Advantages And Disadvantages Of Supercritical Fluid Chromatography Engineering Essay

Advantages And Disadvantages Of Supercritical Fluid Chromatography Engineering Essay Even though high performance liquid chromatography is a widely used technique for extractions of analytes in many classes, SFC has clear advantages over it. In HPLC a substantial amount of organic solvent is generated with each extraction, which then needs to be disposed. However, the disposal of the organic solvents is expensive at $5 $10 per gallon, whereas SFC uses considerably less or no organic solvent which leads to a decrease in analysis costs [1]. In replacement of organic solvents an inert environmentally friendly mobile phase is used, often carbon dioxide which can be collected from the atmosphere, as it is energy efficient in the isolation of the desired products [2]. Also without the use organic solvents the product is more concentrated compared to HPLC where the solvent must be evaporated, without the need to evaporate any solvent there is a reduction in energy and labour costs [2]. SFC is similar to gas chromatography (GC) in that it has a lower viscosity and higher diffusion coefficient than HPLC which allows for quicker, more efficient separations as it more effective at entering porous solid materials than liquid solvents. The separation time can be cut down from hours or days to a few tens of minutes [3]. As seen in Table 1, supercritical fluids lie between liquids and gases, which allows for SFC to use features of both HPLC and GC. Due to supercritical fluids having gas like and liquid like density it has a greater solvating power so SFC has a larger molecular range which includes non-volatile molecules which methods like GC do not include [1, 4]. Also, unlike GC which does not analyse thermally unstable compounds, SFC is able to due to the low critical temperatures of supercritical fluids such as carbon dioxide (31oC) [1] ; an advantage of supercritical fluid carbon dioxide is that it has a varied solvating strength that allows for selective extractions [5]. Along with this by altering the temperature and/or pressure it is possible to achieve higher selectivity. The range of detectors is also wider for SFC compared to GC or HPLC this is because in SFC the mobile phase can be liquid or gas like, so GC and HPLC detectors can be used [1]. For example SFC with flame ionization detection (FID) can provide quantification of resolved materials with a sensitivity of 0.1 ng [4]. Due to the range of detectors available for SFC and the low critical temperature of the carbon dioxide mobile phase, the detection and analysis of thermally labile compounds has been successful [3, 5]. Another advantage SFC has over HPLC is separation of chiral compounds, in HPLC the process is very time consuming, in SFC however, due to the lower viscosity of the supercritical fluids, the chiral separation can be run at a flow rate of up to 5 times faster than that of the HPLC all while avoiding pressure build up. The higher flow rate of SFC consequently means that the productivity is higher than HPLC methods [2]. When used in large scale extractions, fluid carbon dioxide can be recycled and then reused this minimize the amount of waste generated [3]. Property Gas Supercritical Fluid Liquid Density g/cm3 (0.6-2) x 10-3 0.2-0.5 0.6-1.6 Diffusion Coefficient cm2/s (1-4) x 10-1 10-3-10-4 (0.2-2) x 10-5 Viscosity g cm-1 s-1 (1-3) x 10-4 (1-3) x 10-4 (0.2-3) x 10-2Table 1: Comparison of Properties of Supercritical Fluids, Liquids and Gases [1] Due to the fact that SFC has features of both GC and HPLC, SFC has diversity in the columns that can be used which are either open tubular (GC) or packed (HPLC). In packed column SFC by choosing suitable column dimensions and particle size [6], this can cause an increase in the number of theoretical plates (over 100,000) [2, 6]. Further advantage is SFC is very clean; mobile phase contaminants are usually trace quantities of other gases. The mobile phase is very free of dissolved oxygen and is not particularly reactive and the mobile phase is easily and rapidly removed [2]. A disadvantage of using carbon dioxide as the mobile phase is it does not elute very polar or ionic compounds; this is overcome by using an organic modifier. However, there are some disadvantages of SFC these include that if molecules are highly polar they are not soluble in the mobile phase. Usually SFC only moves a small amount of a large specimen onto the column Limited availability However, these limitations have been overcome through instrumental modifications that more appropriately address purifications of micro-scale and nano-scale quantities of physiological molecules. More