Question 1 – Single Agent System Recommendation
A detailed analysis of the operating characteristics of the reservation system with one agent as proposed by the vice president of administration. What is your recommendation concerning a single-agent system?
The analysis shows that a single-agent system with one agent would not be a feasible solution as shown by Figure 1. Forty-four percent, (44%) of the calls would be blocked answered, and fifty-six percent (56%) of the calls are would be answered. The airline wants desires that a minimum of eighty-five percent (85%) of the calls are answered and thereforeyielding this choice is as not acceptable.
Figure 1 – Calculations for One Agent with No Waiting Line (Blocking) Scenario
Figure.1 Waiting line model- 1 Agent with no waiting line
Mean ARRIVAL rate λ=1/3.75= .2667 customers/minute custoers per minute or 16 customers/hour customers per hour
Mean SERVICE rate μ=1/3 min〖= .3333 customers/minute or 20 customers/hour customers per hour〗
Pj=((λ/μ)"^j)/j!/" ∑_(i=0)^k▒〖((λ/μ)"^i)" 〗/i!)
Sec. 11.8
K= # of servers
K=1
P1=((.2667/.3333)"^1)/1!/" ∑_(i=0)^1▒〖((.2667/.3333)"^0)" 〗/i!)
.8/(1+.8)=.44
P1= .44 x 100= 44%
Average number of units in waiting line, Lq
Lq means no queues allowed
Average number of units in system: L= (λ/μ)(1-P1) (11.32)
L= (.2667/.3333)(1-.44)= .448
Average time a unit spends in waiting, Wq = 0 not allowed
Average time a unit spends in system
W= Wq + (1/μ) Lq= L- (λ/μ) W= (Lq/ λ ) + (1/ μ) W= ((L)-( (λ/μ))/ λ)+(1/ μ)
((.448)-(.8)/(16)) + (1/20) = .028 x 60 min.= 1.68 min.
The current single agent will only answer forty-four (44%) of the incoming calls which is below the eighty-five percent (85%) company policy target.
Question 2 – Number of Agents Required Recommendation
A detailed analysis of the operating characteristics of the reservation system based on your recommendation regarding the number of agents Regional should use.
Regional Airlines should use two (2) agents with a block waiting system when comparing Figure 2, 3, and 4, as this would fulfill the requirement of eight-five percent (85%) of calls answered, as well as keeping minimize overall coststhe cost down.
Figure 2. Figure 2 – Calculations for Two Agents with No Waiting Line (Blocking) Scenario Waiting line model- 2 agents with no waiting (blocking)
Pj=((λ/μ)"^j)/j!/" ∑_(i=0)^k▒〖((λ/μ)"^i)" 〗/i!)
P2=((.2667/.3333)"^2)/2!/" ∑_(i=0)^2▒〖((.2667/.3333)"^i)" 〗/i!)
P2= (.32)/(1+.8+.32)= .15094
15% of calls will be blocked with two (2) agents
Average customer in system: 2.54 minutes
L= (λ/μ)(1-P2)= (.8)(1-.15094)= .67924
W= Wq + (1/μ) Lq= L- (λ/μ) W= (Lq/ λ ) + (1/ μ) W= ((L)-( (λ/μ))/ λ)+(1/ μ)
((.67924)-(.2667/.3333))/.2667+(1/.3333)= 2.54 minutes
Figure 3. Single Agent –waiting is allowed (M/M/1)
Figure 3 – Calculations for One Agent with Waiting Allowed (M/M/1) Scenario
Mean ARRIVAL rate λ=1/3.75= .2667 customers/minute custoers per minute or 16 customers/hour customers per hour
Mean SERVICE rate μ=1/3 min〖= .3333 customers/minute or 20 customers/hour customers per hour〗
P0= 1- (λ/μ) 1-(.8) = .20 20% probability that there are no customers in the system
L = Average number of customers in the waiting line
L= (λ )^2/( μ(μ- λ)) = (.2667)^2/( .3333(.3333- .2667)) = 3.2 customers in the waiting line
Average number in system L= Lq + λ/μ = 3.2 + (.2667/.3333) = 4.0002 customers
Average minutes a customer spends waiting (on hold)
Wq= Lq/ λ = 3.2/.2667 = 11.9985 minutes ~12 minutes waiting
Customer average minutes in system W= Wq + (1/μ) = 12 minutes + (1/.3333) = 15 minutes
Probability that a customer waits for service Pw= (λ/μ)=.2667/.3333= .8 80% chance of waiting
“n” units in system
Pn= (λ/μ)^n Po
Po= (.2667/.3333)0(.20) = .2000
P1= (.2667/.3333)1(.20) = .1600
P2= (.2667/.3333)2(.20) = .1280
P3= .1025
P4= .0819
Figure 4 – Calculations Figure 4. for Two Agents with Waiting Allowed (M/M/2) Scenario Two Agents- waiting is allowed (M/M/2
)
Po=1"/" ∑_(n=0)^(k-1)▒〖(λ/μ)^n/n!+(λ/μ)^k/k!(1/(1-λ/kμ))〗
According to standard numbers from Ch.apter 11 (tTable 11.4)1
Ratio = .2667/.3333 = Po = .4286 42.86%
The probability that there are no customers in the system is 42.86%
Avg number of customers in waiting line
Lq=( (λ/μ)^k μ λ))/ (k-1)!(k μ- λ)2 x Po
Lq= (.2667/.3333)2(.2667)(.3333) / (2-1)!(2 x .3333 – .2667)2 x (.4286) = .1524
Average number of customers in the system
L= Lq + λ/μ = .1524 + (.2667/.3333) = .9526 ~ 1 customer per minute at all points in the system currently
Wq = Average number of minutes a customer spends waiting
Wq= Lq/λ = (.1524/.2667) = .571 min ~34 seconds
W A = Average number of minutes a customer spends in the system
W= Wq + 1/ μ = .571 + (1/.3333) = 3.5713 minutes
Pw = Probability a customer waits for service
Pw= 1/k! (μ/λ)^k (k μ/ k μ-λ) = (.5)(.64)(1.67)(.4286) = .2290 22.90%
Probability “n” units in system k= 2
Pn= ((λ/μ)^n/n! Po.or Pn= ((λ/μ)^n//k!k(n-k)Po n>k k=2
Po= .4286
Pn1 = .3429
Pn2 = .1372
Pn3 = .0549
Pn4 = .0219
Question 3 – Advantages and Disadvantages of the Expanded System
A detailed analysis of the advantages or disadvantages of the expanded system. Discuss the number of waiting for callers the expanded system would need to accommodate.
