Operations ResearchRegional airlines case analysisApurb Sinha                 Executive PGDM (2010 – 11)<br />Contents TOC...
Calls to the reservation agent occur randomly at an average of one call every 3.75 mins.
Historical service data shows that the agent spends an average of 3 mins with each customer.
The waiting line model of Poisson arrivals and exponential service time appears reasonable.
Cost of ticket reservation agent is $20 per hour.
Acceptable customer service goal is to answer 85% of the incoming calls immediately.</li></ul>Opinion and proposed solutio...
The average number of units in the waiting line.
The average number of units in the system.
The average time a unit spends in a waiting line.
The average time a unit spends in the system.
The probability that an arriving unit has to wait for service.</li></ul>All problems that depend upon the queues can be an...
The mean arrival rate (ƛ) = 1 customer per 3.75 mins = 16 customer per hour.
The mean service rate(µ) = 1 customer per 3 mins = 20 customer per hour.
The calls are taken by the agent only if he is free and not otherwise. All the calls that are not taken by the agent are b...
System utilisation  ρ= ƛμ  = 1620<1</li></ul>Operating characteristics of the system<br /><ul><li>Probability that the j o...
Pj= ƛμj/j!i=0kƛμi/i!
Where k is the number of agents.
At k =1
P1= 16201/1!162000!+162011!</li></ul>P1= 0.81+0.8=0.44<br />On percentage basis P1 indicated that 44% of calls will be blo...
Ls= ƛμ1-P1=16201-.44=0.448 ~ 1
The average number of customers in the system is 1
Wq =  Average time that the customer spends in the waiting line
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Regional Airlines - telephone reservation system analysis

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Regional Airlines - telephone reservation system analysis

  1. 1. Operations ResearchRegional airlines case analysisApurb Sinha Executive PGDM (2010 – 11)<br />Contents TOC o "1-3" h z u Case PAGEREF _Toc283592935 h 4Project Background PAGEREF _Toc283592936 h 6Available data and assumptions PAGEREF _Toc283592937 h 6Opinion and proposed solutions PAGEREF _Toc283592938 h 7Vice President of Administration PAGEREF _Toc283592939 h 7Vice President Marketing PAGEREF _Toc283592940 h 7Telephone Company Representative PAGEREF _Toc283592941 h 7What is waiting line model PAGEREF _Toc283592942 h 8Notation PAGEREF _Toc283592943 h 8Distribution of arrivals PAGEREF _Toc283592944 h 8Distribution of service time PAGEREF _Toc283592945 h 9Queue discipline PAGEREF _Toc283592946 h 9Servers PAGEREF _Toc283592947 h 9History of queuing theory PAGEREF _Toc283592948 h 9Limitations of queuing theory PAGEREF _Toc283592949 h 10Evaluation of the Existing System PAGEREF _Toc283592950 h 10Analysis - Claim of Vice President of Administration PAGEREF _Toc283592951 h 10Diagram PAGEREF _Toc283592952 h 10Waiting line Model - 1 agent with no waiting PAGEREF _Toc283592953 h 11Operating characteristics of the system PAGEREF _Toc283592954 h 12Analysis - Claim of Vice President of marketing PAGEREF _Toc283592955 h 13Assumption PAGEREF _Toc283592956 h 13Diagram – Model PAGEREF _Toc283592957 h 13Waiting line Model - 2 agent with no waiting PAGEREF _Toc283592958 h 14Operating characteristics of the system PAGEREF _Toc283592959 h 14Analysis – Proposed solution by Telephone Company PAGEREF _Toc283592960 h 16Model – with 1 agent PAGEREF _Toc283592961 h 16Model Used: M/M/1 – when waiting is allowed PAGEREF _Toc283592962 h 16Operating characteristics of the system PAGEREF _Toc283592963 h 16Model – with 2 agents PAGEREF _Toc283592964 h 19Model Used: M/M/K where c =2 and waiting is allowed PAGEREF _Toc283592965 h 19Steady state PAGEREF _Toc283592966 h 21Recommendations PAGEREF _Toc283592967 h 22<br />Case<br />Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 am to 11:00 am time period, calls to the reservation agents occur randomly at an average of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system.<br />Regional Airlines’ management believes that offering an efficient telephone reservation system is an important part of establishing an image as a service-oriented airline. If the system is properly implemented, Regional Airlines will establish good customer relations, which in the long run will increase business. However, if the telephone reservations system is frequently overloaded and customers have difficulty contacting an agent, a negative customer reaction may lead to an eventual loss of business. The cost of a ticket reservation agent is $20 per hour. Thus, management wants to provide good service, but it does not want to incur the cost of overstaffing the telephone reservation operation by using more agents than necessary.<br />At a planning meeting, Regional’s management team agreed that an acceptable customer service goal is to answer at least 85% of the incoming calls immediately. During the planning meeting, Regional’s vice president of administration pointed out that the average service rate for an agent is faster than the average arrival rate of the telephone calls. The vice president’s conclusion was that the personnel costs could be minimized by using one agent and that the single agent should be able to handle the telephone reservations and still have some idle time. The vice president of marketing restated the importance of customer service and expressed support for at least two reservation agents.