From the course: Operations Management Foundations

Lines and service facility

From the course: Operations Management Foundations

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Lines and service facility

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- Waiting-line calculations can be simple or extremely complex. It really depends on the system. How many lines, how many workers? Can customers leave the line? Can customers switch lines? Complex systems require complex calculations but no matter how simple or complex, the two most important variables to consider are customer arrival rate. How often do customers join the line? And employee service rate. How many customers can the employee help in a given period of time? If we know those two things, we have the key ingredients in almost any waiting-line formula. Let's first calculate the percentage of time a worker is busy. The percentage of time a worker is busy is equal to the customer arrival rate divided by the employee service rate. So, if six customers arrive per hour and our employee can help eight customers in an hour, we would divide six per hour by eight per hour. In this case, our one worker is busy 75% of the time. If we hired a second worker, they would split up the work. Each of the two workers would be busy 37.5% of the time. And in a three-worker system, a three-way split of the work of a single worker would mean that each worker was busy 25% of the time. Looking at these numbers, it sounds like one worker is all we would need. Having workers busy only 37.5% of the time doesn't sound great. But through some more advanced formulas, we would find that adding one or two additional workers can significantly decrease the average time a customer spends in line. Check this out. When you have only one server, the average time in line is 22-and-a-half minutes. That's a really long wait. When you add a second worker, the average time in line drops to one minute and 14 seconds. Really, it does. And when you have three workers, the average time in line goes all the way down to nine seconds. Shorter lines might mean happier customers that treat our workers well, fewer customers leaving before they get served and returning customers in the future. And perhaps word of mouth will even bring more customers to our business in the future. So, now that we see those numbers, does it mean we definitely need to add a second or third worker? While our customers may say, "Yes," the boss may not agree. Remember, adding a second worker will double our wages in the waiting line system. Plus, if the second worker needs a workstation, a computer, and any other equipment, we'll need to pay for those two. A third worker triples our one-worker costs. I guess the point is there are no easy answers but when you begin to explore waiting line data in conjunction with understanding the psychological aspects of waiting lines, you have the power to make informed decisions that will impact the company, the customer, and our employees. Next time you wait in a long line, consider all the variables. How often are new people joining the line? How long does it take for one person to help one customer? How much time are people waiting in the line before they get served? And finally, how might things change if they added one more server?

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