Prescriptive_Analytics_Mock_Exam_2025

What is the feasible region for a linear programming problem?

• The set of all integer solutions

• The set of all solutions satisfying the constraints

• The set of solutions that maximize the objective

• The region below the objective function line

A transshipment problem differs from a standard transportation problem because it:

• Involves only direct shipping from suppliers to customers

• Allows intermediate transfer nodes such as warehouses

• Uses dummy variables to handle constraints

• Maximizes delivery time

Consider the following mathematical formulation. Which of the following is NOT a feasible solution?

• (x1;x2)=(0;0)

• (x1;X2)=(0;3)

• (x1;X2)=(2,2;1,5)

• (x1;X2)=(1,7;2,0)

Consider the following mathematical formulation. What is the optimal solution for this problem?

• (x1;x2)=(12/7 ; 15/7)

• (x1;x2)=(0 ; 3)

• (x1;x2)=(1,7 ; 2,0)

• (x1;x2)=(3 ; 1,5)

A company's distribution system includes 2 plants, 2 warehouses, and 2 customers. The capacities of the plants and the shipping costs (in Euros) from each plant to each warehouse are as shown in the figure. Assumptions:
- Shipments are only allowed from Plant → Warehouse → Customer.
- No inter-warehouse or direct plant-customer shipments.
- Objective: Minimize total distribution cost while satisfying supply and demand constraints.

How many constraints are there in the original formulation other than domain constraints?

• 4

• 5

• 6

• 7

A company's distribution system includes 2 plants, 2 warehouses, and 2 customers. The capacities of the plants and the shipping costs (in Euros) from each plant to each warehouse are as shown in the figure. Assumptions:
- Shipments are only allowed from Plant → Warehouse → Customer.
- No inter-warehouse or direct plant-customer shipments.
- Objective: Minimize total distribution cost while satisfying supply and demand constraints.

You are given the following values for the optimal solution: x23=200; x35=200; x45=0; x36=0; x46=400; x13=0.  What is the optimal value for x14 and x24?

• x14=200; x24=200

• x14=300; x24=100

• x14=100; x24=300

• None of the above

A company's distribution system includes 2 plants, 2 warehouses, and 2 customers. The capacities of the plants and the shipping costs (in Euros) from each plant to each warehouse are as shown in the figure. Assumptions:
- Shipments are only allowed from Plant → Warehouse → Customer.
- No inter-warehouse or direct plant-customer shipments.
- Objective: Minimize total distribution cost while satisfying supply and demand constraints.

The shadow price of the demand constraint for Customer 5 is 2 Euros. What does this imply?

• The cost would increase by 2 Euros if the demand at Customer 5 increases by one unit

• It is the shipping cost from warehouse 4 to Customer 5

• The total cost would decrease by 2 Euros if the demand at Customer 5 is reduced by one unit

• None of the above

Which option is NOT correct?

• In TSP, each node is visited exactly once.

• In VRP, there is a specific node as the starting and ending node.

• TSP is an extension of VRP with multiple vehicles.

• VRP cannot be solved optimally

Which sentence explains better the behaviour of this plot?

• The optimal cost is achieved when M is much greater than the average demand

• Low M values → high shortage costs dominate., High M values → high holding costs dominate.

• Costs drop initially as M rises since demand variability is absorbed, but rise later due to increasing shortage penalties.

• The total cost first decreases because ordering becomes more frequent, then increases due to increased demand uncertainty.

Based on the following graphs: Why does the optimal replenishment level M increase as the review period T increases in the (T, M) inventory model?

• Because the expected demand and its variability grow over longer review periods

• Because suppliers offer quantity discounts for longer time frames

• Because longer review periods reduce the number of orders placed

• Because holding cost per unit becomes cheaper over longer periods