The Application of Multi Shifts and Break Windows in Employees Scheduling

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1 The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance excellence is by opimizing he uilizaion of company s human resources hrough applying a good scheduling sysem. A company wih a very long service hours usually use muliple shifs. To mainain he cusomer s service wihin res ime, he employees should no res simulaneously in a ime inerval called brea window..ineger Linear Programming model for opimal shif scheduling wih muliple shifs and brea windows is used o deermine he opimal number of employees needed in every shif and brea assignmen. These opimal numbers are used o schedule he company s employees hrough 6 woring days wih wellplanned brea assignmens. Compared wih he radiional sysem, he proposed sysem and model shows several advanages, such as scheduling process required by he new model is faser and easier, employee s defici and surplus are well disribued, he brea assignmens are arranged while mainaining he cusomer s services. Knowing he opimal number of employees will help he manager in developing recruimen plan. Keywords: Employees scheduling, Brea windows, Muli shifs, Ineger Programming 1. Inroducion The shifs scheduling problem arises in a variey of service organizaions such as elephone companies, hospials, deparmen sores and involved scheduling he employees o mee he demand ha changes over days and hours. The company usually serves he cusomer for more han 8 hours per day (he normal woring hours) bu here is a flucuaion in company s service aciviies. This flucuaion happens in weely order, daily and hours, where here are busy days and hours and on he oher hand here are an idle in days and hours. The company can increase cusomer saisfacion by reducing cusomer s waiing ime. There are several alernaives ha can be used o reduce waiing ime. The firs alernaive is by increasing he number of employees bu his alernaive will cause grea increasing of labor cos and high percenage of employee idle ime (especially in idle days and hours). Oher alernaive o overcome his problem is shif allocaion mehod wih good scheduling procedure so ha he employee uilizaion is no oo low in idle ime and no oo high in busy days and hours. This problem will be more complicaed during employee's brea ime because he number of employee is no enough o serve he cusomer. Therefore, he company should arrange he brea ime so ha he employees can enjoy heir res wihou disurbing he service o cusomer. I can be achieved by scheduling he employee's brea ime no simulaneously in Brea Windows. Brea windows are ime inervals wihin which employees mus sar and complee heir breas. The problem is geing complicaed for company who serves 7 days a wee because almos all of he privae companies in Indonesia operae 6 days a wee. The ineger programming model for shif scheduling was originally suggesed by Danzig [1954], bu i does no consider cusomer service in brea ime. The shif scheduling problem wih muliple brea windows was sudied by many researchers, among hem is Ayin T [1996, 1998]. Worforce allocaion in cyclical scheduling problems was suggesed by Baer [1976] and he our scheduling problem involved boh shif scheduling for wor days in a wee and days-off scheduling discuss abou how o schedule he employees who wors 5 days a wee. This concep needs o be modified due he 6 woring days implemened in Indonesia. This paper used ineger programming model formulaed by Ayin T (1996, 1998) combined wih he modificaion of cyclical scheduling inroduced by Baer. In he nex secion, we discuss an example illusraing he proposed approach and formulaion for a specific shif scheduling problem and he analysis of scheduling resuls obained. 2. Problem Formulaion To illusrae our approach, consider a real case involving hree shifs and an hour lunch brea. The company provided seven service days a wee from o Thus, here are 25 ime-inervals a day. The lengh of each inerval is 30 minues. The shifs and brea windows are shown in Table 1 and Figure 1. Table 1. The shifs and brea windows Woring hours Brea window Shif Shif Shif No res Proceedings of he Inernaional Conference on Compuer and Indusrial Managemen, ICIM, Ocober 29-30, 2005, Bango, Thailand 13.1