sophisticated 2D systems (2D-SFC) allow for the interfacing of 2 SFC columns having different column coatings or packing and thus provide for orthogonal separation capabilities [2]. Instrumentation used in SFC Originally, SFC instruments were based on HPLC designs with some modifications, however now the design includes a pumping system, modifier module, post-column nozzle and a separator detector [2]. The mobile phase in SFC is pumped as a liquid and then heated up past supercritical temperature until it reaches the supercritical region. The mobile phase passes through the injection valve before the sample is introduced, which carries the sample into the analytical column. To ensure the mobile phase stays supercritical, pressure restrictors are placed at the sides of the detector or at the end of the column. The pressure restrictors are heated as too avoid clogging [7]. As SFC uses a supercritical fluid as mobile phase, there are two possible types of column setup; one setup is HPLC like which consist of two reciprocating pumps these allow the mobile phase to mix and the introduction of a modifier, a packed column which are placed in an oven the detector used is an optical detector and the pressure and flow rates can be controlled separately [7]. Packed column SFC has recently become popular again over the past decade due to drug discovery and the pharmaceutical industry, as it offers the use of an environmentally friendly mobile phase, carbon dioxide, decrease in waste generation and provides purified materials even on a large scale, when used for drug discovery packed SFC is usually coupled with a mass spectrometer detector [2, 8]. In SFC there are lower eluent viscosity and higher diffusion coefficient which as a result lead to an increase in efficiency and a shorter separation time, the low viscosity causes only slight pressure drops which in tu rn allows for the flow rate to be quicker (3-5 mL min-1) compared to that of HPLC (typically ~1 mL min-1) [1, 8]. The other column setup is capillary SFC which is an extension of GC that includes a syringe pump and a capillary column inside a GC oven with a restrictor with a flame ionisation detector (FID), however, in capillary SFC the flow rate of the pump controls the pressure of the system [6, 7]. Other detection methods are also used for capillary SFC one method is Fourier transform infrared (FT-IR) spectrometry. Capillary SFC is used for high separation power and is more suited for fluids with low density. However, capillary columns have some limitations these include sample loading capacity, detection limits and quantitation [6, 7]. As mentioned FID is mostly used for capillary SFC, although in certain cases FID can be used with packed column SFC when a non-flammable mobile phase is used. However, the mobile phase that is used is usually carbon dioxide which requires an organic modifier to deactivate any unbounded silanol groups in the stationary phase [10] thus causing the mobile phase to become flammable this in turn causes a high background signal and a loss of sensitivity. Alternatively, modifiers like esters or lower alcohols can be used in packed column SFC in order to improve the elution of polar compounds [9]. However, to avoid the use of modifiers, open-tubular capillary columns can be used, since silanol groups are not present in the stationary phase [10]. Compared to capillary columns, packed columns display higher efficiency per unit time; also separations can be transported directly from analytical or preparative liquid chromatography (LC) to SFC. Moreover, a standard liquid chromatograph can easily be converted into a supercritical fluid chromatograph [11]. It has was found that certain separations that were developed on a 50 ÃŽÂ ¼m i.d. capillary column can be repeated with the same or better performance on a 1 mm i.d. (microbore) packed column. The packed column system has the additional advantage of yielding excellent peak area precision. It is also shown that the combination of water and formic acid is an effective modifier for CO2 which can be used with FID [6]. A study using the water and formic acid modifier was conducted by H. E. Schwartz et al. formic acid is used as it has low background noise and therefore is more favourable, however another problem arises when using this modifier and that large gradient humps appeared during the run, these were most probably because of organic impurities in formic acid. A way round this problem is that water is added to the carbon dioxide via the use of an aquafier system, the aquafier system used by H. E. Schwartz et al. was a 15 cm x 4.6 mm i.d. silica column (100-200 mesh) that was saturated with ca. 40% w/w water. The column