财务管理与财务分析运营管理课件C.ppt

1、Waiting Lines,Supplement C,Queue is everywhere,One of the important area of operations management Visible queue Invisible queue: telephone, dial into Internet, Fudan mailbox,Waiting Line Examples,BankCustomersTellerDeposit etc. DoctorsPatientDoctorTreatmentoffice Traffic CarsLightControlledintersect

2、. passage Assy linePartsWorkersAssembly,SituationArrivalsServersSvc. Process,Queuing system,Suggestions for managing queues Determine an acceptable waiting time for your customers Try to divert your customers attention when waiting Inform your customers of what to expect Keep employees not serving t

3、he customer out of sight Segment customers,Queuing system,Suggestions for managing queues (continued) Train your servers to be friendly. (Greet the customers) Encourage customers to come during the slack periods Take a long term perspective toward getting rid of the queues,Waiting Lines,Waiting line

4、: One or more “customers” waiting for service. Customer population: An input that generates potential customers. Service facility: A person (or crew), a machine (or group of machines), or both, necessary to perform the service for the customer. Priority rule: A rule that selects the next customer to

5、 be served by the service facility. Service system: The number of lines and the arrangement of the facilities.,Waiting Line ModelsBasic Elements,Waiting Line Arrangements,Service Facility Arrangements,Channel: One or more facilities required to perform a given service. Phase: A single step in provid

6、ing a service. Priority rule: The policy that determines which customer to serve next.,Service Facility Arrangements,Single channel, single phase,Single channel, multiple phase,Service Facility Arrangements,Multiple channel, single phase,Service Facility Arrangements,Multiple channel, multiple phase

7、,Service Facility Arrangements,Service Facility Arrangements,Mixed Arrangement,Priority Rule,The priority rule determines which customer to serve next. Most service systems use the first-come, first-serve (FCFS) rule. Other priority rules include: Earliest promised due date (EDD) Customer with the s

8、hortest expected processing time (SPT) Preemptive discipline: A rule that allows a customer of higher priority to interrupt the service or another customer.,Distribution of arrivals,Arrival rate: the number of units per period Constant arrival distribution Variable arrival distributions Observing ar

9、rivals from two viewpoints: Analyze the time between successive arrivals Set some time length and try to determine how many arrivals might enter the system within T.,Distribution of arrivals,Exponential distribution pdf (density) : the mean number of arrivals per time period Poisson Distribution Pro

10、bability of exactly n arrivals during T periods, factorial,Probability DistributionsArrival Times,Example C.1 Arrival rate = 2/hour,Customer Arrivals are usually random and can be described by a Poisson distribution.,Probability that n customers will arrive,Interarrival times: The time between custo

11、mer arrivals.,Probability that 4 customers will arrive,Mean = T Variance = T,The exponential distribution describes the probability that the service time will be no more than T time periods.,Probability DistributionsService time,If the customer service rate is three per hour, what is the probability

12、 that a customer requires less than 10 minutes of service?,P(t T) = 1 e-T, = average number of customers completing service per periodt = service time of the customer T = target service time,Example C.2,Mean = 1/ Variance = (1/ )2,Operating Characteristics,Line Length: Number of customers in line. N

13、umber of Customers in System: Includes customers in line and being serviced. Waiting Time in Line: Waiting for service to begin. Total Time in System: Elapsed time between entering the line and exiting the system. Service Facility Utilization: Reflects the percentage of time servers are busy.,The si

14、mplest waiting line model involves a single server and a single line of customers. Assumptions: The customer population is infinite and patient. The customers arrive according to a Poisson distribution, with a mean arrival rate of The service distribution is exponential with a mean service rate of T

15、he mean service rate exceeds the mean arrival rate. Customers are served on a first-come, first-served basis. The length of the waiting line is unlimited.,Lq = Average number of customers in the waiting line = L,Wq = Average waiting time in line = W,Rn = Probability that n customers are in the syste

16、m = (1 r)rn,Single-Channel, Single-Phase System,Arrival rate (l= 30/hour, Service rate (m = 35/hour,Average time in line = Wq = 0.857(0.20) = 0.17 hour, or 10.28 minutes,Average number in line = Lq = 0.857(6) = 5.14 customers,Example C.3,Application C.1,Example C.4,Example C.4,Example C.4,Applicatio

17、n C.2,Multiple-Channel, Single-Phase System,With the multiple-server model, customers form a single line and choose one of s servers when one is available. The service system has only one phase. There are s identical servers. The service distribution for each is exponential. Mean service time is 1/m

18、 The service rate (s exceeds the arrival rate ().,American Parcel Service is concerned about the amount of time the companys trucks are idle, waiting to be unloaded. The terminal operates with four unloading bays. Each bay requires a crew of two employees, and each crew costs $30/hr. The estimated c

19、ost of an idle truck is $50/hr. Trucks arrive at an average rate of three per hour, according to a Poisson distribution. Unloading a truck averages one hour with exponential service times. 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time

20、 = 1 hour,Multiple-Server Model Example C.5,Multiple-Server Model,4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour,Application C.3,Application C.3,hrs. (or 4.224 minutes),Littles Law,Littles Law relates the number of customers in a waiting-line system to the waiting time of customers. L = W L is the average number of customers in the system. is the customer arrival rate. W is the average time spent in system, including service.,In the finite-source model, the single-server model assumptions ar