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future position in management using Simulation and Queuing analysis
Simulation represents a major divergence from the topics presented in the previous chapters of this text. Previous topics usually dealt with mathematical models and formulas that could be applied to certain types of problems. The solution approaches to these problems were, for the most part, analytical. However, not all real-world problems can be solved by applying a specific type of technique and then performing the calculations. Some problem situations are too complex to be represented by the concise techniques presented so far in this text. In such cases, simulation is an alternative form of analysis. Analogue simulation is a form of simulation that is familiar to most people. In analogue simulation, an original physical system is replaced by an analogous physical system that is easier to manipulate. Much of the experimentation in staffed spaceflight was conducted using physical simulation that re-created the conditions of space. For example, conditions of weightlessness were simulated using rooms filled with water. Other examples include wind tunnels that simulate the conditions of flight and treadmills that simulate automobile tire wear in a laboratory instead of on the road. This chapter is concerned with an alternative type of simulation, computer mathematical simulation. In this form of simulation, systems are replicated with mathematical models, which are analyzed using a computer. This form of simulation has become very popular and has been applied to a wide variety of business problems. One reason for its popularity is that it offers a means of analyzing very complex systems that cannot be analyzed by using the other management science techniques in this text. However, because such complex systems are beyond the scope of this text, we will not present actual simulation models; instead, we will present simplified simulation models of systems that can also be analyzed analytically. We will begin with one of the simplest forms of simulation models, which encompasses the Monte Carlo process for simulating random variables.
Waiting in queues-waiting lines-is one of the most common occurrences in everyone's life. Anyone who has gone shopping or to a movie has experienced the inconvenience of waiting in line to make purchases or buy a ticket. Not only do people spend a significant portion of their time waiting in lines, but products queue up in production plants, machinery waits in line to be serviced, planes wait to take off and land, and so on. Because time is a valuable resource, the reduction of waiting time is an important topic of analysis. The improvement of service with respect to waiting time has also become more important in recent years because of the increased emphasis on quality, especially in service-related operations. When customers go to a bank to take out a loan, cash a check, or make a deposit; take their car to a dealer for service or repair; or shop at the grocery store; they increasingly equate quality service with rapid service. Aware of this, more and more companies are focusing on reducing waiting time as an important component of quality improvement. In general, companies are able to reduce waiting time and provide faster service by increasing their service capacity, which usually means adding more servers; such as more tellers at a bank, more mechanics at a car dealership, or more checkout clerks at a grocery store. However, increasing service capacity in this manner has a monetary cost, and therein lies the basis of waiting line analysis: the trade-off between the cost of improved service and the cost of making customers wait. Like decision analysis, queuing analysis is a probabilistic form of analysis, not a deterministic technique. Thus, the results of queuing analysis, referred to as operating characteristics, are probabilistic. These operating statistics (such as the average time a person must wait in line to be served) are used by the manager of the operation containing the queue to make decisions. A number of different queuing models exist to deal with different queuing systems. We will eventually discuss many of these queuing variations, but we will concentrate on two of the most common types of systems-the single-server system and the multiple-server system.
Elements of Waiting Line Analysis Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served. However, this does not mean that the service operation is understaffed or does not have the overall capacity to handle the influx of customers. In fact, most businesses and organizations have sufficient serving capacity available to handle their customers in the long run. Waiting lines result because customers do not arrive at a constant, evenly paced rate, nor are they all served in an equal amount of time. Customers arrive at random times, and the time required to serve them individually is not the same. Thus, a waiting line is continually increasing and decreasing in length (and is sometimes empty), and it approaches an average rate of customer arrivals and an average time to serve the customer in the long run. For example, the checkout counters at a grocery store may have enough clerks to serve an average of 100 customers in an hour, and in any particular hour only 60 customers might arrive. However, at specific points in time during the hour, waiting lines may form because more than an average number of customers arrive, and they make more than an average number of purchases. Decisions about waiting lines and the management of waiting lines are based on these averages for customer arrivals and service times. They are used in queuing formulas to compute operating characteristics, such as the average number of customers waiting in line and the average time a customer must wait in line. Different sets of formulas are used, depending on the type of waiting line system being investigated. For example, a bank drive-up teller window that has one bank clerk serving a single line of customers in cars is different from a single line of passengers at an airport ticket counter that is served by three or four airline agents. In the next section, we present the different elements and components that make up waiting lines before we look at queuing formulas in the following sections.
Providing quick service is an important aspect of quality customer service.
Queuing analysis is the probabilistic analysis of waiting lines.
Operating characteristics are average values for characteristics that describe the performance of a waiting line system.
the single-server Waiting line system 609
The Single-Server Waiting Line System A single server with a single waiting line is the simplest form of queuing system. As such, it will be used to demonstrate the fundamentals of a queuing system. As an example of this kind of system, consider Fast Shop Market.