<br />The current telephone reservation system design does not allow callers to wait. Callers who attempt to reach a reservations agent when all agents are occupied receive a busy signal and are blocked from the system. A representative from the telephone company suggested that Regional Airlines consider an expanded system that accommodates waiting. In the expanded system, when a customer calls and all agents are busy, a recorded message tells the customer that the call is being held in the order received and that an agent will be available shortly. The customer can stay on the line and listen to background music while waiting for an agent. Regional’s management will need more information before switching to the expanded system.<br />Prepare a managerial report for Regional Airlines analyzing the telephone reservation system. Evaluate both the system that does not allow waiting and the expanded system that allows waiting. Consider the following in your report:<br />1.A detailed analysis of the operating characteristics of the reservations system with one agent as proposed by the vice president of administration. What is your recommendation concerning a single-agent system?<br />2.A detailed analysis of the operating characteristics of the reservation system based on your recommendation regarding the number of agents Regional should use.<br />3.What appears to be the advantages or disadvantages of the expanded system? Discuss the number of waiting calls the expanded system would need to accommodate.<br />The telephone arrival data are for the 10:00 am to 11:00 am time period; however, the arrival rate of incoming calls is expected to change from hour to hour. Describe how your waiting line analysis could be used to develop a ticket agent staffing plan that would enable the company to provide different levels of staffing for the ticket reservation system at different times during the day. Indicate the information that you would need to develop this staffing plan.<br />Project Background<br />The airline company wants to provide an efficient telephone reservation system. This will help them to establish good customer relations which in a long run will increase the business.<br />The management wants to provide a good service but it does not want to incur unnecessary cost by overstaffing the telephone reservation system.<br />The current telephone system design does not allow the caller to wait. The caller who attempts to reach a reservation system, when all agents are busy is sent a busy tone and blocks them from the system.<br />Available data and assumptions<br /><ul><li>The system is being designed to handle calls between 10:00 AM and 11:00 AM
  2. 2. Calls to the reservation agent occur randomly at an average of one call every 3.75 mins.
  3. 3. Historical service data shows that the agent spends an average of 3 mins with each customer.
  4. 4. The waiting line model of Poisson arrivals and exponential service time appears reasonable.
  5. 5. Cost of ticket reservation agent is $20 per hour.
  6. 6. Acceptable customer service goal is to answer 85% of the incoming calls immediately.</li></ul>Opinion and proposed solutions<br />The problem has been discussed upon by the management within them and the telephone company and they have the following proposals.<br />Vice President of Administration<br />He pointed out that the past data shows that the average service rate of the service agent has been more than the average arrival rate of the telephone calls hence the system can be handled by using one agent. The agent will be able to handle the telephone calls and still have idle time.<br />Vice President Marketing<br />The VP Marketing restated the importance of customer service and expresses and supports the idea of having at least 2 agents to support the system.<br />Telephone Company Representative<br />The representative from the telephone company suggests that the regional airline considers an expanded system to accommodate the waiting customers. In this new expanded system, when a customer calls when all the agent are busy , then a recorded message tells the customer that the call is being held in the order received and that an agent will be available shortly. The customer can stay on the line and listen to the music while waiting for the agent.<br />What is waiting line model<br />The case is a pure case of waiting line model of operations research. The waiting line model can best be understood by remembering a time when you had to wait somewhere in a long line, such as at a banks, fast food restaurant, store like big bazaar, or any local market. For these waiting-in-line places, the time waiting is unacceptable and a waste of your time. <br />Many models have been developed to help bosses and managers help them for better decisions when the operation of a department has to consider long waiting lines. The whole idea is how to optimize the available scarce resources to optimize the services and hence optimize profit. <br />In management science theory, there is a model, known as queuing theory, which deals with waiting lines. Waiting-line models usually consist of mathematical formulas that can be used to determine the operating characteristics for a waiting line and include the following:<br /><ul><li>The probability that no units are in the system.
