Exam 10: Distribution Network Models

Correct Answer:

Answered by Examlex AI Copilot

When there are unacceptable routes in a transportation linear program, several adjustments can be made to address this issue.

1. Remove the unacceptable routes: The first and most straightforward adjustment is to simply remove the unacceptable routes from the transportation network. This may involve finding alternative routes or modes of transportation to replace the unacceptable ones.

2. Add constraints: Another approach is to add constraints to the linear program that explicitly prohibit the use of the unacceptable routes. This can be done by setting upper bounds on the flow of goods through these routes or by adding binary variables to indicate whether a route is used or not.

3. Modify costs: The costs associated with using the unacceptable routes can be adjusted to reflect their undesirability. This can be done by increasing the transportation costs for these routes or by introducing penalty costs for using them.

4. Introduce alternative routes: If possible, alternative routes that are acceptable can be introduced into the transportation network to replace the unacceptable ones. This may involve identifying new transportation providers or reconfiguring the existing network.

By making these adjustments, the transportation linear program can be modified to ensure that only acceptable routes are used for transporting goods, thereby improving the efficiency and effectiveness of the transportation network.

Correct Answer:

Answered by Examlex AI Copilot

The transshipment problem involves determining the optimal flow of goods from multiple sources to multiple destinations, while also allowing for intermediate transshipment points where goods can be temporarily stored and transferred. In the LP formulation of the transshipment problem, the following variables and constraints are necessary:

Variables:
1. Flow variables: These represent the amount of goods flowing from a source to a destination, or from a transshipment point to another point. These variables are typically denoted as Xij, where i represents the source or transshipment point, and j represents the destination or transshipment point.

Constraints:
1. Supply constraints: These constraints ensure that the total amount of goods leaving each source does not exceed its supply capacity.
2. Demand constraints: These constraints ensure that the total amount of goods arriving at each destination meets its demand requirements.
3. Transshipment constraints: These constraints ensure that the total amount of goods entering a transshipment point equals the total amount leaving the transshipment point, taking into account any storage or transfer capabilities at the transshipment point.
4. Non-negativity constraints: These constraints ensure that the flow variables are non-negative, as goods cannot flow in negative quantities.

By formulating the transshipment problem as an LP with these variables and constraints, it becomes possible to optimize the flow of goods while satisfying the supply, demand, and transshipment requirements.