Test 2

What is the objective function of the following maximal flow problem?

Max X41

The objective function for the ILP problem can never

be better than the optimal solution to its LP relaxation.

A network flow problem that allows gains or losses along the arcs is called a

generalized network flow model.

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)?

.80X13 +.95X23 −X35 −X36 −X37 =0

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network depicts this problem. What is the balance of flow constraint for node 7 (Diesel)?

.90 X37 + .95 X47 = 75

The right hand side value for the ending node in a shorthand path has a value of

1

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as Xi = the amount of product i produced Yi = 1 if Xi > 0 and 0 if Xi = 0 Using the approach discussed in the text, what is the appropriate value for M1 in the linking constraint for product A?

16

The constraint x13 - x23 - x34 >= 50 indicates that

50 units are required at node 3

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. How many binary variables are required in the formulation of this problem?

A. 3

Which of the following is not a benefit of using binary variables?

A. With only 2 values, Solver can work faster.

Suppose you want to minimize an objective function z = 2x1+3x2. Both decision variables must be integer. The optimal solution to the LP relaxation will:

A. be smaller than the optimal IP solution

The setup cost incurred in preparing a machine to produce a batch of product is an example of a

A. fixed charge.

ILP problems are computationally

A. more demanding than their LP relaxations

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?

A.X1 +X2 +X3 +X4 =1

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as Xi = the amount of product i produced Yi = 1 if Xi > 0 and 0 if Xi = 0 What is the objective function for this problem?

B.MAX:17X1 +21X2 −60Y1 −80Y2

A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected?

B.X1 +X2 +X3 +X4 ≤2

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. How many decision variables (normal and binary) are required in the formulation of this problem?

C. 9

How are binary variables specified in the Analytic Solver Platform (ASP)?

C. By specifying changing cells as BINARY in the Variable Type/Bound area of ASP.

A company must invest in project 1 in order to invest in project 2. Which of the following constraints ensures that project 1 will be chosen if project 2 is invested in?

C. X1 − X2 ≥ 0

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

C. variable costs.

A company is planning next month's production. It has to pay a setup cost to produce a batch of X4's so if it does produce a batch it wants to produce at least 100 units. Which of the following pairs of constraints show the relationship(s) between the setup variable Y4 and the production quantity variable X4?

C.X4≤M4Y4 and X4≥100Y4

If a company selects Project 1 then it must also select either Project 2 or Project 3 (or both). Which of the following constraints enforces this condition?

D. X1 − X2 − X3 ≤ 0

A production company wants to ensure that if Product 1 is produced, production of Product 1 does not exceed production of Product 2. Which of the following constraints enforce this condition?

D. X1 ≤ X2

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3?

D. X32 ≤ M3Y3 and X31 ≥ 70Y3

what is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

Indicates unmet demand at demand nodes

Which balance of flow rule should be applied to each node in a network flow problem when Total Supply > Total Demand

Inflow - Outflow >= Supply or Demand

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

LP relaxation.

What is the objective function for the following shortest path problem?

MIN50X12 +200X13 +100X24 +35X34

Which of the following are potential pitfalls of using a nonzero integer tolerance factor in the Analytic Solver Platform?

No assurance the returned solution is optimal.

What formula should be entered in cell G18 in this Excel Model

SUMPRODUCT(B6:B16, G6:G16)

Consider modeling a warehouse with three in-flow arcs and three outflow arcs. The warehouse node is a transshipment node but has a capacity of 100. How would one modify the network model to avoid adding a side constraint that limits either the sum of in-flows or the sum of the out-flows to 100?

Separate the warehouse node into two nodes, connected by a single arc, with capacity of 100.

What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?

The model solution is not guaranteed to be an integer.

For a network with n nodes, a spanning tree is

a set of (n-1) arcs that connects all nodes and contains no loops.

How could a network be modified if demand exceeds supply

add a dummy supply

Supply quantities for supply nodes in a transshipment problem are customarily indicated by

negative numbers

The equipment replacement problem is an example of which network problem?

shortest path problem

A node which can both send to and receive from other nodes is a

transshipment node

What is the constraint for node 2 in the following maximal flow problem?

x12 - x23 - x24 = 0

What is the correct constraint for node 2 in the following diagram? 1) -200 -> 2) +100 -> 3) +50

x12 - x23 >= 100

What is the constraint 2 for the following shortest path problem?

x12 - x24 = 0