Exam 6: Distribution and Network Models

The problem which deals with the distribution of goods from several sources to several destinations is the

Fodak must schedule its production of camera film for the first four months of the year. Film demand (in 1,000s of rolls) in January, February, March and April is expected to be 300, 500, 650 and 400, respectively. Fodak's production capacity is 500 thousand rolls of film per month. The film business is highly competitive, so Fodak cannot afford to lose sales or keep its customers waiting. Meeting month i 's demand with month i +1's production is unacceptable. Film produced in month i can be used to meet demand in month i or can be held in inventory to meet demand in month i +1 or month i +2 (but not later due to the film's limited shelflife). There is no film in inventory at the start of January. The film's production and delivery cost per thousand rolls will be $500 in January and February. This cost will increase to $600 in March and April due to a new labor contract. Any film put in inventory requires additional transport costing $100 per thousand rolls. It costs $50 per thousand rolls to hold film in inventory from one month to the next. a. Modeling this problem as a transshipment problem, draw the network representation. b. Formulate and solve this problem as a linear program.

A foreman is trying to assign crews to produce the maximum number of parts per hour of a certain product. He has three crews and four possible work centers. The estimated number of parts per hour for each crew at each work center is summarized below. Solve for the optimal assignment of crews to work centers.

Write the linear program for this transshipment problem.

Draw the network for this assignment problem. Min 10x_1A + 12x_1B + 15x_1C + 25x_1D + 11x_2A + 14x_2B + 19x_2C + 32x_2D + 18x_3A + 21x_3B + 23x_3C + 29x_3D + 15x_4A + 20x_4B + 26x_4C + 28x_4D s.t. x_1A + x_1B + x_1C + x_1D = 1 x_2A + x_2B + x_2C + x_2D = 1 x_3A + x_3B + x_3C + x_3D = 1 x_4A + x_4B + x_4C + x_4D = 1 x_1A + x_2A + x_3A + x_4A = 1 x_1B + x _2B + x_3B + x_4B = 1 x_1C + x _2C + x_3C + x_4C = 1 x_1D + x_2D + x_3D + x_4D = 1

The shortest-route problem finds the shortest-route

A dummy origin in a transportation problem is used when supply exceeds demand.

The parts of a network that represent the origins are

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,

A clothing distributor has four warehouses which serve four large cities. Each warehouse has a monthly capacity of 5,000 blue jeans. They are considering using a transportation LP approach to match demand and capacity. The following table provides data on their shipping cost, capacity, and demand constraints on a per-month basis. Develop a linear programming model for this problem. ?

​Is it a coincidence to obtain integer solutions to network problems? Explain.

Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Give the network model and the linear programming model for this problem. ​ Shipping costs are: ​

A transportation problem with 3 sources and 4 destinations will have 7 decision variables.

Draw the network for this transportation problem. Min 2X_AX + 3X_AY + 5X_AZ+ 9X_BX + 12X_BY + 10X_BZ s.t. X_AX + X_AY + X_AZ ≤ 500 X _BX + X_BY + X_BZ ≤ 400 X_AX + X_BX = 300 X_AY + X_BY = 300 X_AZ + X_BZ = 300 X_ij ≥ 0

Consider the network below. Formulate the LP for finding the shortest-route path from node 1 to node 7. ​

In the general linear programming model of the assignment problem,

The maximal flow problem can be formulated as a capacitated transshipment problem.

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

Flow in a transportation network is limited to one direction.

In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes.