EXAM 2 BUS 190
Activities K, M and S immediately follow activity H, and their latest start times are 14, 18, and 11. The latest finish time for activity H a. is 11. b. is 14. c. is 18. d. cannot be determined.
A
For inventory systems with constant demand and a fixed lead time, a. the reorder point = lead-time demand. b. the reorder point > lead-time demand. c. the reorder point < lead-time demand. d. the reorder point is unrelated to lead-time demand.
A
In CPM, for activities with more than one immediate predecessor activity, which of the following is used to compute its earliest finish (EF) time a. largest EF among the immediate predecessors b. smallest LF among the immediate predecessors c. smallest EF among the immediate predecessors d. average of EFs among the immediate predecessors
A
Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done? a. x1 + x2 + x3 ≥ 2 b. x1 + x2 + x3 ≤ 2 c. x1 + x2 + x3 = 2 d. x1 − x2 = 0
A
Most practical applications of integer linear programming involve a. only 0-1 integer variables and not ordinary integer variables. b. mostly ordinary integer variables and a small number of 0-1 integer variables. c. only ordinary integer variables. d. a near equal number of ordinary integer variables and 0-1 integer variables.
A
Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. each of these choices are true.
A
The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost.
A
The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means a. agent 3 can be assigned to 2 tasks. b. agent 2 can be assigned to 3 tasks. c. a mixture of agents 1, 2, 3, and 4 will be assigned to tasks. d. there is no feasible solution.
A
The assignment problem is a special case of the a. transportation problem. b. transshipment problem. c. maximal flow problem. d. shortest-route problem.
A
The main difference between CPM and PERT is a. the use of different activity time estimates. b. PERT analysis is less expensive to conduct. c. PERT lends itself to computerization while CPM networks must be constructed manually d. CPM integrates time and cost performance while PERT is based solely on time performance.
A
The number of units shipped from origin i to destination j is represented by a. xij. b. xji. c. cij. d. cji.
A
The solution to the LP Relaxation of a maximization integer linear program provides a. an upper bound for the value of the objective function. b. a lower bound for the value of the objective function. c. an upper bound for the value of the decision variables d. a lower bound for the value of the decision variables
A
Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables? a. supply chain design b. bank location c. capital budgeting d. product design and market share optimization
A
Which of the following applications modeled in the textbook is an example of a fixed cost problem? a. supply chain design b. bank location c. capital budgeting d. product design and market share optimization
A
Arcs in a project network indicate a. completion times. b. precedence relationships. c. activities. d. the critical path.
B
Constraints in a transshipment problem a. correspond to arcs. b. include a variable for every arc. c. require the sum of the shipments out of an origin node to equal supply. d. All of the alternatives are correct.
B
Inventory models in which the rate of demand is constant are called a. fixed models. b. deterministic models. c. JIT models. d. requirements models.
B
Slack equals a. LF − EF. b. EF − LF. c. EF − LS. d. LF − ES.
B
The EOQ model a. determines only how frequently to order. b. considers total cost. c. minimizes both ordering and holding costs. d. All of the alternatives are correct.
B
The shortest-route problem finds the shortest-route a. from the source to the sink. b. from the source to any other node. c. from any node to any other node. d. from any node to the sink.
B
To perform sensitivity analysis involving an integer linear program, it is recommended to a. use the dual prices very cautiously. b. make multiple computer runs. c. use the same approach as you would for a linear program. d. use LP relaxation.
B
When activity times are uncertain, a. assume they are normally distributed. b. calculate the expected time, using (a + 4m + b)/6. c. use the most likely time. d. calculate the expected time, using (a + m + b)/3.
B
Which cost would not be considered part of a holding cost? a. cost of capital b. shipping cost c. insurance cost d. warehouse overhead
B
Which is not a significant challenge of project scheduling? a. deadlines exist. b. activities are independent. c. many employees could be required. d. delays are costly.
B
Which of the following is a general rule for crashing activities? a. Crash only non-critical activities. b. Crash activities with zero slack. c. Crash activities with the greatest number of predecessors. d. Crash the path with the fewest activities.
B
Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be appropriate b. using 0-1 variables for modeling flexibility c. increased ease of solution d. provision for solution procedures for transportation and assignment problems
B
A critical activity is a. an activity that consumes no time but shows precedence between events. b. a milestone accomplishment within the project. c. an activity with zero slack. d. the beginning of an event.
C
Arcs in a transshipment problem a. must connect every node to a transshipment node. b. represent the cost of shipments. c. indicate the direction of the flow. d. All of the alternatives are correct.
C
For the EOQ model, which of the following relationships is incorrect? a. As the order quantity increases, the number of orders placed annually decreases. b. As the order quantity increases, annual holding cost increases. c. As the order quantity increases, annual ordering cost increases. d. As the order quantity increases, average inventory increases.
C
In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible? a. x1 = 5, x2 = 3, x3 = 0 b. x1 = 4, x2 = .389, x3 = 1 c. x1 = 2, x2 = 3, x3 = .578 d. x1 = 0, x2 = 8, x3 = 0
C
In an all-integer linear program, a. all objective function coefficients must be integer. b. all right-hand side values must be integer. c. all variables must be integer. d. all objective function coefficients and right-hand side values must be integer.
C
Rounding the solution of an LP Relaxation to the nearest integer values provides a. a feasible but not necessarily optimal integer solution. b. an integer solution that is optimal. c. an integer solution that might be neither feasible nor optimal. d. an infeasible solution.
C
Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation and should be disregarded. d. is most useful for 0 - 1 models.
