CASE - STAFFING A CALL CENTER
Califo Californi rnia a Childr Children’s en’s Hospit Hospital al has been receivi receiving ng numerou numerous s custome customerr compla complaint ints s because of its confusing, decentralized appointment and registration process. When customers customers want to make appointments appointments or register register child patients, patients, they must contact the clinic clinic or department they plan to visit. Several problems eist with this current strategy. strategy. !arents do not always know the most appropriate clinic or department they must visit to address their children’s children’s ailments. "hey therefore spend a significant significant amount of time on the phone being transferred from clinic to clinic until they reach the most appropriate clinic for their needs. "he hospital also does not publish the phone numbers of all clinic and departments, and parents must therefore invest a large amount of time in detective work to track down the correct phone number. #inally, the various clinics and depa depart rtme ment nts s do not not comm commun unic icat ate e with with each each othe other. r. #or #or eam eampl ple, e, when when a doct doctor or schedul schedules es a referra referrall with with a collea colleague gue locate located d in anothe anotherr depart departmen mentt or clinic, clinic, that department or clinic almost never receives word of the referral. "he parent must contact the correct department or clinic and provide the needed referral information. $n effort efforts s to reengin reengineer eer and improv improve e its appoin appointme tment nt and registr registrati ation on process process,, the children’s hospital has decided to centralize the process by establishing one call center devoted eclusively to appointments and registration. "he hospital is currently in the middle of the planning stages for the call center. %enny &avis, the hospital manager, plans to operate the call center from ' (.). to * !.). during the weekdays. Several months ago, the hospital hired an ambitious management consulting firm. Creati Creative ve Chaos Chaos Consul Consultan tants, ts, to forecas forecastt the number of calls calls the call call center center would would receive each hour of the day. Since all appointment and registration related calls would be received by the call center, the consultants decided that they could forecast the calls at the call center by totaling the number of appointment and registration+ related calls received by all clinics and departments. "he team members visited all the clinics and departments, where they diligently recorded every call relating to appointments and registration. "hey then totaled these calls and altered the totals to account for calls missed during data collection. "hey also altered totals to account for repeat calls that occur occurre red d when when the the same same paren parentt call called ed the the hospi hospita tall many many time times s becau because se of the the conf confus usio ion n surro surroun undi ding ng the the dece decent ntra rali lize zed d proce process ss.. Creat Creativ ive e Chao Chaos s Consu Consult ltan ants ts determined the average number of calls the call center should epect during each hour of a weekday. "he following table provides the forecasts. Work Shift Average Number of Calls ' (.).* (.). - calls per hour * (.).// (.). 01 calls per hour // (.)./ !.). ' calls per hour / !.).2 !.). *1 calls per hour 2 !.).1 !.). 0 calls per hour 1 !.).' !.). 21 calls per hour ' !.).* !.). / calls per hour (fter (fter the consult consultant ants s submit submitted ted these these forecas forecasts, ts, %enny %enny became became interes interested ted in the percentage of calls from Spanish speakers since the hospital services many Spanish patients. %enny knows that he has to hire some operators who speak Spanish to handle
these calls. "he consultants performed further data collection and determined that on average, 3 percent of the calls were from Spanish speakers. 4iven these call forecasts5 %enny must now decide how to staff the call center during each 3 hour shift of a weekday. &uring the forecasting pro6ect, Creative Chaos Consultants closely observed the operators working at the individual clinics and departments and determined the number of calls operators process per hour. "he consultants informed %enny that an operator is able to process an average of si calls per hour. %enny also knows that he has both full+time and part+time workers available to staff the call center. ( full+time employee works 0 hours per day, but because of paperwork that must also be completed5 the employee spends only - hours per day on the phone. "o balance the schedule, the employee alternates the 3+hour shifts between answering phones and completing paperwork. #ull+time employees can start their day either by answering phones or by completing paperwork on the first shift. "he full+time employees speak either Spanish or 7nglish, but none of them are bilingual. 8oth Spanish+speaking and 7nglish+speaking employees are paid 9/ per hour for work before 1 !.). and 9/3 per hour for work after 1 !.). "he full+time employees can begin work at the beginning of the ' (.). to * (.). shift, * (.). to // (.). shift, // (.). to / !.). shift, or / !.). to 2 !.). shift. "he part+time employees work for - hours, only answer calls, and only speak 7nglish. "hey can start work at the beginning of the 2 !.). to 1 !.). shift or the 1 !.). to ' !.). shift, and like the full+time employees, they are paid 9/ per hour for work before 1 !.). and 9/3 per hour for work after 1 !.). #or the following analysis consider only the labor cost for the time employees spend answering phones. "he cost for paperwork time is charged to other cost centers. (a) How many Spanish+speaking operators and how many 7nglish speaking operators does the hospital need to staff the call center during each 3+hour shift of the day in order to answer all calls: !lease provide an integer number since half a human operator makes no sense. (b) %enny needs to determine how many full+time employees who speak Spanish, full+ time employees who speak 7nglish, and part+time employees he should hire to begin on each shift. Creative Chaos Consultants advise him that linear programming can be used to do this in such a way as to minimize operating costs while answering all calls. #ormulate a linear programming model of this problem. (c) ;btain an optimal solution for the linear programming model formulated in part < b= to guide %enny’s decision.