was placed between the pump outlet and injection valve. A test mixture of the formic acid and water modifier was performed by H. E. Schwartz et al. and prodcued the chromatogram as seen in Figure 1[6]. Figure 1 Chromatogram of a test mixture of formic acid/water/CO2 mobile phase. Peak identification (from left to right): n-eicosane, anthraquinone, n-triacontane, tocopherol acetate, cholesterol [6]. In Figure 1 the baseline rises this was due to the pressure program used, however due to the addition of water to the mobile phase which prevented the accumulation of formic acid on the head of the column no hump is visible. In Figure 1 it can also be seen that all the peaks have good shape and resolution even for the more polar compounds like anthraquinone, tocopherol acetate and cholesterol [6]. Mobile phases and stationary phases used in SFC In SFC the density of the mobile phase is about 200-500 times greater to that in gas chromatography. Compounds with high molecular weights are not usually detectable in gas chromatography, however with the density of the mobile phase being greater they can therefore be chromatographed [12]. A wide range of compounds have been tested for use as SFC mobile phases, however, a variety of these required special conditions, and would therefore not be suitable. This resulted in carbon dioxide CO2 being used as it was easily obtainable, low cost and safe [13], along with the critical temperature being 31oC and critical pressure being 73.8 atm [14]. A problem with CO2 as a mobile phase in a packed column is that if CO2 mobilizes a species then there is a possibility that the compound will be irreversibly adsorbed onto the column, this is because of the high activity of most sorbents, this does not happen in capillary SFC as inert fused silica open-tubular column are used. To avoid adsorption onto the column, surface activity needs to be decreased; this has been achieved by using modifiers [14]. There are two main reasons why modifiers are added to the mobile phase, first is that only a small amount of modifier is added in order to deactivate the sorbent active sites, second is when the modifier is added in higher concentrations (level of modifier needed is à ¢Ã¢â‚¬ °Ã‚ ¥1%)it improves the solubility of the analyte in the mobile phase [14]. One problem with using modifiers is they have a high response when a FID is used; this high response causes an increase in the baseline. The alternative to using FID which helps relieve this problem is the use of a ultra-violet absorption detector, although it is not as applicable to organic compounds compared to FID [14]. This is only true for packed SFC, as when capillary SFC is used most separations are done using only CO2, which is compatible with FID. Having only CO2 as the solid phase can cause slight defects on the chromatograms such as very broad peaks and not well resolved, as well as longer retention times, this is solved by adding a small amount of water to the mobile phase, hence improving the peaks and decreasing the retention time [12]. Modifiers which can be used with the mobile phase include methanol, acetonitrile, chloroform and formic acid. Methanol is the most popular modifier being used in both packed and capillary SFC, even though the addition of water speeds up elution of polar compounds in capillary SFC [12]; methanol has a greater effect when used with silica-packed columns [14]. The solubility of methanol, acetonitrile and chloroform in CO2 was studied by K. L. Maguire and R. B. Denyszyn, they found out that when the pressure is below 90 for methanol/CO2 there was little effect on solubility, but when raised above 90 there was a substantial increase. Acetonitrile/CO2 had very little pressure dependence but small temperature dependence. Finally, chloroform/CO2 both pressure and temperature had a small effect on solubility, when either was raised the solubility of chloroform increased [14]. Research by G. L. Pariente and P. R. Griffiths showed when carboxylic acid groups were present in the analyte the retention time was greatly increased while still using CO2 mobile phase. The cause of this could be due to that the solubility of these polar molecules is low and the solvation is not great enough to overcome the strong hydrogen bonds. The alternative mobile phase used was chlorofluorocarbon (CCl2F2), in comparison to CO2 which had a capacity factor greater than 20 for isophthalic acid; CCl2F2 had a capacity factor of 3.9. These results suggest that CCl2F2 has sufficient free energy of solvation to overcome the hydrogen bonds [14]. Even though CO2 ­ is the most extensively used mobile phase it is no more polar than hexane [15], so alternatives including