  7. 7. The average number of units in the waiting line.
  8. 8. The average number of units in the system.
  9. 9. The average time a unit spends in a waiting line.
  10. 10. The average time a unit spends in the system.
  11. 11. The probability that an arriving unit has to wait for service.</li></ul>All problems that depend upon the queues can be analysed by keeping the above theory in mind.<br />The following defines the structure of a waiting line/Queuing system:<br />Notation<br />The model is expressed in the notation A/B/C, which designates a queuing system having A as inter arrival time distribution, B as service time distribution, and C as number of servers<br />Distribution of arrivals <br /><ul><li>This expresses the arrival of customers into the system, which means the number of the telephone calls that arrived in the regional airline office for reservation and is handled by the customer service agent. The arrival rate is supposed to follow a Poisson distribution with parameter as the mean arrival rate. </li></ul>Distribution of service time <br />This means the time that each application will take in the process; it is usually a random variable.<br />Queue discipline <br /> The queue discipline determines the manner in which the system handles the customers. It defines the way in which they will be served, the order in which they will be served and the way in which the resources will be divided amongst the customers. There are four main queue disciplines First-In-First-Out, Last-In-First-out, Resource-Sharing and Priority based.<br />Servers<br />The servers refer to the number of point of services available in the system. Through which the customer has to go. There can be single server based channel and a multiple server based channels.<br />History of queuing theory<br />Queuing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the (back of the) queue, waiting in the queue (essentially a storage process), and being served at the front of the queue. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.<br />The word queue comes, via French, from the Latin cauda, meaning tail. The spelling "queuing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the profession is named "Queuing Systems".<br />Agner Krarup Erlang, a Danish engineer who worked for the Copenhagen Telephone Exchange, published the first paper on queuing theory in 1909.<br />David G. Kendall introduced an A/B/C queuing notation in 1953. Important work on queuing theory used in modern packet switching networks was performed in the early 1960s by Leonard Klein rock.<br />Limitations of queuing theory<br />The assumptions of classical queuing theory may be too restrictive to be able to model real-world situations exactly. The complexity of production lines with product-specific characteristics cannot be handled with those models. Therefore specialized tools have been developed to simulate, analyze, visualize and optimize time dynamic queuing line behaviour.<br />Evaluation of the Existing System<br />Analysis - Claim of Vice President of Administration<br />The VP administration that average service rate of the service agent has been more than the average arrival rate of the telephone calls hence the system can be handled by using one agent. The agent will be able to handle the telephone calls and still have idle time. The claim is totally in line with the one of his KRA of cost saving in mind. <br />Diagram<br />The system will look as diagram below.<br />There is a single customer service agent and there is no waiting line allowed. Which means when the agent is busy the calling customer gets a busy signal and is blocked from entering the system.<br />Waiting line Model - 1 agent with no waiting<br />This model is a variation of the waiting line model (M/M/1) in which no waiting is allowed. The calling customer expects the agent to answer but if the agent is busy, a busy tone is send to the customer and the customer is blocked from entering the system. Incoming calls arriving when the agent is busy are blocked and are cleared from the system. Such customer may be lost i.e. may not choose to call again or may attempt to return to the system by calling in some other time.<br />The following are the assumptions for the model<br /><ul><li>The system has only one agent.
  12. 12. The mean arrival rate (ƛ) = 1 customer per 3.75 mins = 16 customer per hour.
  13. 13. The mean service rate(µ) = 1 customer per 3 mins = 20 customer per hour.
  14. 14. The calls are taken by the agent only if he is free and not otherwise. All the calls that are not taken by the agent are blocked from entering the system.
  15. 15. System utilisation ρ= ƛμ = 1620<1</li></ul>Operating characteristics of the system<br /><ul><li>Probability that the j of the k agent will be busy is given by
  16. 16. Pj= ƛμj/j!i=0kƛμi/i!
  17. 17.
  18. 18. Where k is the number of agents.
