2Service BusinessesA service business is the management of organizations whose primary business requires interaction with the customer to produce the serviceGenerally classified according to who the customer is:Financial servicesHealth careA contrast to manufacturing5
4Characteristics of Workers, Operations, and Innovations Relative to the Degree of Customer/Service Contact
5Queuing Theory Waiting occurs in Service facility Fast-food restaurantspost officegrocery storebankManufacturingEquipment awaiting repairPhone or computer networkProduct ordersWhy is there waiting?
6Customer Service Population Sources FiniteInfiniteExample: Number of machines needing repair when a company only has three machines.Example: The number of people who could wait in a line for gasoline.4
7Service Pattern Service Pattern Constant Variable Example: Items coming down an automated assembly line.Example: People spending time shopping.5
8The Queuing System Queuing System Length Number of Lines & Queue DisciplineNumber of Lines &Line StructuresQueuingSystemService TimeDistribution
9Examples of Line Structures SinglePhaseMultiphaseOne-personbarber shopCar washHospitaladmissionsBank tellers’windowsSingle ChannelMultichannel6
10Measures of System Performance Average number of customers waitingIn the queueIn the systemAverage time customers waitSystem utilization
11Number of Servers Single Server Multiple Servers Multiple Single Servers
13Some Models 1. Single server, exponential service time (M/M/1) 2. Multiple servers, exponential service time (M/M/s)A TaxonomyM / M / sArrival Service Number ofDistribution Distribution ServerswhereM = exponential distribution (“Markovian”)
14l = customer arrival rate Givenl = customer arrival ratem = service rate (1/m = average service time)s = number of serversCalculateLq = average number of customers in the queueL = average number of customers in the systemWq = average waiting time in the queueW = average waiting time (including service)Pn = probability of having n customers in the systemr = system utilizationNote regarding Little’s Law: L = l * W and Lq = l * Wq
15Model 1: M/M/1 ExampleThe reference desk at a library receives request for assistance at an average rate of 10 per hour (Poisson distribution). There is only one librarian at the reference desk, and he can serve customers in an average of 5 minutes (exponential distribution). What are the measures of performance for this system? How much would the waiting time decrease if another server were added?
16Application of Queuing Theory We can use the results from queuing theory to make the following types of decisions:How many servers to employWhether to use one fast server or a number of slower serversWhether to have general purpose or faster specific serversGoal: Minimize total cost = cost of servers + cost of waiting
17Example #1: How Many Servers? In the service department of an auto repair shop, mechanics requiring parts for auto repair present their request forms at the parts department counter. A parts clerk fills a request while the mechanics wait. Mechanics arrive at an average rate of 40 per hour (Poisson). A clerk can fill requests in 3 minutes (exponential). If the parts clerks are paid $6 per hour and the mechanics are paid $18 per hour, what is the optimal number of clerks to staff the counter.Service Cost = s * CsWaiting Cost = l * W * CwS = 4 IS THE SMALLEST
18Example #2: How Many Servers? Beefy Burgers is trying to decide how many registers to have open during their busiest time, the lunch hour. Customers arrive during the lunch hour at a rate of 98 customers per hour (Poisson distribution). Each service takes an average of 3 minutes (exponential distribution). Management would not like the average customer to wait longer than five minutes in the system. How many registers should they open?Need at least 5 (why?) Increment from there
19Choose s = 6 since W = 0.0751 hour is less than 5 minutes. For six serversChoose s = 6 since W = hour is less than 5 minutes.
20Example #3: One Fast Server or Many Slow Servers? Beefy Burgers is considering changing the way that they serve customers. For most of the day (all but their lunch hour), they have three registers open. Customers arrive at an average rate of 50 per hour. Each cashier takes the customer’s order, collects the money, and then gets the burgers and pours the drinks. This takes an average of 3 minutes per customer (exponential distribution). They are considering having just one cash register. While one person takes the order and collects the money, another will pour the drinks and another will get the burgers. The three together think they can serve a customer in an average of 1 minute. Should they switch to one register?
213 Slow Servers 1 Fast Server W is less for one fast server, so choose this option.
22Example 4: Southern Railroad The Southern Railroad Company has been subcontracting for painting of its railroad cars as needed. Management has decided the company might save money by doing the work itself. They are considering two alternatives. Alternative 1 is to provide two paint shops, where painting is to be done by hand (one car at a time in each shop) for a total hourly cost of $70. The painting time for a car would be 6 hours on average (assume an exponential painting distribution) to paint one car. Alternative 2 is to provide one spray shop at a cost of $175 per hour. Cars would be painted one at a time and it would take three hours on average (assume an exponential painting distribution) to paint one car. For each alternative, cars arrive randomly at a rate of one every 5 hours. The cost of idle time per car is $150 per hour.Estimate the average waiting time in the system saved by alternative 2.What is the expected total cost per hour for each alternative? Which is the least expensive?Answer: Alt 2 saves 1.87 hours. Cost of Alt 1 is: $ / hour and cost of Alt 2 is $ /hour.
23Example 5A large furniture company has a warehouse that serves multiple stores. In the warehouse, a single crew with four members is used to load/unload trucks. Management currently is downsizing to cut costs and wants to make a decision about crew size.Trucks arrive at the loading dock at a mean rate of one per hour. The time required by the crew to unload/and-or load a truck has an exponential distribution (regardless of crew size). The mean of the distribution for a four member crew is 15 minutes – i.e., 4 trucks per hour. If the crew size is changed, the service rate is proportional to its size – i.e., a three member crew could do 3 per hour, etc.The cost of providing each member of the crew is $20 per hour and the cost for a truck waiting is $30 per hour. The company has a service goal such that the likelihood of a truck spending more than one hour being served is 5% or less.For the current configuration, what is the average waiting time in the system? What is the average number of trucks waiting to be unloaded (not including the truck currently being unloaded? What is the probability that a truck waits more than one hour to be unloaded? What is the total cost of the four person crew?Suppose the company is looking at alternatives. One is a three member crew. What is the cost of this crew? Compare the statistics mentioned in part a) with comparable statistics for the three member crew. Would you select the three member crew over the crew in part a)? Why or why not?One person suggested that rather than have one four member crew, the firm should use two, two member crews, where each crew could load/unload two trucks per hour. What is the cost of this solution? What is the probability that a truck waits longer than one hour for loading/unloading? Would you recommend that they implement this solution? Why or why not?