CCl2F2 have been investigated, however the critical temperatures must not be too high as one of the main advantages of SFC is that elution can take place at mild temperatures. Another example is ammonia (NH3), as it possesses a high dipole moment and relatively low critical temperature, however supercritical NH3 reacts with siloxane linkages and when left for an extended time the siloxane stationary phase for capillary SFC breaks down too [14]. Therefore, a more useful way of eluting polar compounds is CO2  ­and the use of a modifier [15]. For packed SFC more or less all of the stationary phases used in HPLC are used in SFC, most of these are silica-based, chemically bonded or encapsulated, or polymeric [8]. Evaluation of stationary phases of SFC was originally carried out by Schoenmakers et al. this was however, only done using pure CO2 as the mobile phase, and certain phases did not perform well, if a modifier was used these phases would have performed better. When CO2 and a modifier is used as a mobile phase the stationary phase also becomes modified in that both CO2 ­ and the modifier adsorb onto the stationary phase. Depending on the stationary phase depends on the level of adsorption, for CO2 all phases adsorb the same but more polar phases adsorb more modifier than less polar phases. This causes the stationary phase to become more polar than the mobile phase, which in turn will cause polar solutes to interact more with stationary phase increasing retention time. Other stationary phases that have been studied include octadecylsiloxane-bonded silica (ODS), cyanopropylsiloxane- bonded silica, divinylbenzene-ODS, polydimethylsiloxane and porous graphitic carbon (PGC) stationary phases in supercritical [8]. In capillary SFC a problem arises in that normal GC stationary phases dissolve in the supercritical fluid mobile phase as they have a high solvating power. In order to correct the problem a non-extractable stationary phase is needed, examples of this are bonded phase where the stationary phase is attached to the column to surface groups via covalent bonds and cross linked phase where polymer chains within the stationary phase are attached to each other. In order to create non-extractable stationary phase, the process of coating must be undertaken, there are two types of coating, dynamic and static. The most favoured for SFC is static, as dynamic can lead to poor column efficiency and a thick stationary phase is not possible. In static coating the stationary phase is first dissolved in supercritical fluid and forced into the column, to avoid the removal of the phase cross link phase is used as it occurs between the polymers and not between polymer and substrate, and therefore can be applied to glass and fused silica columns [16]. Conclusion

Leadership purpose reflective essay Essay

?After watching this interview, I feel that a well defined leadership purpose statement is the distinction between a good leader and a great leader. Carolyn McKnight’s interview on leadership purpose statements really opened my eyes to the power of these statements, and the time and energy one needs to put into creating a leadership purpose statement. At first it seemed that completing a statement this powerful would be a very daunting task. After watching Mrs. McKnight’s interview, I am confident in my ability to come up with a statement, and that I will have the courage to follow through with it. The most significant thing in a true leadership purpose statement is authenticity according to Mrs. McKnight. Webster’s defines authenticity as† real or genuine†. Taking this and Mrs. McKnight’s statements into account I took a minute to think about how authentic I am. I realized that I know myself well enough to know where my strengths and weaknesses lie. Another aspect of my life that makes me believe in my authenticity is that many people have told me they value my opinions. This is because I always tell them exactly how it is even when I know it is not what they want to hear. With this knowledge I am able to establish creditability and responsiveness with other people. The question was asked â€Å"How do you begin to determine leadership purpose? † Mrs. McKnight gave several examples of what one can do to find this. â€Å"What is the root of my life? † was one question she brought up that can help you find a purpose. I immediately identified the roots of my life as hard work, determination, and dedication. I attribute all my success in my life to these three principles. I started to think about failures that I have had in my life. It made me wonder if I would be able to find a place where I got off course and did not apply one of these principles. Another statement