THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017. IE 1055/2025 Homework 11 Due April 12, 2017 1. (20 pts) A single new facility is to be located relative to five existing facilities, which are located at the points P1 = (0,0), P2 = (1,3), P3 = (3,2), P4 = (4,1), and P5 = (5,4). The "weights" between the new facility and each existing facility are w1 = 4, w2 = 2, w3 = 6, w4 = 2, and w5 = 6. Rectilinear distance is to be used. (a) Determine the location for the new facility that minimizes the sum of the weighted distances. (b) Suppose a local ordinance requires that the new facility location satisfy the following constraints: x*  4 and y*  1 Where should the new facility be located in order to satisfy the local ordinance in an optimum fashion if the objective is still to minimize the sum of the weighted distances? How do you know this is an optimal location? Answer (20 Pts): . (a) (10 pts)  20iw 20/2=10 for the median condition X Y X value facility cum. wt Yvalue facility cum. wt 0 1 4 0 1 4 1 2 6 (6 10) 1 4 6 (6<10) 3 3 12 (12>10) 2 3 12(12>10) 4 4 14 3 2 14 5 5 20 4 5 20 x*=3 y*=2 The cost of the optimal solution is found by evaluating the point (3,2) cost = 4(|3-0|+|2-0|)+2(|3-1|+|2-3|)+6(|3-3|+|2-2|)+2(|3-4|+|2-1|)+6(|3-5|+|2-4|)=54THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017. (b) (10 pts) See the diagram on the next page. The candidates for the optimal solution based on looking at the diagram are (3,1) & (4,1). Evaluating their costs results in: (3,1) = 4 (|3-0|+|1-0|)+2(|3-1|+|1-3|)+6(|3-3|+|1-2|)+2(|3-4|+|1-1|)+6(|3-5|+|1-4|)=62 (4,1) = 4 (|4-0|+|1-0|)+2(|4-1|+|1-3|)+6(|4-3|+|1-2|)+2(|4-4|+|1-1|)+6(|4-5|+|1-4|)=66 Thus, (3,1) is optimal solution. You can also examine the blue contour line that runs through (3,1) and clearly see that it does not intersect any other point in the region bounded by (0,0), (0,1), (4,0), and (4,1). Note, the blue contour line runs through (3,1), (2,2), (2.5, 3), (3,3.5), (4,3), (4.5, 2), (4,1.5), (3, 1). ‐5 ‐5/2‐1‐1/213/2 ‐1 ‐21/2 15/25/32/31/323 ‐1‐3/2 ‐2/3‐1 ‐12 ‐8‐12 ‐8 4 8 20 20 844 2 6 266 2 6 2 4 (3, 3.5)(2.5,3)(2,2)(3,1)(4.5, 2) (4,1.5)(4,3)(5, 4) (1,3)(3,2)(4, 1)(0, 0) THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017. 2. (30 pts) In class we discussed a solution procedure for solving the minimax problem that entailed calculating values c1 to c5. We also discussed a related procedure for finding a minimax contour line using values c1(k) to c4(k). Create an Excel worksheet that will do these calculations automatically and find the two endpoints of the optimal minimax line segment or the 4 corner points of the minimax contour line box. The input to the Excel worksheet would be the x and y coordinates of the existing locations. Your Excel sheet should be able to handle a problem with up to 20 existing facilities. Use the minimax example problem solved in class to verity that your Excel worksheet calculates the values correctly. Submit the Excel worksheet using the HW 12 Excel assignment in the Assignments Folder on courseweb. Name your file “HW12Excel Name1, Name2, Name3” using the last names of your group members. Answer (30 Pts): Answers will vary depending on the Excel file submitted. 3. (20 pts) Compare and contrast warehouse operations at a Giant Eagle distribution center versus a Sears distribution center. Answer (20 Pts): - Many facets of the operations would be similar. For example, in both cases the DC is filling orders for individual stores and each store is pretty large. Both handle a wide range of different items. These different items may require picking entire cases/cartons or individual items. - Some facets would be different. Giant Eagle has to deal with FDA regulations since they are primarily handling food items. In addition, they have to be more concerned with refrigeration and frozen food requirements. - Giant Eagle will probably have more frequent orders to fill – partially due to the perishable nature of many foods. - Sears is likely to have more large items to move – grills, trampolines, lawn tractors, etc. and overall due to difference in the size of the products, the type, size and capacity of the material handling equipment will probably vary more for Sears. - Sears is more likely to have hazardous materials – paints, etc. - Both can have seasonal effects – though Sears may have more while Giant Eagle has more staple items that are demanded throughout the year. 4. (30 pts) You are an IE working at the Pittsburgh distribution center for Thriftco a large retail pharmacy chain. Thriftco is about to purchase a fleet of new fork trucks and is trying to decide between two different models - the Raymond 2090 and the Hyster 770A. Utilize the information below to answer the given questions.THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017. - Thriftco runs their distribution center for two eight hour shifts, Monday to Friday. - The Pittsburgh distribution center has an annual movement of 7.5 million feet per truck for their fork truck fleet. - Operator wages are $14 per hour. - Thriftco uses a minimum attractive rate of return of 10% when considering capital investments. Raymond Hyster 2090 770A Fuel cost ($ per foot) .0015 .0023 Maintenance cost ($ per day) 40 32 Lifetime (yrs) 10 12 Initial cost ($) 58000 45000 Salvage value ($) 8000 6500 a. Conduct an economic analysis to determine which fork truck will be cheaper to use based on the given information. b. What costs are likely to change over time? What would be the impact of those costs changing? (Don’t repeat the economic analysis – merely comment on their effects.) c. What other factors (not mentioned in the problem) would be important to consider in the economic analysis? Answer (30 Pts): a. - The economic analysis will be based on finding the annual equivalent cost of the two options. Note, you cannot just do an NPV analysis because the lifetimes of the two trucks are different. - Also, note that the operator wage rate is irrelevant because operator wages must be paid in either case. Please see the included Excel