Systems Optimization Sample Midterm 2

Systems Optimization Mid Term Exam Instructions You have two hours to complete the exam from the time you first begin it. Watch your time. If you are having difficulty with a question, you might wish to pass over it and return to it later if you have enough time at the end of the exam. The exam is open book: you may use any notes or text material. You are encouraged to use Excel to build your models. The exam is to be done individually, without collaboration with anyone else. Problem 1 (20 points) Consider the case of Auto power Europe trying to ship motors from the ports to the plants. The carriers are negotiating over the shipments. Answer each of the following questions arising during the discussions based on the information in the following Sensitivity Report (see the next page) a) What are the basic variables in this optimal solution? b) Is this the only optimal solution? c) One carrier would like to win business between Antwerp and Tilburg. At what price per unit would Auto power be willing to use this route? d) If we could shift a small amount of production from one plant to another, all else being equal, what plant would it be best to move production from and what plant should we move the production to? Microsoft Excel 8.0a Sensitivity Report Worksheet: [02TransportationModel.xls]Sheet1 Report Created: 2/9/02 4:27:30 PM Adjustable Cells Cell $C$9 $D$9 $E$9 $F$9 $C$10 $D$10 $E$10 $F$10 $C$11 $D$11 $E$11 $F$11 Name Amsterdam Leipzig Amsterdam Nancy Amsterdam Liege Amsterdam Tilburg Antwerp Leipzig Antwerp Nancy Antwerp Liege Antwerp Tilburg The Hague Leipzig The Hague Nancy The Hague Liege The Hague Tilburg Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 120 1E+30 0 23 130 1E+30 22.5 200 41 98.5 41 300 59.5 0 17.5 9 61 1E+30 8.5 700 40 8.5 1E+30 127 100 1E+30 126.5 118 110 1E+30 118 400 102.5 0 120 200 90 22.5 8.5 99 122 1E+30 98.5 200 42 17.5 0 Constraints Cell $C$12 $D$12 $E$12 $F$12 $G$9 $G$10 $G$11 Name Total Leipzig Total Nancy Total Liege Total Tilburg Amsterdam Total Antwerp Total The Hague Total Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 400 120 400 0 300 900 108 900 0 200 200 41 200 0 200 500 60 500 0 300 500 0 500 1E+30 700 (68) 700 200 0 800 (18) 800 300 0 Problem 2 (30 points) Extend the Transportation model for Auto power to accommodate the following enhancements. Demands for Auto power’s products outstrip its available supply of motors. In fact, demand in Liege has risen to 300. For various reasons including the competitive nature of the markets and the relative sizes of the customers, we estimate the cost of backordering (failing to meet current demand) at each plant to be: Plant Leipzig Liege Nancy Tilburg Cost per motor backordered $50 $70 $30 $100 a) Using the spreadsheet ExtendTransportation.xls, build a a Network Flow model that simultaneously minimizes the shipping and backordering costs. b) Formulate a (pseudo) AMPL model of the problem (Do not worry about reading the data, just formulate the model by describing the sets, parameters, variables, objective and constraints Problem 3 (30 points) Suppose the Singapore Electric Generator Company must send its completed generators to Australia for testing before they can be sold. This process takes an entire month so that, for example, generators made in January are not available for sale until February. Extend the Singapore Electric Generator Model accommodates this delay. Problem 4 (20 points) Provide brief answers to the following questions. (a) Give an example of an optimal, but not basic solution to a network flow problem. (b) How many basic variables will there be in a basic feasible solution to a balanced Transportation Problem (supply equals demand) like Auto power’s, but with 4 ports and 5 plants?