that stood out to me under this question was â€Å"Find what gives you meaning. † My achievements are what give me meaning. I learned more about why I feel this way after I took the Strenghts Finder assessment. It pointed out that I was an â€Å"Achiever† and could not be satisfied at the end of the day without feeling that I had achieved something. Every goal that I accomplish makes me feel more confident and more ambitious about what else I can achieve. Out of the examples she gave these are the two I think that will help me determine my leadership purpose statement. The part of the interview that discussed people struggling with conflict, with their leadership purpose was something that I really focused on. Early on in the interview an example was given that an â€Å"acorn will become an oak†. When the subject of struggle comes up Mrs. McKnight ensures us of this fact and mentions to not fight it. She goes on to talk about all the people pleasing we do throughout our lives. This was a huge eye opener to me because I notice my need to please people, like my family. This causes conflict with the telling it straight attitude that I try to maintain with the people in my life. When I find myself trying too hard to please people, I lose some authenticity and it weakens my purpose. She stated that we really need to find what we want and not what other people want for us. I can see myself struggling with this as I develop my leadership purpose statement. I liked that she mentioned having the courage to follow what you deeply want. To me, people who can follow a path to what they want while sticking to it through the good times and the bad are really courageous. Emotional intelligence was another key area brought up in the interview. The three areas that were brought up under this topic are self awareness, social awareness and self regulation. Our text book offers another interesting point that supports Mrs. McKnight’s insights. The text book says that mental intelligence will get you into a management position but it stops being helpful after entry into that position. A leader needs to have good emotional intelligence to continue to lead. Self awareness has to do with my purpose and I am working towards finding that in this class. I know that I worry about how other people perceive me but I do not think that is the same thing as recognizing it, which is social awareness. I think that I will have to spend some time mastering the first two elements of emotional intelligence before I can work on self regulation. I do not know how I can stick to a path and make corrections to get back to it, until I have established a clear path. There were some interesting comments made about behaviors that help us get closer to our purpose. A reflective practice of checking in twice a day was brought up. I thought about how I might do this and I know that I would struggle with this significantly. I worry about how honest I would be with myself, so I would have to check in with my wife or a close friend that will keep honest with my feelings. I would have never thought that some kind of physical activity would help me get closer to my purpose. After hearing Mrs. McKnight talk about these practices I can see how it would help. A great example of a physical activity that can help you is the one Mrs. Enders gave on how posture and stance help the way people perceive you as a leader. I hunch over, it is mainly because I am tall and do not like being overly imposing to others. It is something that I can work on physically that might help me with my purpose. The examples of purpose statements that were given were amazing. I think that the statement â€Å"I am a drop of water, flowing peacefully, showing love carving deep canyons out of granite† was an insightful statement. I think this will stay with me for a long time not because of how insightful I found it but because of the story that went with it. The fact that the CEO was able to recognize that he was not following his statement and quit his job in order to find a path back to it, was very inspirational. I want to have that kind of courage and belief in my purpose statement and I will think of this story heavily, while I am creating it. After watching this interview a few times in preparation for this paper, it really helped me get a grasp on the concept of a leadership purpose statement. This interview has given me a good set of tools for not only creating a good purpose statement, but knowing how to stay true to it, and knowing how to deal with obstacles I will face while trying to live by it. By taking the time to reflect on this interview I started to learn more about a subject I have not spent much time on; Myself.