The expanded system of with 1 one (1) to two (2) agents with call waiting, has the advantage of improvesing customer service relations through a more efficient call system that which allows for almost no waiting. The disadvantage of this system is that it would create another cost to Regional aAirlines of by adding an additional agent and expanding the call system that is currently implemented. Furthermore, by analyzingFurther analysis in Ttables 1-4, delineates the pros vs. cons of each system and demonstrates the potential maximizing benefits from selecting 2 two (2) agents with call waiting. Analysis and internal group discussions yielded thatT the two2-agent system with call waiting is the most efficient system; , however it is costlier more expensive to Regional Airlines due to the required cost of addingto add one more additional agent and change implementation of the from blocked system to call waiting system.
According to the calculations in fFigures 1-4, ‘s calculation, the purpose of this analysis is to individually assess the waiting line models individually and compare the results to company policy policy and expectations as demonstrated on in Tables 1-4.
Table 1 – Assessment of Current Company Choice – 1 Agent with No Waiting (Blocking)Table 1. Current company choice (fail company policy)
Individual Assessment of Waiting Line Model – 1 Aagent with Nno Wwaiting Lline
Business Con Business Pro Customer Con Customer Pro
56% of customers at any moment do not get any service. Quick Service for the 44% that do get service If you are part of the 56% that gets turned away it will foster ill feelings If you are part of the 44%, you get speedy service
56% of possible lost revenue The majority will get a bad image of the company and reflect negatively on company review sites. If you are part of the 44% that got speedy service, you may become a repeat customer
Fail to reach 85% service company policy
Table 2 – Assessment of Two Agents with No Waiting (Blocking)Table 2. Second Choice (meets company policy)
Individual Assessment of Waiting Line Model- 2 agent with no waiting (block)
Business Con Business Pro Customer Con Customer Pro
15% of lost customers Reach company policy at 85% If you are part of the 15% that gets blocked, you will be angry 85% of customers only take 2.54 minutes of service
Additional $20/hr for second agent 2.54 minutes of service Negative feedback on reviews (more likely to leave negative reviews)
15% of business turned away
Table 3 (fail company policy)Table 3 – Assessment of One Agent with Waiting (No Blocking)
Individual Assessment of Waiting Line Model- 1 agent where waiting is allowed (M/M/1)
Business Con Business Pro Customer Con Customer Pro
56% of customers at any moment do not get any service. Quick Service for the 44% that do get service If you are part of the 56% that gets turned away it will foster ill feelings If you are part of the 44%, you get speedy service
56% of possible lost revenue The majority will get a bad image of the company and reflect negatively on company review sites. If you are part of the 44% that got speedy service, you may become a repeat customer
Fail to reach 85% service company policy 80% chance of waiting for service
Table 4. Top ChoiceTable 4 – Assessment of Two Agents with Waiting (No Blocking)
Individual Assessment of Waiting Line Model- 2 agents where waiting is allowed (M/M/2)
Business Con Business Pro Customer Con Customer Pro
Pay for 2 agents Everybody gets served Wait for 34 seconds
(22.9% probability of waiting) Everyone gets service
Pay for waiting service Assume 1 customer per minute at all points in system Fast efficient service at 3.5713 min avg. customer in system
No one turned away, maxing out profitability No one turned away
Things to considerConsiderations: AvgAverage. booking airfare is ~$379.2 In essence, one additional customer would justify the addition of a second agent. In business, a return on investment mentality is crucial to justify expenditures/costs as well as maximize profitability. It is justified to add call waiting and an additional agent as this will pay for itself and maximize profitability. This will also increase positive company perception to the customers by efficient service. A case could be made for 2 agents with no call waiting, but that also means that 15% of people are being blocked. Yes, that means that company policy is minimally met, but as proven by the addition of call waiting, the company can take care of all customers that call between 10-11am and have it pay off at the end to maximize profitability. In the psychology of waiting, people perceive a service/product worth obtaining as having to wait a certain amount of time.3 Much like people that perceive the word “free” as of less value, people that don’t wait for service also may not perceive the service as valuable or perceive the service/product as inferior to other competing factors.