Anyone who has ever waited at a sto

Anyone who has ever waited at a stoplight, at McDonald’s, or at the registrar’s office has experienced the dynamics of waiting lines. Perhaps one of the best examples of effective management of waiting lines is that of Walt Disney World. One day the park may have only 25,000 customers, but on another day the numbers may top 90,000. Careful analysis of process flows, technology for peoplemover (materials handling) equipment, capacity, and layout keeps the waiting times for attractions to acceptable levels.A waiting line is one or more “customers” waiting for service. The customers can be people or inanimate objects, such as machines requiring maintenance, sales orders waiting for shipping, or inventory items waiting to be used. A waiting line forms because of a temporary imbalance between the demand for service and the capacity of the system to provide the service. In most real-life waiting-line problems, the demand rate varies; that is, customers arrive at unpredictable intervals. Most often, the rate of producing the service also varies, depending on customer needs. Suppose that bank customers arrive at an average rate of 15 per hour throughout the day and that the bank can process an average of 20 customers per hour. Why would a waiting line ever develop? The answers are that the customer arrival rate varies throughout the day and the time required to process a customer can vary. During the noon hour, 30 customers may arrive at the bank. Some of them may have complicated transactions requiring above-average process times. The waiting line may grow to 15 customers for a period of time before it eventually disappears. Even though the bank manager provided for more than enough capacity on average, waiting lines can still develop.In a similar fashion, waiting lines can develop even if the time to process a customer is constant. For example, a subway train is computer controlled to arrive at stations along its route. Each train is programmed to arrive at a station, say, every 15 minutes. Even with the constant service time, waiting lines develop while riders wait for the next train or cannot get on a train because of the size of the crowd at a busy time of the day. Consequently, variability in the rate of demand determines the sizes of the waiting lines in this case. In general, if no variability in the demand or service rate occurs and enough capacity is provided, no waiting lines form.Waiting-line theory applies to service as well as manufacturing firms, relating customer arrival and service-system processing characteristics to service-system output characteristics. In our discussion, we use the term service broadly—the act of doing work for a customer. The service system might be hair cutting at a hair salon, satisfying customer complaints, or processing a production order of parts on a certain machine. Other examples of customers and services include lines of theatergoers waiting to purchase tickets, trucks waiting to be unloaded at a warehouse, machines waiting to be repaired by a maintenance crew, and patients waiting to be examined by a physician. Regardless of the situation, waiting-line problems have several common elements.The analysis of waiting lines is of concern to managers because it affects process design, capacity planning, process performance, and ultimately, supply chain performance. In this supplement we discuss why waiting lines form, the uses of waiting-line models in operations management, and the structure of waiting-line models. We also discuss the decisions managers address with these models. Waiting lines can also be analyzed using computer simulation. Software such as SimQuick or Excel spreadsheets can be used to analyze the problems in this supplement.