Regional Airlines Case Study

Case 2: Regional Airlines Case 2: Regional Airlines Case Introduction A+ for effort, Customer Service Pays for Itself In an extremely regulated and thus relatively uniform industry such as the commercial airline industry, the successful airline is the organization which sets itself apart from the competition. Within an industry that requires customer planning to interface with flight schedules and security measures, a major operational aspect which can aid an airline in gaining an edge on the competition is customer service.The effective consumption of air travel (finding flights, buying tickets, getting through the airport, boarding a plane, and finally reaching the final destination) is not the same simple consumer –supplier relationship that the consumer experiences in a trip through the Wal-Mart checkout counter; the nature of air travel makes the interaction between the airline and the customer very complex.Almost every facet of the complex relationship between the airlin e and customer can generate a large amount of stress for the consumer; consumers find poor customer service in the face of tight travel deadlines and paid for travel plans that did not necessarily go as intended extremely frustrating. Analysis Investigating Salient Case Issues To capitalize on offering a high level of effective customer service, an investment must be made.The airline must ensure their customer service department not only understands that customer service is highly valued in the organizational environment but also must ensure that the customer service department has the tools and resources to offer effective customer service (Graham, 2012). Like any business investment, the organization must make smart decisions when providing customer service resources; for instance a call center of fifty employees which only answers two calls an hour is a humongous waste of resources that would be better allocated towards another goal.The problem of understand that an investment to wards more effective customer service is needed, but at what cost to make that investment, is the problem which faces Regional Airlines in the case study on page 539 of the 2012 Anderson, et al, text: An Introduction to Management Science Regional Airlines is expanding its customer service operation by setting up a new phone system for the purpose of providing ticketing services and customer assistance over the phone.The airline is going ahead with the new phone system; however, two major decision points exist, how many agents to allocate to the line (one or two) and what complexity of system in which to invest (a system that provides a holding function versus one that does not). The expected call load for the new operation is one call every 3. 75 minutes, available metrics indicate that on each call a ticket agent spends 3 minutes with a customer; effectively this results that for every customer attended to, there will be 45 seconds of downtime (Anderson, et al, 2012).Unfortunately for Regional Air, those figures are only averages, there will be an indeterminate amount of calls which meet or exceed the 3. 75 minute span in between calls. The decision between systems which provides a hold function versus the one that does not will determine will determine if that customer is placed on hold or if the call is just dropped. Placing an unanswered call on hold provides a buffer for the agent to end the call and then service the holding customer; however, for a customer that stays on hold for an inordinate amount of time will begin to feel less and less like a well-served customer.The expected call load versus the time it takes for an agent to deal with each call is the basis of allocating only one agent to man the call system. The second option of allocating two or more agents is in effect, insurance that each call will be answered in a timely fashion and callers will not have to wait for extended periods of time. The decision of how many agents to allocate to the phone system is based upon the apparent cost for an extra agent sitting around not actively engaged in a call; however this view is relatively short sighted because it does not take into account the revenue lost from dropped calls and dissatisfied customers.The salient issue of the case is determining what the appropriate level of investiture to make for the phone system to provide an expected (and beneficial) level of customer service Group Discussion Exploring Simulations Simulation is a quantitative technique developed for studying alternative courses of action by building a model of that system and then conducting a series of repeated trial and error experiments to predict the behavior of the system over a period of time (Srivastava, Shenoy, & Sharma, 1989, p. 753). Of all the simulations waiting line simulations are of the most important to the customer service industry.In the airline industry long waiting times can lead to poor customer service scores and diminished sales. Reg ional Airlines is establishing a new telephone system for handling flight reservations (Anderson, Sweeney, Williams, Camm, & Martin, 2012). The airlines main goal is to decrease the wait time at its call centers and increase sales. Regional’s management team agrees that its goal should be to answer 85% of its incoming calls immediately. The following analyzes Regional Airline’s (RA) current reservation system and ways to improve it. Analysis of Current SystemCurrently RA is answering one call every 3. 