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).
What was the objective in the Foster Generators transportation problem?
To minimize the total transportation cost of shipping generators.
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.
In the Ryan Electronics transshipment problem, what type of nodes represent warehouses?
Transshipment nodes.
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.
What was the main decision in the Eastborne Realty investment problem?
How many townhouses and apartment buildings to purchase to maximize cash flow.
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.
In the Ice-Cold Refrigerator capital budgeting problem, what type of variables were used for project selection?
Binary (0-1) decision variables.
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.
In the PDC decision tree, what is the recommended decision if the probability of strong demand is high?
Build a large condominium complex.