BIT 3434 Test 2

A transportation problem: a. Is a special case of transshipment problem. b. Contains no nonnegative slacks. c. Contains no nonpositive slacks. d. Is complex and requires solver support to find an optimal solution. Hide Feedback

a

Binary integer variables (or binary variables) can: a. Assume only two integer values: 0 and 1. b. Make the IP problem infeasible. c. Make the IP model hard to solve. d. Force the decision maker to select unwanted alternatives.

a

Consider a linking constraint X≤ MY, where X is a continuous variable representing a quantity of a product to produce, Y is a 0-1 (binary) variable an M is an arbitrarily large number. Suppose that Y=1. This condition means that: a. The product can be produced in any quantity. b. Production quantity of the product is limited. c. The magnitude of M serves as a bound on production quantity. d. The product cannot be produced.

a

Goal programming: a. Involves solving problems containing a collection of goals that we would like to achieve. b. Is not an iterative solution procedure. c. Requires the use of only hard constraints. d. Requires firm RHS values of the constraints.

a

If you use the simplex method to solve any minimum cost network flow model having integer constraint RHS values, then: a. The optimal solution automatically assumes integer values. b. The problem cannot be solved using network modeling. c. The problem is infeasible. d. Additional 0-1 variables are needed to model this situation.

a

Solving the LP relaxation to the ILP problem and rounding the solution manually rounded up to their closest integer values is not a good solution approach because: a. The resulting solution may be infeasible. b. You are guaranteed feasibility. c. The approach is too simple. d. You are guaranteed optimality.

a

Suppose that in goal programming (GP) we assign arbitrarily large weights to deviations from these goals to ensure that undesirable deviations from them never occur. This approach is called: a. Preemptive GP. b. Forcing. c. Reactive GP. d. Inclusive GP.

a

Suppose that the objective function for a GP problem is: MIN 1/ti(wdminus + wdplus) . The term ti represents: a. The target value for goal i. b. The amount of underachievement for goal i. c. The amount of overachievement for goal i. d. The weighted sum of over and underachievement for goal i. Hide Feedback

a

Suppose that the objective function for a GP problem is: MIN: ∑(wd-,wd+). The terms w- and w+ represent: a. Numeric constants that can be assigned values to weight the various deviational variables in the problem. b. Desirability of a positive deviation from the target value. c. Desirability of a negative deviation from the target value. d. The exponentially decreasing weights representing the relative importance of a deviational variable.

a

The equipment replacement problem is a type of problem that can be modeled as a(n): a. Shortest path problem. b. Assignment problem. c. Minimal spanning tree problem. d. Transportation problem.

a

The first step in formulating ILP problems is: a. Defining the decision variables. b. Defining the constraints. c. Defining the objective function. d. Implementing the model in a spreadsheet.

a

The objective function in a minimal spanning tree problem is to: a. Determine the set of arcs that connect all the nodes in a network. b. Minimize the number of constraints in the network formulation. c. Simplify the modeling effort. d. Optimize the objective function value.

a

The term 'iterative solution procedure' means that: a. The decision maker investigates a variety of solutions to find one that is most satisfactory. b. The solution algorithm executes in cycles. c. Optimal solution can be found quickly. d. A known number of iterations is required to find the optimal solution to the problem.

a

A problem is referred to as an integer linear programming (ILP) problem when: a. All decision variables assume the values of 0 or 1. b. Some or all of the decision variables in an LP problem are restricted to assuming only integer values. c. All decision variables assume integer values. d. Only one decision variable assumes integer values.

b

A transshipment node can have: a. A net supply and demand. b. Either a net supply or demand, but not both. c. Both a net supply and demand. d. Neither a net supply nor demand.

b

An integrality condition imposed on a variable indicates that: a. The variable has a lower bound. b. The variable must assume only integer values. c. The variable has an upper bound.

b

Any integer variable in an ILP that assumes a fractional value in the optimal solution to the relaxed problem can be designated as a: a. Candidate for manually rounding up to the nearest integer value. b. A branching variable in the B&B technique. c. Candidate for manually rounding down to the nearest integer value. d. Dummy variable.

b

Any shortest path problem can be modeled as a transshipment problem by: a. Forcing the net flow on all arcs to be equal to +1. b. Assigning a supply of 1 to the starting node, a demand of 1 to the ending node, and a demand of 0 to all other nodes in the network. c. Forcing the net flow on all arcs to be equal to -1. d. This cannot be done because the shortest path problem is more general than the transshipment problem.

b

Consider the constraint:X1+dminus-dplus= 5. Suppose that X1 = 3 in the optimal solution. The values of deviational variables dminus and dplus are: a. d-1 = 1 and d+1= 1. b. d-1 = 2 and d+1 = 0. c. d-1 = 0 and d+1 = 0. d. d-1 = 3 and d+1 = -1.

b

In MOLP, a decision alternative is dominated if: a. The problem has multiple alternatives with the same value of all objectives. b. There is another alternative that produces a better value for at least one objective without worsening the value of the other objectives. c. The problem is infeasible. d. There is only one alternative.

