Practice Questions

Linear programming involves optimizing a linear function subject to linear constraints and non-negativity restrictions. The term not involved in linear programming is linear scale, which is used to visually show the scale of a map or drawing.

A dummy activity is an imaginary activity used on network diagrams to show the dependency, logic, or relationship of one activity over another. It does not consume any time or resources and is used when two or more activities have the same head and tail events. It is an alternative to an existing pattern and is not a true activity.

Imaginary and alternative to existing pattern

In linear programming, a redundant constraint is a constraint that can be removed without changing the feasible region. Adding a redundant constraint while solving a linear programming model will have no effect on the existing solution. Various methods are available to identify redundant constraints. The problem can be written in the form of linear equations to optimize the objective function subjected to a set of linear constraints or restrictions.

the solution space will get further constrained

Monte Carlo simulation is used for analyzing waiting line problems that cannot be analyzed mathematically or when observed distributions cannot be fitted to a certain mathematical distribution. It involves replacing the actual universe of an item with its theoretical counterpart described by an assumed probability distribution and using a random number table for sampling. This technique allows for risk analysis and helps decision-makers with a range of possible outcomes and their probabilities. Queuing theory is the mathematical study of waiting for a queue and is used to predict queue lengths and waiting times

In PERT, the project variance is calculated by summing the variances of the activities that lie on the critical path. The activities on the critical path are the ones that, if delayed, would delay the entire project. Therefore, understanding the variance along this path can give an indication of the potential variation in the project's duration.

Sum of variance of the activities along critical path of the project

Sum of squares of the total floats of all activities in the project

Sum of squares of free floats of all activities along the critical path of the in the project.

Sum of variance of all activities of the project

The Simplex method improves the initial feasible solution until the optimum solution is reached. If all replacement ratios are negative, the solution is unbounded. If artificial variables are present in the base, the solution is infeasible. If some values in the constant column are zero, the solution is degenerate. Multiple optimal solutions exist if a non-basic variable in the final simplex table has a net zero contribution. In the given scenario, if all entries in the pivot column are negative or zero, the solution is unbounded.

Critical activity in PERT analysis has zero float and lies on the critical path. Float is the relaxation or delay provided to any activity. Total Float (TF) is the maximum delay, Free Float (FF) is the relax or delay without affecting EST (Earliest start time) of successor activity and Independent Float (IF) is relax or delay without affecting EST of successor activity and LFT (Latest Finish Time) of predecessor activity.

Jockeying is a behavior in queuing theory where a customer shifts from one parallel queue to another in the hope of getting faster service. There are four types of customer behaviors: jockeying, balking, reneging, and cheaters. Balking is when a customer does not join the queue, reneging is when a customer joins the queue but leaves as it moves slowly, and cheaters take illegal means to get service faster.

shifting from one queue to another parallel queue

PERT is event-oriented while CPM is activity-oriented.

PERT is probabilistic while CPM is deterministic.

Levelling and smoothing are the techniques related to resource scheduling in CPM.

Dummy activity is used to indicate that an activity following it cannot start unless the preceding activity is complete. It represents a logical precedence relationship and takes zero time and resources to perform. It is used to establish uniqueness in the network when two or more activities start from a single node and terminate at the same node

In Emerson's efficiency plan of wage incentive system, the bonus is paid to workers whose performance exceeds 66.67% efficiency. This method encourages higher productivity by rewarding those who achieve a significant level of efficiency in their work.

Workers whose performance exceeds 66.67% efficiency

Workers whose performance exceeds 50% efficiency

It is mainly used for construction programme

Negative slack occurs when the latest allowable occurrence time (TL) is less than the earliest expected time (TE), indicating the project is behind schedule due to a lack of resources. Slack time can be calculated using the equation Slack = TL - TE. Positive slack indicates the project is ahead of schedule with excess resources, while zero slack means the project is on schedule with adequate resources.

PERT estimates use Beta distribution to calculate expected duration of an activity. It considers optimistic, most likely and pessimistic time. Poisson distribution predicts the probability of certain events happening.

Queuing theory's ratio of mean arrival rate to mean service rate is known as utilization factor. It shows the percentage of time the server is busy and the probability of a new customer having to wait. Arrival rate is represented by λ (follows Poisson distribution) and service rate by µ (follows exponential distribution). If λ > μ, the queue length will keep increasing, and after a certain time, incoming population will not get service.

Slack time is the difference between event times and represents the amount of time a task can be delayed before the project finish date is delayed. It is calculated as the difference between the latest allowable occurrence time (TL) and the earliest expected time (TE).

Proposed allowable time and the earliest expected time

Normal allowable time and the latest expected time

Latest allowable time and the normal expected time

Latest allowable time and the earliest expected time

The amount of time by which an activity can be delayed without affecting the project completion time is called total float.

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