Flashcards and Answers – CH 6 – Assignment Writing
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The problem which deals with the distribution of goods from several sources to several destinations is the
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transportation problem
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The parts of a network that represent the origins are
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the nodes
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The objective of the transportation problem is to
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minimize the cost of shipping products from several origins to several destinations.
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The number of units shipped from origin i to destination j is represented by
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xij
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Which of the following is not true regarding the linear programming formulation of a transportation problem?
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The number of constraints is (number of origins) × (number of destinations).
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The difference between the transportation and assignment problems is that
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each supply and demand value is 1 in the assignment problem
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In the general linear programming model of the assignment problem,
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one agent is assigned to one and only one task.
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The assignment problem is a special case of the
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transportation problem.
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Which of the following is not true regarding an LP model of the assignment problem?
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All constraints are of the ≥ form.
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The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means
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agent 3 can be assigned to 2 tasks.
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Arcs in a transshipment problem
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indicate the direction of the flow.
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Constraints in a transshipment problem
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include a variable for every arc.
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In a transshipment problem, shipments
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can occur between any two nodes.
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Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network,
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the branches and the operations center are all nodes and the streets are the arcs.
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The shortest-route problem finds the shortest-route
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from the source to any other node.
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Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city. When represented with a network,
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the arcs represent one way streets.
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We assume in the maximal flow problem that
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the flow out of a node is equal to the flow into the node.
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(T/F) Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.
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T
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(T/F) Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.
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T
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(T/F) A transportation problem with 3 sources and 4 destinations will have 7 decision variables.
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F
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(T/F) If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.
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T
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(T/F) The capacitated transportation problem includes constraints which reflect limited capacity on a route.
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T
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(T/F) 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.
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F
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(T/F) A transshipment constraint must contain a variable for every arc entering or leaving the node.
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T
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(T/F) The shortest-route problem is a special case of the transshipment problem
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T
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(T/F) Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.
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T
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(T/F) A dummy origin in a transportation problem is used when supply exceeds demand.
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F
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(T/F) When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation.
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T
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(T/F) In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.
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F
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(T/F) The maximal flow problem can be formulated as a capacitated transshipment problem.
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T
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(T/F) The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.
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T
