ADM2302 A, B, C, D, E Fall 2015 Assignment # 3 Assignment #3 Transportation Problems, Integer and Binary Programming and Goal programming, ADM2302 students are reminded that submitted assignments must be neat, readable, and well-organized. Assignment marks will be adjusted for sloppiness, poor grammar and spelling, as well as for technical errors. Please note that: While working together is encouraged, plagiarism on assignments will not be accepted. Each student must sign the individual statement of integrity to be included with the submission. Each student must provide an individual original submission of completed Assignment #3. Students should submit a PDF of their type-written (i.e., not handwritten) assignment via blackboard learn by the due-date on Tuesday, November 17, 11:59 P.M. Problem1: This problem is a combination of binary integer programming and transportation problem A company has 6 sales centers in Ontario and has decided to open new depots to deliver its products from the depots to the sales centers. There are two types of cost associated with the delivery: set-up costs (fixed costs) are capital costs which may usually be written off over several years, and transportation costs which depend on the distance covered. We assume that they have been put on some comparable basis, by taking the costs over a year. There are 6 sites available for the construction of new depots to deliver products to the sales centers. The following table (Table 1) gives the transportation costs (in thousand dollars) of delivering the entire demand of each sales center from a depot (not the unit costs). Certain deliveries that are impossible are marked with the infinity symbol . Sales Centers Depot 1 2 3 4 5 6 1 100 80 50 50 60 100 2 120 90 60 70 65 100 3 140 110 80 80 75 130 4 160 125 100 100 80 150 5 190 150 130 6 200 180 150 Table 1: Transportation costs for satisfying entire demand of each sales center The construction costs (fixed cost) for each depot as well as the capacity of each depot are listed in Table 2. Fall 2015 Page 1 ADM2302 A, B, C, D, E Fall 2015 Assignment # 3 Depot 1 2 3 4 5 6 Cost(1000$) 3500 9000 10000 4000 3000 9000 Capacity(tons) 300 250 100 180 275 300 Table 2: Fixed costs and capacity limits of the depot locations There are estimations for demand of each sales center which are shown in the following table. Sales center Demand (tons) 1 2 3 4 120 80 75 100 Table 3: Demand data 5 110 6 100 Considering that the demand of a sales center needs to be satisfied and a sales center may be delivered to from several depots, which depots should be opened to minimize the total cost of construction and of delivery, while satisfying all demands? Formulate algebraically the corresponding model for this problem, but Do NOT solve the problem. Problem2: A car rental company has decided to provide roadside services for 6 zones in a large city. The company wants to determine where (zone) to locate the roadside assistances. To reduce the company's costs the manager wants to locate a minimum number of roadside assistance and ensure that at least one assistance is near 15 minutes of each zone. The times (in minutes) required to drive between zones are: To From 1 2 3 4 5 6 1 0 10 20 30 20 20 2 10 0 25 35 20 10 3 20 25 0 15 30 20 4 30 35 15 0 15 25 5 20 20 30 15 0 14 6 20 10 20 25 14 0 Formulate an integer/binary programming model that will select the minimum number of roadside assistance that the company will need to achieve its policy objective. Do NOT solve the problem. Fall 2015 Page 2 ADM2302 A, B, C, D, E Fall 2015 Assignment # 3 Problem3: Capital budgeting A firm has 6 projects that it would like to undertake over the next 5 years but because of budget limitations not all can be selected. The total budget that the firm has considered to invest in the projects is $12,400,000. The following table displays the expected revenue (NPV) of each project after 5 years and the required yearly capital for each investment. Table 1: Investment Details Capital (in $000) required per year Investment/ Project 1 2 3 4 5 6 Expected NPV ($000) $2700 $3330 $7010 $5770 $2900 $4870 Year 1 $ 975 $1200 $2500 $1550 $1400 $1900 Year 2 $ 350 $ 200 $1200 $1350 $ 350 $1900 Year 3 $ 200 $ 200 $ 850 $ 675 $87.5 $ 350 Year 4 $ 100 $ 200 $ 400 $ 337.5 $ 21.875 $ 350 Year 5 $ 50 $ 200 $ 400 $168.75 $ 0 $ 350 The capital available in time period each year is shown in the following table: (The $12,400,000 in investment capital is spread over the 5 years) Year 1 $ 5800 Capital (in $000) allocated per year Year 2 Year 3 Year 4 $ 3500 $ 1300 $ 900 Year 5 $ 900 In addition, the firm must follow a few federal and state laws regarding these projects: 1. 2. 3. Surplus capital funds in any year cannot be carried over from year to year. If the firm decides to invest in the second investment/project, it must also invest in the fourth. If the firm decides to invest in the first investment/project, it cannot invest in the third investment/project. Considering the budget limitations and the laws, which of the investments/projects should be chosen to maximize potential NPV? (Recommend the firm)Formulate the Integer Linear Programming model in algebraic form, and using Excel's Solver to find a solution. Provide a printout of your answer report (Attach the excel file to your submission) Fall 2015 Page 3 ADM2302 A, B, C, D, E Fall 2015 Assignment # 3 Problem4: Goal Programming A large bookstore in Ottawa operates 7 days per week. This bookstore needs the following number of full-time employees working each day of the week: Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Number of employees 47 22 28 35 34 43 53 Each employee must work 5 consecutive days each week and then have 2 days off. For example, any employee who works Sunday through Thursday has Friday and Saturday off. This bookstore currently has a total of 60 employees available to work. The director of the department has developed the following set of prioritized goals for employee scheduling: (1) The store wants to avoid hiring any additional employees. Weight=40 (2) The most important days for the department to be fully staffed are Saturday and Sunday. Weight=31 (3) The next most important day to be fully staffed is Friday. Weight=25 (4) The department would like to be fully staffed the remaining 4 days in the week. Weight=20 Formulate a goal programming model to determine the number of employees who should begin their 5-day workweek each day of the week to achieve the department's objectives. Do NOT solve the problem. Fall 2015 Page 4