chapter11 liner model programing.pptx
- 3. Waiting line models that have been develop to help managers make better decision concerning the operation of waiting lines. We also showed how an economics analysis of the waiting line could be conducted by developing a total cost model that includes the cost associated with units waiting for services and the cost required to operate the service facility.
- 4. Models have been develop to help managers understand and make better decisions concerning the operation of waiting lines. In management science terminology ,a waiting lines is also known as queue and the body of knowledge dealing with waiting lines is known as queueing theory.
- 5. Waiting line models- consist of mathematics formulas and relationships that can be used to determine the operating characteristics (performance measures)for a waiting line. Operating characteristics of interest include these: 1.The probability that no units are in the system (I,e the system is idle) 2.The average number of units in the waiting line.
- 6. 3.The average number of units in the system(the number of units in the service time)plus the number of units being served). 4.The average time a unit spend in the waiting line. 5.The average time a unit spend in the system (the waiting time plus the service time). 6.The probability that an arriving unit as to wait for service.
- 7. Structure of a waiting line system Burger Dome is concerned that the methods currently used to serve customers are resulting in excessive waiting times and a possible loss of sale. Management wants to conduct a waiting line study to help determine the best approach to reduce waiting times and improve service
- 8. Single –serve waiting line each customer entering the Burger Dome restaurant is served by a single order-filling station that handles order placement ,bill payment and food delivery. Distribution of Arrivals –Defined the arrival process for a waiting line involves determining the probability distribution for the number of arrivals in a given period of time.
- 9. Distribution of Service Times-is the time a customer spends as the service facility once the service has started. Exponential probability distribution- Formulas are available for providing useful information about the operation of the waiting line. Queue Discipline-(FCFS) –First come and First served basis. For example ,when people board an airplane the last passengers to board are typically the first to deplane since many airlines have the passengers with seat assignment in the back of the plane board first.
- 10. Steady-State Operation- the beginning or startup period is referred to as the transient period. The transient period ends when the system reaches the normal or steady-state operation. Waiting line models describe the steady-state operating characteristics of a waiting line. Managers’ Use of waiting line models -This condition indicates a fairly high probability that Burger Dome will experiences some long waiting lines if it continues to use the single –server operation.
- 11. Improving the waiting line operation- Waiting line models often indicates when improvements in operating characteristics are desirable. 1.Increasing the service rate by making a creative design change or by using new technology. 2.Add one or more servers so that more customers can be served simultaneously. Excel Solution of Waiting Line Models- Waiting line models are easily implemented with the aid of spreadsheets.
- 12. Multiple-server waiting line- consists of two or more server that are assumed to be identical in terms of service capability. For multiple-server systems there are two typical queueing possibilities. 1.arriving customers wait in a single waiting line (called a “pooled” or “shared” queue) and then move to the first available server for processing. 2.Each server has a “dedicated” queue and an arriving customer selects one of these lines to join(and typically is not allowed to switch lines).
- 13. Economics Analysis of Waiting Lines- To conduct an economics analysis of a waiting line we must obtain reasonable estimates of the waiting cost and the service cost. Constant Service Times- Such a waiting line can occur in production and manufacturing environments where machine- controlled service times are generally constant. Waiting Line Models With Finite Calling Populations-Infinite calling population –In technique terms when no limits is placed on how many units seek service.
- 14. Finite calling population-In this situation the arrival rate for the system change ,depending on the number of unity in the waiting line. 1.The arrivals for each units follow a poison probability distribution ,with arrival rate. 2.The service times follow an exponential probability distribution with service rate . 3.The population of units that may seek service.
- 15. THANK YOU!! “Let us always meet each other with a smile for the smile is the beginning of love”.