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Krajewski IN Supplement C - Supplement C Waiting Lines A...

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Supplement C Waiting Lines A. Why Waiting Lines Form 1. Define “customers” in waiting lines. 2. Why waiting lines form? a. Temporary imbalance between demand for service and capacity of the system. b. Can develop even if the time to process is constant due to variability in demand. 3. If both demand and service rates are constant, and service rate > than demand, no waiting line forms. B. Uses of Waiting-Line Theory 1. Applies to many service or manufacturing situations. 2. Service is the act of processing a customer (or manufacturing job). a. Hair cutting in a hair salon b. Satisfying customer complaints c. Processing production orders C. Structure of Waiting Line Problems 1. Customer population a. The source of input to the service system. b. Whether the input source is finite or infinite will have an effect on the waiting line characteristics. When several customers from a finite source are already in the waiting line, the chance of new customer arrivals is reduced. When the input source is infinite, customers already in the waiting line do not affect probability of another arrival. c. Whether the customers are patient or impatient also affects waiting line characteristics. Patient customers wait until served. Impatient customer arrivals either balk at long lines (leave immediately), or join the line and renege (leave after becoming discouraged with slow progress). 2. The service system a. Number of lines b. A single-line arrangement is favored when servers are capable of general service. C-1
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C-2 Waiting Lines Keeps servers uniformly busy Levels waiting times among customers, gives sense of fairness. c. A multiple-line arrangement is favored when servers provide a limited set of services. Customers wait in the appropriate line for a particular service. d. Arrangement of service facilities Single-channel, single-phase Customers form one line All services performed by a single-server facility Single-channel, multiple-phase Servers specialize in one part of service Customers form one line and proceed sequentially from one service facility to the next Multiple-channel, single-phase Used when demand is large enough to warrant providing the same service at more than one facility Or when the services offered by the facilities are different Multiple-channel, multiple-phase Occurs when customers can be served by one of the first-phased facilities But then require service from a second-phase facility, and so on. Mixed arrangement Unique services Services can’t be described neatly in phases Job shop use of various machines and different routings 3. Priority rule a. First-come, first-served (FCFS)—priority discipline is assumed.
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