  19. 19. At k =1
  20. 20. P1= 16201/1!162000!+162011!</li></ul>P1= 0.81+0.8=0.44<br />On percentage basis P1 indicated that 44% of calls will be blocked.<br />Probability that there are no customer in the system is 1-p1 = 56%<br /><ul><li>Lq = Average number of customers waiting in the queue. </li></ul>Since the queue is not allowed hence operating characteristic Lq is zero <br /><ul><li>Ls = Average number of customers in the system
  21. 21. Ls= ƛμ1-P1=16201-.44=0.448 ~ 1
  22. 22. The average number of customers in the system is 1
  23. 23. Wq = Average time that the customer spends in the waiting line
  24. 24. Since the queue is not allowed hence operating characteristic Wq is zero
  25. 25. Ws = Average time that the customer spends in the system </li></ul>Ws = Ls/ƛ = 0.448/20 = 0.0224 hours = 1.34 mins<br />The above table shows that the 1 agent system will be able to answer to only 44% of the calls as soon as they arrive. This is not as per the company policy of answering at least 85% calls as they arrive.<br />Analysis - Claim of Vice President of marketing<br /> The VP Marketing restated the importance of customer service and expresses and supports the idea of having at least 2 agents to support the system. <br />Assumption<br />The assumption is that the both the agents are equally capable of handling the customers and have chance of serving the customer<br />Diagram – Model<br />Waiting line Model - 2 agent with no waiting<br />This model is a variation of the waiting line model (M/M/2) in which no waiting is allowed. The calling customer expects the either of the agents to answer but if both the agent is busy, a busy tone is send to the customer and the customer is blocked from entering the system. Incoming calls arriving when the agent is busy are blocked and are cleared from the system. Such customer may be lost i.e. may not choose to call again or may attempt to return to the system by calling in some other time.<br />The following are the assumptions for the model<br /><ul><li>The system has 2 agents that are of equal capability of handelling calls.
  26. 26. The mean arrival rate (ƛ) = 1 customer per 3.75 mins = 16 customer per hour.
  27. 27. The mean service rate(µ) = 1 customer per 3 mins = 20 customer per hour per agent.
  28. 28. The calls are taken by either of the agents only if they are free and not otherwise. All the calls that are not taken by the agents are blocked from entering the system.
  29. 29. System utilisation ρ= ƛμ </li></ul>Operating characteristics of the system<br /><ul><li>Probability that the j of the k agent will be busy is given by
  30. 30. Pj= ƛμj/j!i=0kƛμi/i!
  31. 31.
  32. 32. Where k is the number of agents.
  33. 33. At k =2
  34. 34. P2= 16202/2!162000!+162011!+ 162022!</li></ul>P2 = .15094<br />On percentage basis P2 indicated that 15% of calls will be blocked.<br />Hence 85% of the calls will be answered as and when it come which is in line with the company policy.<br /><ul><li>Ls = Average number of customers in the system
  35. 35. Ls= ƛμ1-P2=16201-0.15094=0.78 ~ 1
  36. 36. The average number of customers in the system is 1.Therefore the average number of agents that will be busy is 1.
  37. 37. Lq = Average number of customers waiting in the queue. </li></ul>Since the queue is not allowed hence operating characteristic Lq is zero <br /><ul><li>Wq = Average time that the customer spends in the waiting line
  38. 38. Since the queue is not allowed hence operating characteristic Wq is zero
  39. 39. Ws = Average time that the customer spends in the system </li></ul>Ws = Ls/ƛ = 0.78/20 = 0.039 hours = 2.34 mins<br /><ul><li>If we consider the system having the 1 more extra agent then the system will be able to answer 97% of calls as and when it comes.</li></ul>Analysis – Proposed solution by Telephone Company <br /><ul><li>The representative from the telephone company suggests that the regional airline considers an expanded system to accommodate the waiting customers. In this new expanded system, when a customer calls when all the agent are busy , then a recorded message tells the customer that the call is being held in the order received and that an agent will be available shortly. The customer can stay on the line and listen to the music while waiting for the agent.</li></ul>Model – with 1 agent<br />Model Used: M/M/1 – when waiting is allowed<br />Mean arrival rate (ƛ): 1 customer in 3.75 mins = 60/3.75 = 16 customer per hour<br />Mean service rate (µ): 3 mins per customer = 60/3 = 20 customers per hour<br />Since ƛ < µ hence the model M/M/1 can be applied.<br />Operating characteristics of the system<br /><ul><li>The probability that no units are in the system.
  40. 40. P0 = 1-ƛ/µ = 1 – 16/20 = 1 – 0.8 = 0.20
  41. 41. There is a 20% chance that there are no customers in the system.