75 minutes during 10:00 a. m. to 11:00 a. m. time period (? (average arrival time) = 60 minutes / 3. 75 minutes = 16 calls per hour). The average service time is 3 minutes per customer ( µ (service rate) = 60 minutes / 3 minutes = 20 calls per hour). With only one reservation agent, the probability that a caller will be blocked because of a busy signal is P1 = . 4444 ? o = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /0! (16/20)o / 0! + (16/20)1 /1! = . 5556 ?1 = ( ? / ? ) 1/0! i=1k ? /? 1 /i! = ( 16 / 20 ) 1/0! (16/20)o / 0! + (16/20)1 /1! = . 444 With two reservation agents, the probability that a caller will be blocked because of a busy signal is P2 = . 1509. ?o = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /0! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 4717 ? 1 = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /1! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 3774 ? 2 = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /2! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 1509 Regional Airlines’ current phone reservation system will answer an approximate of 85% of phone calls with two employed reservation agents.However, the other 15% will be blocked because of a busy signal. Customers who do not get a hold of an agent may not call back and contribute to negative customer service reaction and adversely affect the business. Analysis of Agents Needed Proposed expanded system will allow callers to wait. Instead of being blocke d when all lines are busy, customers can choose to stay on the line and calls will be answered in the order received. With only one reservation agent for Regional Airlines in the expanded system, 80% (Pw) of incoming calls will end up waiting. The average waiting time is also at 12 minutes (Wq).Cited numbers above show a horrendous system that is both undesirable and a business model doomed for failure. So in order for RA to realize the benefits of the expanded system, it needs to employ two or more reservation agents. Po=1- ? /? = 1-1620=0. 20 Lq = ? 2 ? (? – ? ) = 16 2 20 (20 – 16) = 3. 2 L =Lq + ? /  µ= 3. +1620=4 wq+Lq / ? =3. 216=0. 20 hours=12 minutes W = wq + 1/ µ = 0. 20 + 1/20 = 0. 25 hours = 15 minutes Pw= =1620=0. 80=80% At the planning meeting, Regional Airlines’ management team agreed that answering at least 85% of the calls is an acceptable customer service goal.This means that the probability of waiting will have to be 15% or less. Pw= 1k! k k? k? – ? Po k = 2 agents Pw= 12! 16202 2 202 20- 16 0. 4286= 0. 2286 k = 3 agents Pw= 13! 16203 3 203 20- 16 0. 4472= 0. 0520 Po=0. 4472 Lq=0. 0189 L=0. 8189 Wq=0. 0012 hours=0. 07 minutes W=0. 0512 hours=3. 97 minutes Using three agents clearly meets the company’s goal. With three reservation agents, only 5% of the calls will be waiting, which is way below the 15% targeted cap in order to meet the goal of 85% answered calls. Average waiting time is also at a minimum, calculated at 0. 012 hours or 0. 07 minutes. System Recommendation The current telephone reservation system design does not allow callers to wait; callers instead must attempt to reach a reservation agent when all agents are not occupied. Should callers reach the service line when all agents are busy they will be met with a busy signal. The management at RA is seeking to switch to an expanded telephone system to combat this problem. Based on the calculations in the previous paragraphs, RA will need appro ximately 3 reservations agents to run an expanded phone system.Group 3 recommends that the company employ the multiple channels waiting line which consists of two or more service channels that are assumed to be identical in terms of service capability (Anderson, et. al. , 2012). Regional airlines could support at least a two-channel operation to service the needs of its customers. MANAGERIAL REPORT ASSUMPTIONS: a. One call every 3. 75 minutes during 10:00 a. m. to 11:00 a. m. time period ? (average arrival time) = 60 minutes / 3. 75 minutes = 16 calls per hour b. Average service time of 3 minutes with each customer  µ (service rate) = 60 minutes / 3 minutes = 20 calls per hour 1.An analysis of the current reservation system that does not allow callers to wait. How many reservation agents are needed to meet the service goal? With only one reservation agent, the probability that a caller will be blocked because of a busy signal is P1 = . 4444 ? o = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /0! (16/20)o / 0! + (16/20)1 /1! = . 5556 ?1 = ( ? / ? ) 1/0! i=1k ? /? 1 /i! = ( 16 / 20 ) 1/0! (16/20)o / 0! + (16/20)1 /1! = . 4444 With two reservation agents, the probability that a caller will be blocked because of a busy signal is P2 = . 509. ?o = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /0! