MGT 2251 Exam 2

Cable TV companies would employ the shortest-route technique to play our the cases connected individual houses. T/F

False

When formulating a transportation problem with 2 sources and 4 destination as an LP problem, which of the following statements is true? A. There will be 6 decision variables and 8 constraints (excluding non-negativity) B. There will be 6 decision variables and 4 constraints (excluding non-negativity) C. There will be 8 decision variables and 6 constraints (excluding non-negativity) D. There will be 4 decision variables and 6 constraints (excluding non-negativity)

There will be 8 decisions variables and 6 constraints (excluding non-negativity)

A transportation problem with intermediate points is called a transshipment problem. T/F

True

A traveling salesperson might use the shortest route technique to minimize the distance traveled to reach one of his/her customers. T/F

True

A typical transportation problem may ask the question, "How many of X should be shipped to point E from source A?" T/F

True

Which of the following is false? A. Maximal-flow technique can be used to study traffic congestions problem between two points on a road network B. Internet service providers typically employ minimal-spanning tree technique to provide able and internet connections to houses C. Package delivery companies use shortest route techniques to deliver packages D. Water supply companies would employ the shortest-route technique to lay out pipes to individual homes

Water supply companies would employ the shortest-route technique to lay out the pipes connecting individual houses

Facility Location Analysis (Key Characteristics)

- Transportation method is useful here - Final decisions involves minimizing total shipping and production costs - solve two transportation problems, one for each combination -Xij= number of units shipped from source i to destination j -Constraints: quantities coming from each source to destination j must = demand at j. And, total leaving i to various j's must must be <= supply at i.

Assignment Problem (Key Characteristics)

-Define type of function -Network Model: supply of 1, demand of 1 -Define decision variable: Xij= 1 if the person is assigned to a project, 0 if not -Objective: minimize total costs or time of performing tasks at hand -Special type of transshipment problem where the supply at the source and the demand at the destination must equal 1 -Each person may only be assigned to one job, each job needs only one person -Constraints: supply coming from each source must be <= 1 and demand being received at each destination must = 1.

Transportation Problem (Key Characteristics)

-distribution of goods from several points of supply to a number of points of demand. -given capacity of goods at source, requirements at destination -objective: minimize total transportation and production costs -Xij= number of units shipped from source i to destination j - contraints: the quantity leaving source i must be <= to supply at source i and amount of demand coming into destination j must = required demand

Facility Location Analysis (Transportation method is especially useful)

Alternate locations are to be evaluated, subjective factors are considered, final decisions also involved minimizing total shipping and production costs. Solve two transportation problems, one for each combo.

Minimal-spanning Tree Problem

Connecting all the points of a network together while minimizing the distance between them.

Shortest-Route Problem constraints

Constraints only specify the number of units going into a node must equal the number of units going out of the node

Transportation Problem

Deals with the distribution of goods from several points of supple (sources) to a number of points of demand (destinations) Usually given the capacity of goods at each source and the requirements at each destination. Typically the objective is to minimize total transportation and production costs.

Assignment Problem

Determines the most efficient assignment of people or equipment to particular tasks. Objective is to minimize total cost or task time. Constraints = or <= 1. Use binary for 1=assignment 0=not assigned

Maximal-Flow Problem

Determining the maximum amount of material that can flow from one point (the source) to another (the sink) in a network. Special type of transshipment problem with one source, one destination, and a number of transshipment points. The number shipped through the network is the flow. (Not represented in cell-format)

In a transportation problem, each destination must be supplied by one and only one source. T/F

False

In the assignment problem, the costs for a fake? row will be equal to the lowest cost of the column for each respective cell in that row. T/F

False

In the minimal-spanning tree technique, it is necessary to start at the last node in the network. T/F

False

Lines connecting nodes on a network are called links. T/F

False

The minimal spanning tree technique finds the shortest route to a series of destinations. T/F

False

The shortest route technique is the same as the minimal spanning tree technique. T/F

False

The transshipment problem is a maximization problem. T/F

False

Shortest-Route Problem

Find the shortest distance from one location to the other. Can be modeled as a LP with 0-1 variables as a special type of transshipment problem. Or using a specialized algorithm. One source with a supply of 1, and one destination with a demand of 1, and a number of transshipment points.

Transshipment Problem

Items are being moved from a source to a destination through an intermediate point. There are source, destination, and transshipment nodes. Sources have supply quantities and destinations have demand quantities. Typically to minimize transportation costs.

A technique that allows a researcher to determine the greatest amount of material that can move through a network is called: A. Maximal-flow B. Maximal-spanning C. Shortest-route D. Maximal-tree

Maximal-flow

Maximal-Flow Contraints

The first set is to restrict the amount of flow on any arc to the capacity of that arc. The second set is to indicate the amount of flow out of the node will equal the amount of flow going into that node.

Assignment problems involve determining the most efficient assignment of people to projects, salesmen to territories, contracts to bidders, and so on. T/F

True

Busy highways are often analyzed with the maximal flow technique. T/F

True

In a transportation problem, a single source may supply something to all destinations. T/F

True

In the maximal-flow model technique a zero (0) means no flow or on-way arc. T/F

True

In the minimal-spanning tree technique, if there is a tie for the nearest node, that suggests there may be more than one optimal solution. T/F

True

The maximal-flow model assumes that there is a net flow from "source" to "sink".

True

The maximal-flow model might be of use to an engineer looking for spare capacity in an oil pipeline system. T/F

True

The maximal-flow modell technique might be used by the US Army Corps of Engineers to study water run-off in an attempt to minimize danger from floods. T/F

True

The maximal-flow technique would be helpful to city planners in determining how freeways should be expanded. T/F

True

The minimal-spanning tree technique determines the path through the network that connects all the points while minimizing total distance. T/F

True

The objective of a transportation problem solution is to schedule shipments from sources to destinations while minimizing total transportation and production costs. T/F

True

The objective of an assignment problem most often is to minimize the total costs or time of performing the assigned tasks. T/F

True

The points on the network are referred to as nodes. T/F

True

The shortest route model assumes that one is trying to connect two end points in the shortest manner possible, rather than attempting to connect all nodes in the model. T/F

True

The shortest-route technique might be used by someone palling a vacation in order to minimize the required amount of driving. T/F

True

Transportation companies would definitely be interested in the shortest-route technique to optimize travel. T/F

True

Transportation model may be used when a firm is trying to decide where to location a new facility. T/F

True

We may begin the maximal-flow technique by picking an arbitrary path through the network. T/F

True

In a minimal-spanning tree problem, the optimal solution has been found when: A. all nodes have been connected and are part of the tree B. the start node and the finish node are connected by a continuous path C. the flow from the start bode is equal to the flow into the finish node D. all arcs have been selected to be a part of the tree

all nodes have been connected and are part of the tree

The first step in the minimal-spanning tree technique is to: A. select the node with the highest distance b/t it and any other node B. select the node that is closest to the origin C. select any arc that connects 2 nodes D. select any node

select any node

The original or beginning node in a network is called a(n): A. arc B. branch C. source D. mouth E. sink

source

In solving a facility location problem in which there are two possible location being considered, the transportation algorithm may be used. In doing this: A. two sources would be added to the existing rows and the enlarged problem would be solved B. two separate transportation problems would be solved C. costs of zero would be used for each of the new facilities D. the problem would be a transshipment problem

two separate transportation problems would be solved