Most waiting line problems are centered on the question of finding the ideal level of services that a firm should provide. Supermarkets must decide how many cash register checkout positions should be opened. Gasoline stations must decide how many pumps should be opened and how many attendants should be on duty. Manufacturing plants must determine the optimal number of mechanics to have on duty each shift to repair machines that break down. Banks must decide how many teller windows to keep open to serve customers during various hours of the day. In most cases, this level of service is an option over which management has control. An extra teller, for example, can be borrowed from another chore or can be hired and trained quickly if demand warrants it. This may not always be the case, though. A plant may not be able to locate or hire skilled mechanics to repair sophisticated electronic machinery.

When an organization does have control, its objective is usually to find a happy medium between two extremes. On the one hand, a firm can retain a large staff and provide many service facilities. This may result in excellent customer service, with seldom more than one or two customers in a queue. Customers are kept happy with the quick response and appreciate the convenience. This, however, can become expensive.

The other extreme is to have the minimum possible number of checkout lines, gas pumps, or teller windows open. This keeps the service cost down but may result in customer dissatisfaction. How many times would you return to a large discount department store that had only one cash register open during the day you shop? As the average length of the queue increases and poor service results, customers and goodwill may be lost.

Most managers recognize the trade-off that must take place between the cost of providing good service and the cost of customer waiting time. They want queues that are short enough so that customers don’t become unhappy and either storm out without buying or buy but never return. But they are willing to allow some waiting in line if it is balanced by a significant savings in service costs.

One means of evaluating a service facility is thus to look at a total expected cost, a concept illustrated in Figure 12.1. Total expected cost is the sum of expected service costs plus expected waiting costs.

Service costs are seen to increase as a firm attempts to raise its level of service. For example, if three teams of stevedores, instead of two, are employed to unload a cargo ship, service costs are increased by the additional price of wages. As service improves in speed, however, the cost of time spent waiting in lines decreases. This waiting cost may reflect lost productivity of workers while their tools or machines are awaiting repairs or may simply be an estimate of the costs of customers lost because of poor service and long queues.

Three Rivers Shipping Company Example

As an illustration, let’s look at the case of the Three Rivers Shipping Company. Three Rivers runs a huge docking facility located on the Ohio River near Pittsburgh. Approximately five ships arrive to unload their cargoes of steel and ore during every 12-hour work shift. Each hour that a ship sits idle in line waiting to be unloaded costs the firm a great deal of money, about $1,000 per hour. From experience, management estimates that if one team of stevedores is on duty to handle the unloading work, each ship will wait an average of 7 hours to be unloaded. If two teams are working, the average waiting time drops to 4 hours; for three teams, it’s 3 hours; and for four teams of stevedores, it’s only 2 hours. But each additional team of stevedores is also an expensive proposition, due to union contracts.

Figure 12.1 Full Alternative Text

Three Rivers’ superintendent would like to determine the optimal number of teams of stevedores to have on duty each shift. The objective is to minimize the total expected costs. This analysis is summarized in Table 12.1. To minimize the sum of service costs and waiting costs, the firm makes the decision to employ two teams of stevedores each shift.