b

In a typical path problem, the supply node flow constraint RHS is equal to: a. +1. b. -1. c. 2. d. 0.

b

In multi objective linear programming (MOLP) minimization problem, one way to minimize undesirable deviation from target for a goal in the optimal solution is to: a. Assign a zero value to the weight associated with this goal in the objective function. b. Assign a large value to the weight associated with this goal in the objective function. c. Remove the goal from the objective function. d. Assign a small positive value to the weight associated with this goal in the objective function.

b

In some situations, the decision to produce a product results in a lump-sum cost, or fixed-charge, in addition to a per-unit cost or profit. These types of problems are known as: a. LP problems. b. Fixed-charge or fixed-cost problems. c. IP problems. d. Relaxed problems.

b

One advantage of using the MINIMAX objective to analyze MOLP problems is that: a. It generates multiple optimal solutions. b. The solutions generated are always Pareto optimal. c. It limits the number of objectives. d. The model is easy to formulate and solve.

b

One approach to finding the optimal integer solution to a problem is to ignore the integrality conditions and solve the problem as if it were a standard LP problem where all the variables are assumed to be continuous. This solution approach is referred to as: a. Simplex. b. LP relaxation. c. Discretization. d. Simplification.

b

Sunk costs are: a. Influenced by economies of scale. b. Irrelevant for decision-making purposes because, by definition, decisions do not influence these costs. c. Larger than variable costs. d. Equivalent to fixed costs.

b

Suppose that all goal constraints in a goal programming problem are hard and the objective is: MIN Σ(dminus + dplus) . Then: a. The optimal value of the objective function is zero. b. All goals must be met exactly. c. The problem is infeasible. d. The optimal value of the objective function is negative.

b

Suppose that you solved a LP relaxed formulation of the maximization problem and found that the optimal objective function value is 500. The objective function value for the optimal solution to the original ILP problem can never be: a. Integer. b. Higher than 500, which is the objective function value for the optimal solution to its LP relaxation. c. Continuous. d. Lower than 500, which is the objective function value for the optimal solution to its LP relaxation.

b

Suppose that you solved a LP relaxed formulation of the minimization problem and found that the optimal objective function value is 500. The objective function value for the optimal solution to the original ILP problem can never be: a. Integer. b. Lower than 500, which is the objective function value for the optimal solution to its LP relaxation. c. Higher than 500, which is the objective function value for the optimal solution to its LP relaxation. d. Continuous.

b

The term 'Pareto optimal' means that: a. Optimal solution can be found by relaxing one or more hard constraints. b. In general, we can be certain that no other feasible solution allows an increase in any objective without decreasing at least one other objective. c. The problem is infeasible under ordinary conditions. d. Optimality can be achieved even when one or more of the hard constraints is violated.

b

The triple bottom line (3BL) concept involves decisions with considerations of: a. Cost, profit and revenue. b. Profit, people and planet. c. Ethics, cost and sustainability. d. Profit, environment and sustainability.

b

What is the constraint for node 3 in the following shortest path problem? (1) -> (2)(3) -> (4) a. -X13 + X34 ≤=1. b. -X13 + X34 = 0. c. -X12 + X24 = 0. d. 30X13 + 45X34 = 0.

b

What is the objective function for the following shortest path problem? (1) -> (2)(3) -> (4) a. -X12 + X24 = 0. b. Min 20X12 + 30X13 + 50X24 + 45X34 c. Max 20X12 + 30X13 + 50X24 + 45X34. d. -X13 + X34 = 0.

b

A MINIMAX objective is sometimes helpful in goal programming (GP) when: a. You want to maximize the minimum deviation from a set of goals. b. You do not want to explore points on the edge of the feasible region. c. You want to minimize the maximum deviation from any goal. d. You do not want to explore corner points of the feasible region.

c

By default, Solver uses a suboptimality tolerance factor of 5%. This means that: a. No integer solution can be found. b. A B&B procedure is not effective in finding a solution to the problem. c. Integer solution was found within the stated tolerance. d. Additional computations are required to find the optimal solution.

c

Deviational variables: a. Must take a value of zero in the optimal solution to the problem. b. Represent the amount by which each goal's target value is underachieved. c. Represent the amount by which each goal deviates from its target value. d. Represent the amount by which each goal's target value is overachieved

c

In a transshipment problem formulation, the decision variables are of the form: a. Si, which is the supply at source i. b. Dj, which is the demand at destination j. c. Xij, which is the number of items shipped (or flowing) from node i to node j. d. Yk, which is a variable indicating whether arc k is used or not.

c

Suppose you want to find the minimum shipping cost using a transportation problem formulation. Further, you want to not ship any product from source i to destination j. When modeling this situation you should: a. Set all slacks to 0. b. Set all constraints to ≤ type. c. Assign a large cost, cij = M, to the shipment quantity (Xij) between source i and destination j. d. Force the shipping cost, cij to zero.

c

The balance of flow constraints: a. Are of = type. b. Are of ≤ type. c. Define a relationship between inflow and outflow for each node in a network. d. Are of ≥ type.

