Network Flow Models
What are the three main components of a network flow model?
Nodes, arcs, and functions associated with arcs/nodes (e.g., costs, supplies, demands).
What is an all-integer linear programming model?
A linear program where all variables are restricted to integer values.
What are the three elements of a decision problem?
Decision alternatives, states of nature, and resulting payoffs.
What is the objective function in a linear programming model?
A mathematical expression that defines the goal of the optimization (e.g., minimize cost, maximize profit).
A method used to determine the value of additional information before making a decision, calculated as the difference between the expected value with and without the new information.
What is the Expected Value of Perfect Information (EVPI)?
What is the primary objective of the transportation problem?
To minimize the cost of shipping goods from origins to destinations.
What is the LP relaxation of an integer linear program?
The linear program obtained by dropping the integer constraints.
What is the optimistic approach to decision-making?
Selecting the alternative with the highest possible payoff.
What is the role of constraints in a linear programming model?
To restrict the solution space based on problem requirements.
This optimization problem focuses on determining the most efficient path between two points in a network, often used for routing logistics and navigation systems.
What is the shortest-route problem?
Define the transshipment problem.
A transportation problem with intermediate nodes (warehouses) added to the network.
How are binary variables used in integer programming?
They are restricted to values 0 or 1, often representing yes/no decisions.
Define the minimax regret approach.
Choosing the decision that minimizes the maximum regret.
In the Pittsburgh Development Corp. example, what two states of nature are considered?
Strong demand and weak demand.
A constraint-based approach in optimization where some decision variables must take whole number values, often used in production planning and capital budgeting.
What is mixed-integer programming?
What distinguishes the assignment problem from other network flow problems?
Each agent is assigned to one and only one task.
What is the difference between a feasible solution and an optimal solution in integer linear programming?
A feasible solution satisfies all constraints, while an optimal solution is the feasible solution that maximizes or minimizes the objective function.
How is the expected value of perfect information (EVPI) calculated?
EVPI = |EV with perfect information − EV without perfect information|.
In a fixed-cost problem, what is the purpose of introducing binary variables?
To model the fixed costs associated with production setup decisions.
A logistics strategy where goods pass through centers before reaching their final destination, allowing for more efficient distribution and cost savings.
What is the transshipment model?
Name the one variation of the transportation problem when total supply does not equal total demand.
Adding a dummy origin/destination for excess supply or unmet demand.
What is a mixed-integer linear programming model?
A model where only a subset of variables are restricted to integers.
What does a risk profile show in decision analysis?
The possible payoffs along with their associated probabilities.
How does sensitivity analysis aid decision-making?
By studying how changes in inputs affect the recommended decision.
This method is used to assess how changes in input values, such as probabilities or costs, affect the recommended decision alternative, helping decision-makers understand the robustness of their choices.
What is sensitivity analysis?