>=40 Y1 <= Y2 (if NY is opened, then LA must be opened) Y1+Y2+Y3+Y4<=2 (at most two warehouses can be opened) Y2+Y4 >=1 (either AT or LA must be opened. Both are ok) 1
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2) A convenience store chain is planning to enter a growing market and must determine where to open several new stores. The following map shows the major streets in the area being considered and proposed locations for convenience stores indicated by squares. A 1 2 3 4 5 B C D E 2 1 3 4 5 6 7 8 9 10 Stores are going to be placed at the intersections of streets running north-south and east-west so that they can serve two streets. Adjacent streets are 1 mile apart. All travel must follow the street network, so distance is determined with a rectilinear metric. For instance, the distances between corners A1 and C2 is 3 miles. The chain wants to maximize the number of stores to be opened with the following restrictions: No two stores selected can be on the same street (either north-south or east-west). Stores must be at least three miles apart. Stores exactly three miles apart are acceptable. For example, if a
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