Study Guide for Exam 2 Student 2019 PDF

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Study Guide Exam 2...

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St udyGui def o rEx am 2 Topic 4.1 &4.2/Chapter 6: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Be able to identify the special features of the transportation problem. Become familiar with the types of problems that can be solved by applying a transportation model. Be able to develop linear programming models of the transportation problem. Know how to handle the cases of (1) unequal supply and demand, (2) unacceptable routes, and (3) maximization objective for a transportation problem. Be able to identify the special features of the assignment problem. Become familiar with the types of problems that can be solved by applying an assignment model. Be able to develop linear programming models of the assignment problem.

10.

Be familiar with the special features of the transshipment problem. Become familiar with the types of problems that can be solved by applying a transshipment model. Be able to develop linear programming models of the transshipment problem.

11. 12.

Know the basic characteristics of the shortest route problem. Be able to develop a linear programming model and solve the shortest route problem.

13.

Understand the following terms: network flow problem transportation problem origin destination assignment problem

capacitated transshipment problem shortest route maximal flow transshipment problem

True or False __1. Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints. __2. A transportation problem with 3 sources and 4 destinations will have 7 decision variables. __3. When the number of agents exceeds the number of tasks in an assignment problem, one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution. __ 4. A transshipment constraint must contain a variable for every arc entering or leaving the node. __5. The shortest-route problem is a special case of the transshipment problem. __6. When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation. __7. The number of variables is (number of origins) x (number of destinations) in the linear programming formulation of a transportation problem. __8. The assignment problem is a special case of the transportation problem in which all supply and demand values equal one. 9. The shortest route network problem could help identify the best route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois. Multiple Choice ___ 1. The problem which deals with the distribution of goods from several sources to several destinations is the a. maximal flow problem b. transportation problem c. assignment problem d. shortest-route problem ___ 2. In the general linear programming model of the assignment problem, a. one agent can do parts of several tasks. b. one task can be done by several agents. c. each agent is assigned to its own best task. d. one agent is assigned to one and only one task. ___3. The objective of the transportation problem is to a. identify one origin that can satisfy total demand at the destinations and at the same time

minimize total shipping cost. b. minimize the number of origins used to satisfy total demand at the destinations. c. minimize the number of shipments necessary to satisfy total demand at the destinations. d. minimize the cost of shipping products from several origins to several destinations. ___ 4. If a transportation problem has four origins and five destinations, except for non-negative constraints, the LP formulation of the problem will have a. 5 constraints b. 9 constraints c. 18 constraints d. 20 constraints ___5. Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network, a. the branches are the arcs and the operations center is the node. b. the branches are the nodes and the operations center is the source. c. the branches and the operations center are all nodes and the streets are the arcs. d. the branches are the network and the operations center is the node. Problems

1. A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly match capacities and requirements. Data on transportation costs (in dollars per unit), capacities, and requirements are given below. Plant A B C Requirement

Warehouse 1 2 3 5 6 10 3 7 8 4 9 2 800 200 300

Capacities 400 600 300

Write down the linear programming model for this problem.

2. Three employees are available to perform two jobs. The time it takes each person to perform each job is given in the following table. Determine the algebraic model to assign employees to the jobs that minimizing the total time required. Person Job 1 Job 2 1 22 minutes 16 minutes 2 27 minutes 18 minutes 3 16 minutes 21 minutes

3. Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Formulate the algebraic model for finding the shortest distance from the source node (node 1) to nodes 6.

4. The Western Paper Company manufactures paper at two factories (F1 and F2) on the West

coast. Their products are shipped by rail to a pair of depots (D1 and D2), one in the Midwest and one in the South. At the depots, the products are repackaged and sent by truck to three reginal warehouses (W1, W2, and W3) around the country, in response to replenishment orders. Each of the factories has a known monthly production capacity and the three regional warehouses have placed their demands for next month. The following tables summarize the data that have been collected for this planning problem. (To) DC (From) Factory D1 D2 Capacity F1 $1.28 1.67 2500 F2 $1.33 1.40 2500

(From) DC D1 D2 Requirement

W1 $.68 $.57 1700

(To) Warehouse W2 .42 .30 1500

W3 .32 .44 1800

The network representing the shipping routes are shown below.

Knowing the costs of transporting goods from factories to DCs and from DCs to warehouses as in the above table, Western Paper is interested in planning its shipment at the minimum possible cost. Please write down the Algebraic model for this problem....