Exam 6: Distribution and Network Models

A transportation problem with three sources and four destinations will have seven decision variables.

In an assignment problem,one agent can be assigned to several tasks.

Consider the following shortest-route problem involving six cities with the distances given.Draw the network for this problem and formulate the LP for finding the shortest distance from City 1 to City 6.

The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.

The shortest-route problem is a special case of the transshipment problem.

There are two specific types of problems common in supply chain models that can be solved using linear programing: transportation problems and transshipment problems.

In a capacitated transshipment problem,some or all of the transfer points are subject to capacity restrictions.

Arcs in a transshipment problem

The assignment problem constraint x₃₁ + x₃₂ + x₃₃ + x₃₄ ≤ 2 means

The assignment problem is a special case of the transportation problem in which one agent is assigned to one,and only one,task.

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,

In a maximal flow problem,

The shortest-route problem finds the shortest route

A plant manager for a sporting goods manufacturer is in charge of assigning the manufacture of four new aluminum products to four different departments.Because of varying expertise and workloads,the different departments can produce the new products at various rates.If only one product is to be produced by each department and the daily output rates are given in the table below,which department should manufacture which product to maximize total daily product output? (Note: Department 1 does not have the facilities to produce golf clubs.) ​ ​ Formulate this assignment problem as a linear program.

RVW (Restored Volkswagens)buys 15 used VW's at each of two car auctions each week held at different locations.It then transports the cars to repair shops it contracts with.When they are restored to RVW's specifications,RVW sells 10 each to three different used car lots.Various costs are associated with the average purchase and transportation prices from each auction to each repair shop.There are also transportation costs from the repair shops to the used car lots.RVW is concerned with minimizing its total cost given the costs in the table below.

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.

A network of railway lines connects the main lines entering and leaving a city.Speed limits,track reconstruction,and train length restrictions lead to the flow diagram below,where the numbers represent how many cars can pass per hour.Formulate an LP to find the maximal flow in cars per hour from node 1 to node F.​

In the general linear programming model of the assignment problem,

A transshipment problem is a generalization of the transportation problem in which certain nodes are neither supply nodes nor destination nodes.

Draw the network for this assignment problem.