C
The difference between the transportation and assignment problems is that a. total supply must equal total demand in the transportation problem b. the number of origins must equal the number of destinations in the transportation problem c. each supply and demand value is 1 in the assignment problem d. there are many differences between the transportation and assignment problems
C
Which of the following is always true about a critical activity? a. LS = EF. b. LF = LS. c. ES = LS. d. EF = ES.
C
Which of the following is not true regarding the linear programming formulation of a transportation problem? a. Costs appear only in the objective function. b. The number of variables is (number of origins) x (number of destinations). c. The number of constraints is (number of origins) x (number of destinations). d. The constraints' left-hand side coefficients are either 0 or 1
C
A requirement that two 0-1 variables both be either in or out of a solution together is a a. k out of n alternatives constraint b. conditional constraint c. mutually exclusive constraint d. corequisite constraint
D
For an activity with more than one immediate successor activity, its latest-finish time is equal to the a. largest latest-finish time among its immediate successors. b. smallest latest-finish time among its immediate successors. c. largest latest-start time among its immediate successors. d. smallest latest-start time among its immediate successors.
D
In deciding which activities to crash, one must a. crash all critical activities. b. crash largest-duration activities. c. crash lowest-cost activities. d. crash activities on the critical path(s) only.
D
In the general linear programming model of the assignment problem, a. one agent can do parts of several tasks. b. one task can be done by several agents. c. each agent is assigned to its own best task. d. one agent is assigned to one and only one task.
D
LP relaxation refers to a. eliminating nonbinding constraints b. rounding down non-integer valued decision variables c. dropping the integer requirements for the decision variables d. accepting a non-optimal, but feasible, solution
D
PERT and CPM a. are most valuable when a small number of activities must be scheduled. b. have different features and are not applied to the same situation. c. do not require a chronological relationship among activities. d. have been combined to develop a procedure that uses the best of each.
D
The critical path a. is any path that goes from the starting node to the completion node. b. is a combination of all paths. c. is the shortest path. d. is the longest path.
D
The objective of the transportation problem is to a. identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. b. minimize the number of origins used to satisfy total demand at the destinations. c. minimize the number of shipments necessary to satisfy total demand at the destinations. d. minimize the cost of shipping products from several origins to several destinations.
D
To calculate an activity's latest finish time, you should consider its a. predecessors' latest finish times b. predecessors' latest start times c. successors' earliest start times d. successors' latest start times
D
Which of the following is not implied when average inventory is Q/2, where Q is the order quantity? a. An entire order quantity arrives at one time. b. The previous order quantity is entirely depleted when the next order arrives. c. An order quantity is depleted at a uniform rate over time. d. Backorders are permitted.
D
A dummy origin in a transportation problem is used when supply exceeds demand
F
A multiple choice constraint involves selecting k out of n alternatives, where k ≥ 2
F
A transportation problem with 3 sources and 4 destinations will have 7 variables in the objective function.
F
As lead time for an item increases, the cycle time increases.
F
Crashing refers to an unanticipated delay in a critical path activity that causes the total time to exceed its limit.
F
Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program
F
Holding cost is not dependent on holding rate.
F
If Project 5 must be completed before Project 6, the constraint would be x5 − x6 ≤ 0.
F
If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution.
F
In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes.
F
In the EOP (production) model, setup cost is not important
F
In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded
F
PERT and CPM are applicable only when there is no dependence among activities
F
The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.
F
The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.
F
The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.
F
The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.
F
The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem
F
The time between placing orders is the lead time.
F
When activity times are uncertain, an activity's most likely time is the same as its expected time
F
Precedence relationships among activities is critical in CPM analysis but not in PERT.
F
A critical activity can be part of a noncritical path.
T
A model where demand is considered known and not subject to uncertainty is also known as Deterministic Inventory Model
T
A transshipment problem is a generalization of the transportation problem in which certain nodes are neither supply nodes nor destination nodes
T
Activities require time to complete while events do not
T
All activities on a critical path have zero slack time.
T
Constant demand is a key assumption of the EOQ model.
T
Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.
T
Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs
T
Flow in a transportation network is limited to one direction
T
If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.
T
If the optimal solution to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.
T
If x1 + x2 ≤ 500y1 and y1 is 0 - 1, then if y1 is 0, x1 and x2 will be 0
T
In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred
T
In the EOQ model, the average inventory per cycle over many cycles is Q/2.
T
In the EOQ model, the objective function is to minimize total cost.
T
In the general assignment problem, one agent can be assigned to several tasks
T
Most practical applications of integer linear programming involve only 0 -1 integer variables.
T
Multiple choice constraints involve binary variables
T
Ordering cost is not dependent on size of the order.
T
The assignment problem is a special case of the transportation problem in which all supply and demand values equal one.
T
The capacitated transportation problem includes constraints which reflect limited capacity on a route.
T
The difference between an activity's earliest finish time and latest finish time equals the difference between its earliest start time and latest start time.
T
The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.
T
The earliest finish time for the final activity is the project duration.
T
The length of time an activity can be delayed without affecting the project completion time is the slack
T
The linear programming model for crashing presented in the textbook assumes that any portion of the activity crash time can be achieved for a corresponding portion of the activity crashing cost.
T
The maximal flow problem can be formulated as a capacitated transshipment problem
T
The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model
T
The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity
T
Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.
T
When activity times are uncertain, total project time is normally distributed with mean equal to the sum of the means of all of the critical activities
T
When demand is independent, it is not related to demand for other components or items produced by the firm.
T