c

The first step in goal programming (GP) is to: a. Defining the hard constraints. b. Defining the goal constraints. c. Define the decision variables. d. Define the goal(s).

c

The most effective and widely used procedure for solving ILP problems is called: a. The cutting plane approach. b. LP relaxation. c. The branch-and-bound (B&B) algorithm. d. Simplex.

c

The net supply for each node in the network is indicated by: a. A positive number next to each node. b. A negative or positive number next to each node. c. A negative number next to each node. d. An absolute value of a number next to each node.

c

The objective in most network flow problems is to: a. Maximize profits. b. Maximize revenue. c. Minimize the total cost, distance, or penalty that must be incurred to solve the problem. d. Minimize the number of decision variables.

c

What is the correct constraint for node 2 in the following diagram? -100(1) -> 50(2) -> 25(3) a. X12 - X23 ≥ 50 b. X12 + X23 ≤ 50 c. X12 + X23 ≥ 50 d. -X12 - X23 = 50

c

You want to assign m jobs to n machines to minimize the assignment total cost. You model this problem as an assignment problem in a standard form. In your formulation: a. Some constraints may have RHS equal to 0. b. Dummy rows must be added if m>n. c. All constraint RHS are strictly equal to 1. d. Dummy columns must be added if m=n.

c

Consider a transportation problem, in which the total demand is greater than the total supply. To bring this problem to a standard form you should: a. Delete one or more destinations so that the total available capacity is not exceeded. b. Add a dummy destination whose demand is equal to the difference between total demand and total supply. c. Do nothing. Just solve the problem. d. Add a dummy supply whose capacity is equal to the difference between total demand and total supply. See "dummy nodes and arcs" in chapter 5 for more information.

d

General integer variables are variables that: a. Cannot be negative. b. Can be allowed to assume continuous values. c. Cannot be positive. d. Could assume any integer value.

d

Goal programming (GP) provides a way of analyzing potential solutions to a decision problem that involves soft constraints. Soft constraints can be stated as: a. '≤' type constraints. b. Nonlinear constraints. c. '≥' type constraints. d. Goals with target values and deviational variables, which measure the amount by which a given solution deviates from a particular goal.

d

In goal programming, hard constraints: a. Can be modeled as linear functions. b. Can be relaxed. c. Are difficult to meet. d. Cannot be violated.

d

Integrality conditions often make a problem: a. More difficult to formulate. b. A continuous problem. c. Easier to solve. d. More difficult (and sometimes impossible) to solve.

d

Many ILP packages allow you to specify a suboptimality tolerance of X% (where X is some numeric value). This number is used to: a. Increase the number of evaluated alternatives. b. Simplify complex computations. c. Remove infeasible alternatives from consideration. d. Tell the B&B algorithm to stop to prevent evaluation of thousands of candidate problems.

d

Multiple objective optimization applies to: a. Maximization problems only. b. Problems with multiple constraints. c. Problems containing one objective function. d. Problems containing more than one objective function.

d

Problems that model a situation when multiple conflicting objectives occur are called: a. Conflict problems. b. Decision problems. c. Stress problems. d. Multiple objective linear programming (MOLP) problems.

d

Suppose that a decision maker wants to select no more than two of the three projects from the set (1, 2, 3). Three binary decision variables X1, X2, and X3are introduced. If Xi=1, project i is selected. This situation can be modeled by introducing a constraint: a. X1 + X2 + X3 = 2. b. X1 + X2 + X3 =1. c. X1 + X2 + X3 ≤ 1. d. X1 + X2 + X3 ≤ 2.

d

Suppose you want to purchase cans of tennis balls online. Let X is an integer variable representing a quantity of a tennis cans to purchase, Y is a 0-1 (binary) variable and M is an arbitrarily large number. The vendor imposes a minimum order size requirement of 24 cans on your transaction. What are the constraints to model this situation? a. X≤ MY and X=24. b. X= MY and X=24Y. c. X= MY and X≥24Y. d. X≤ MY and X≥24Y.

d

The arcs in a network indicate: a. The upper and lower limits on flow quantity. b. The direction of flow. c. The electrical wiring short. d. The valid paths, routes, or connections between the nodes in a network flow problem.

d

The feasible region of the LP relaxation of an ILP problem: a. Is a continuous area. b. Is a subset of the feasible region for the original ILP problem. c. Is a lattice connecting the required integer nodes. d. Always encompasses all the feasible integer solutions to the original ILP problem.

d

The key concept in goal programming (GP) is: a. Limiting the number of soft constraints. b. Relaxing the hard constraints. c. Recognizing the key goals. d. Reconciling trade-offs between conflicting goals.

d

The problem, in which we need to determine the shortest (or least costly) route or path through a network from a starting node to an ending node is called: a. The generalized network flow problem. b. The transportation problem. c. The assignment problem. d. The path problem.

d

The transshipment problem: a. Is the special case of LP problem. b. Can be solved to optimality by manual methods. c. Can be modeled using the transportation algorithm. d. Is the most general type of network flow problems

d