  42. 42. The average number of units in the waiting line.
  43. 43. Lq = ƛ2 /µ(µ-ƛ) =162/20(20-16) =3.2
  44. 44. Average number of customer the waiting line at a given point of time is approximately 4
  45. 45. The average number of units in the system.
  46. 46. L = Lq + ƛ/µ = 4 + (16/20) = 3.2 + 0.8 = 4
  47. 47. At any given point of time there will be 4 customers in the system
  48. 48. The average time a unit spends in a waiting line.
  49. 49. Wq = Lq/ƛ = 4/16 = 0.25 hours = 15 mins
  50. 50. The average time spent by each customer in the waiting line is about 15 min.
  51. 51. The average time a unit spends in the system.
  52. 52. W = Wq + (1/µ) = .25 + (1/20) = 0.3 hours = 18 mins
  53. 53. The probability that an arriving unit has to wait for service.
  54. 54. Pw = ƛ/µ = 20/16 = 0.8
  55. 55. There are 80% chances that a customer will have to wait if he has called up for reservation enquiry.
  56. 56. Steady state
  57. 57. Probability Graph</li></ul>Model – with 2 agents<br />Model Used: M/M/K where c =2 and waiting is allowed<br />Mean arrival rate (µ): 1 customer in 3.75 mins = 60/3.75 = 16 customer per hour<br />Mean service rate (ƛ): 3 mins per customer = 60/3 = 20 customers per hour<br />Number of servers (k) = 2<br />Since ƛ < kµ hence the model M/M/K can be applied where k = 2.<br /><ul><li>The probability that no units are in the system.
  58. 58. P0 =0.376
  59. 59. The probability that there are no customers in the system is 37.6%
  60. 60. The average number of units in the waiting line.
  61. 61. Lq = 0.134
  62. 62. Average number of customer the waiting line at a given point of time is approximately 0.
  63. 63. The average number of units in the system.
  64. 64. L = 0.134 + (16/20) = 0.934 ~ 1
  65. 65. At any given point of time there will be 1 customer in the system
  66. 66. The average time a unit spends in a waiting line.
  67. 67. Wq = 0.134 / 16 = .008375 hours = 0.5025 mins ~ 30 sec
  68. 68. The average time spent by each customer in the waiting line is about 0.5 mins.
  69. 69. The average time a unit spends in the system.
  70. 70. W = Wq + (1/ƛ) = 0.00831 + (1/16) = .05837 hrs = 3.5 mins
  71. 71. The probability that an arriving unit has to wait for service.
  72. 72. Pw = 0 .2005
  73. 73. There are 20% chances that a customer will have to wait if he has called up for reservation enquiry.
  74. 74. Probability </li></ul>Steady state<br />Recommendations<br /><ul><li>The belief of the Vice-President administration that since the average service rate is faster than the average arrival rate, the single agent system should be able to handle all the calls is not correct. The variability in the arrival times and the service times may result in long waiting lines even if the service rate exceeds the arrival rate.
  75. 75. Regional should use 2 agent for the system to achieve the 85% service target.
  76. 76. The advantages and disadvantages of the waiting line is associated with the customer behaviour.
  77. 77. The customer who wants to wait for the turn in the queue will get a chance and hence this will help the company to reduce the number of lost customer and hence lost business due to limited number of service channels.
  78. 78. The disadvantages are the customer behaviour of Balking and Reneging.
  79. 79. The company can either choose to go for 2 agent system with or without the extended system.
  80. 80. 2 agent – no extended system
  81. 81. The company will incur and extra cost of $20 for an additional agent. This can be balanced by the benefit that the company would gain in terms of providing services for more number of customers. The company will be able to answer 85% of the calls as and when it comes. The company needs to establish the cost of loss of business due to the blocked calls. This will help us to determine the benefits associated with having an additional agent in the system.
  82. 82. Extended system:
  83. 83. The cost extended system will be balanced by the increase in the business that the company sees by not blocking the customers from waiting in queue for the use of the system. The company may also have plans for future expansion which will be well supported by the new extended system.
  84. 84. The data needed for the analysis for the staffing at different time of the day will be
  85. 85. Analysis of arrival rates at different hours of the day.
  86. 86. The $ gain by saving each minute by the implementation of the new system
  87. 87. The cost of staff at different points of time in the day.
  88. 88. The efficiency of staff at different times of the day

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