C-1: Identify the various cost implications and the key features of waiting lines.

The primary objective of managing waiting lines is to minimize their total costs throughout any service or manufacturing facility. This total cost is composed of the cost related to customer waiting time and capacity-related cost. The costs related to customer waiting time are tangible and intangible. Tangible costs include wages that must be paid to workers while the facility remains idle and the costs associated with lost productivity. Tangible costs may also include cost of materials used while waiting. Intangible costs include lost sales because customers decided not to wait and received service from a competitor, and costs associated with loss of goodwill as a result of customer dissatisfaction. Capacity-related costs include those costs incurred to maintain existing facility capacity or add additional capacity to provide the required service.

A queue represents a certain number of customers waiting for service at a facility. In queuing theory, a mathematical model of a waiting line system is constructed to predict the lengths of the queues and the associated waiting times in those queues. Several queuing models are available, and to ensure meaningful analysis and results, it is important that the correct model is chosen to represent the waiting line system to be analyzed. The choice of the correct model depends on the following key features of the given waiting line system analyzed: customer population, arrival pattern, queue size and discipline, service system structure, and service pattern.

C-2: Employ the various queuing models and understand when and how to use them to calculate optimal queuing solutions, including the psychology underlying waiting lines.

This module identified several assumptions, including:

a. Arrival rates have a Poisson probability distribution.

b. Service times have a negative exponential distribution.

c. First-in, first-out (FIFO) queue discipline.

d. All models assume that the waiting line system is operating under a steady state condition. In other words, the average arrival and service rates remain stable during analysis.

Three common queuing models are (1) the single-channel or singleserver queuing model, (2) the single-channel or single-server, constant service rate queuing model, and (3) the multiple-channel or multipleserver queuing model.

The single-channel or single-server queuing model is the simplest and the most frequently encountered waiting line problem, in which there is a single service station that will serve a queue of customers waiting in a single line. The single-channel or single-server, constant service rate queuing model is similar to the first model, but it assumes constant service times. In the multiple-channel or multiple-server queuing model, service is provided to customers in a single phase with multiple servers. In such systems, we still assume that customers wait in a single line and receive service from the first available servers on first-come, first-served basis.

Ultimately, waiting lines and queuing theory represent a challenge that is as much psychological as it is computational. As a result, and despite their best efforts to provide sufficient capacity, service providers realize that it is not possible to reduce the length of waiting lines or provide faster service beyond a point. 

Therefore, to reduce customer dissatisfaction associated with long waits, many service providers recognize that there are important perceptual and psychological steps that can be taken to minimize the appearance of excessive waits and, therefore, to minimize customer dissatisfaction. These steps may involve deliberate distractions or other means to minimize the psychological feelings of delay and the dissatisfaction that subsequently accompanies these perceptions.

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