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 4717 ? 1 = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /1! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 3774 ? 2 = ( ? / ? ) ? /0! i=0k ? /? i /i! = ( 16 / 20 ) ? /2! (16/20)o / 0! + (16/20)1 /1! + (16/20) 2 /2! = . 1509 Conclusion: Regional Airlines’ current phone reservation system will answer an approximate of 85% of phone calls with two employed reservation agents. However, the other 15% will be blocked because of a busy signal.Customers who do not get a hold of an agent may not call back and contribute to negative customer service reaction and adversely affect the business. 2. An analysis of the expa nded system proposed by the telephone company. How many agents are needed to meet the service goal? Proposed expanded system will allow callers to wait. Instead of being blocked when all lines are busy, customers can choose to stay on the line and calls will be answered in the order received. With only one reservation agent for Regional Airlines in the expanded system, 80% (Pw) of incoming calls will end up waiting. The average waiting time is also at 12 minutes (Wq).Cited numbers above show a horrendous system that is both undesirable and a business model doomed for failure. So in order for Regional Airlines to realize the benefits of the expanded system, it needs to employ two or more reservation agents. Po=1- ? /? = 1-1620=0. 20 Lq = ? 2 ? (? – ? ) = 16 2 20 (20 – 16) = 3. 2 L =Lq + ? /  µ= 3. +1620=4 wq+Lq / ? =3. 216=0. 20 hours=12 minutes W = wq + 1/ µ = 0. 20 + 1/20 = 0. 25 hours = 15 minutes Pw= =1620=0. 80=80% At the planning meeting, Regional Airlinesâ₠¬â„¢ management team agreed that answering at least 85% of the calls is an acceptable customer service goal.This means that the probability of waiting will have to be 15% or less. Pw= 1k! k k? k? – ? Po k = 2 agents Pw= 12! 16202 2 202 20- 16 0. 4286= 0. 2286 k = 3 agents Pw= 13! 16203 3 203 20- 16 0. 4472= 0. 0520 Po=0. 4472 Lq=0. 0189 L=0. 8189 Wq=0. 0012 hours=0. 07 minutes W=0. 0512 hours=3. 97 minutes Using three agents clearly meets the company’s goal. With three reservation agents, only 5% of the calls will be waiting, which is way below the 15% targeted cap in order to meet the goal of 85% answered calls. Average waiting time is also at a minimum, calculated at 0. 012 hours or 0. 07 minutes. 3. An analysis of the expanded system proposal by the telephone company. 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 bus y, 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.Expanded System with waiting allowed Pw for 1 agent P0= (1-? /? ) 1-16/20=. 20 Lq= ? 2 =16(2)= 3. 2 ?(? – ? ) =20(20-16) L= Lq+( ? /? )=3. 2 +(16/20)=4 Wq =(Lq/ ? )=3. 2/16=. 20 (12 minutes) W=Wq+(1/ ? )=. 20+ (1/20)= . 25 (15 minutes) Pw= ? /? = 16/20=. 80 Expanded System with waiting allowed Pw for 2 agents Pw=1/k! ( ? /? )k k? / k? – ? P0 1/2! (16/20)2 2(20)/2(20)-16 . 4286= . 2286 Expanded System with waiting allowed Pw for 3 agents 1/3! (16/20)3 3(20)/3(20)-16 . 4472= . 520 In order to use this system, Regional Airlines would have to use three agents to keep the customer service of 85% of the calls being answered immediately. The telephone 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 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 you would need to develop this staffing plan.This analysis only covers the 10:00 AM – 11:00 AM time frame. As we have seen with the equations used, we have to have historical data for the other time frames. If the phone lines are open from 08:00AM – 08:00 PM, we could use the data from each hour. Keeping with the 85% rate of phone calls being answered immediately for good customer service and the use of the limited amount of call agents required to save Regional Airlines money, after further analysis, Regional Airlines will have the data need to make the best decisions for their company. 4. Staffing PlanIn order to develop a ticket agent staffing plan that would enable the company to provide different levels of staffing for the ticket reservation syst em at different times during the day, a similar simulation method and analysis used above are needed. By implementing the same application, the right number of reservation agents each hour can be determined. In addition to the number of agents used, it is also possible to use the same information to determine the full-time and part-time shift schedules that meet the company’s customer service goals.But in order for RA to do this, it needs the hourly average arrival rate for the whole day. 5. References Anderson, D. , Sweeney, D. , Williams, T. , Camm, J. , & Martin, K. (2012). An Introduction to Management Science Quantitative Approaches to Decision Making. Mason, OH. South-Western Cengage Learning Graham, J. (2012). Think Like the Customer – Or Lose the Sale. American Salesman, 57(4), 18-23. Srivastava, U. K. , Shenoy, G. V. & Sharma, S. C. (2005). Quantitative techniques for managerial decisions (2nd Edition). New Age International Publishers: New Delhi.

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