2 The busle of he company is very flucuaing. Many cusomers come in he firs wee of he monh, during Saurday and Sunday, and during Bu, during only a few cusomers come. According o Figure 1, Shif 3 is no a pleasan shif for employees. Therefore, he company should give exra ransporaion cos for hem. This paper will focus on developing scheduling model which considers breaing ime of he employees and busy/idle ime of he company. Shif 1 Shif 2 Shif Figure 1. The shifs and brea windows The seps used o conduc his research are described below: 1. Developing a mahemaical model o deermine he number of employees in each ime inerval in planning period by considering busy/idle period and employees brea ime. 2. Deermining a scheduling algorihm for he employees based on: a. The opimal number of employees needed for each shif. b. The scheduling rule which appropriae o company s condiion. c. The number of employees available in he company. 3. Creaing compuer sofware o suppor scheduling process. 3. Model Developmen 3.1 Mahemaical Model in deermining Opimal numbers of employees Ineger Programming Model Minimize: Subjec o : z = C X (1) K a X M ( 1) K TM 1 TM M BM M for all T (2) b X = 0, for all K (3) X, M 0 and Ineger for all and (4) This model is solved wih Branch and Bound mehod using Lingo Opimizaion Sofware. The opimizaion resuls are he opimal numbers of employees in shif 1, 2 and 3 wih heir brea ime schedule. The oal number of employees needed per day is deermined from he oal number of employees needed from shif 1, 2 and 3. This process is carried ou from Monday o Sunday. 3.2 Employees scheduling 6 wor days during 7 service days a wee. To be able o serve he cusomer coninuously, he schedule should be arranged so ha he employees wih 6 woring days a wee can give 7 service days a wee. Firsly we should deermine he algorihm rule hen consruc he scheduling algorihm in accordance wih his rule. The employees can reques in which day hey can be off from wor (one day of 7 woring days). Bu here is a limiaion so ha he scheduling sysem could be well implemened The Employee s Scheduling rule 1. Each employee is scheduled o wor 6 days a wee wih one day-off deermined by he company. 2. The employees assignmen o shif 1 and shif 2 is leveled. 3. The employee's assignmen o shif 3 is made as minimal as possible. 4. The surplus number of employees from he opimal requiremen is allocaed o each day, and allocaed again in every shif along wih his brea regulaion. The shif allocaion prioriy is shif 2, shif 1, and shif The employees can pu forward reques on heir schedule The Scheduling algorihm Based on he scheduling rule, here are 2 sages of he scheduling algorihm, ha is: Sage 1: The day-off deerminaion. a. Each employee is scheduled every day, from Sunday, Saurday, Friday up o Monday, excluding he day having he smalles number of employees demand. If here are wo days or more having he same smalles demand of employees, choose one as he day-off. b. Updae he employees demand/day hen bac o sep a. The resul from his Off-deerminaion sage is he employees day-off in one wee. Sage 2 : The shif and brea deerminaion The employee is assigned in daily basis from Sunday, Saurday, Friday o Monday. The employees opimal requiremen in each shif is allocaed firs hen he surplus number of employees is leveled o all shifs by considering prioriy as follows: shif 2, shif 1, and shif 3. The same concep as employee s allocaion, he brea ime is also allocaed firs in accordance o he opimal value of is number of employees. Then, he surplus number of employees is leveled along wih his brea period The Employee s reques 1. The maximum reques per person per wee is only 2 and i mus be submied before he schedule release. The head of deparmen will decide o approve or rejec he reques. 2. The opion for firs reques can vary no o be scheduled o shif 1, no o be scheduled o shif 2, no o be scheduled o shif 3, or no o be scheduled in a cerain day. Special Issue of he Inernaional Journal of he Compuer, he Inerne and Managemen, Vol. 13 No.SP2, Ocober,

3 B U S T L E C L A S IF IC A T IO N M IN E M P L O Y E E S N E E D E D F O R E V E R Y C L A S IF IC A T IO N B R E A K W IN D O W C U S T O M E R S A R R IV A L D E T E R M IN E M IN E M P L O Y E E S N E E D E D IN E V E R Y T IM E IN T E R V A L S N E E D O F E M P L O Y E E S E V E R Y 3 0 M IN D E T E R M IN E T H E O P T IM A L N U M B E R S O F E M P L O Y E E S O P T IM A L N U M B E R S O F E M P L O Y E E S / D A Y S / S H IF T /R E S T E M P L O Y E E S A V A IL A B L E S C H E D U L IN G R U L E S P S S L IN G O V IS U A L B A S IC S C H E D U L E F O R O N E E M P L O Y E E IN O N E W E E K E M P L O Y E E S S R E Q U E S T S C H E D U L E T H E E M P L O Y E E S M O N, T U E, W E D, T H U, F R I, S A T, S U N F O R i h W E E K S C H E D U L E F O R A L L E M P L O Y E E S IN O N E W E E K S C H E D U L IN G A L G O R IT H M Figure 2. The model and scheduling sysem 3. The second reques opion can vary form no o be scheduled o shif 1, no o be scheduled o shif 2, or no o be scheduled o shif 3 Leave reques by employees is reaed as heir opion o no o be assigned on ha day. The ouline of he model and scheduling sysem for he employee is shown in Figure The Analysis of Scheduling Resuls The Implemenaion of model and sofware o ge he surplus/defici. The surplus/defici of employees needed for all deparmens of he company is shown in Table 2 and he allocaion of surplus/defici for firs wee is shown in Table 3. Table 2. The recapiulaion of employee surplus/defici Wee-i Defici / Surplus (-) Supermare Dep Sore Bazaar Cashier Table 3. The allocaion of employee surplus /defici Day Deparmen Mon Tues Wed. ThursFri Sa Sun Supermare Dep. Sore Bazar Cashier I is shown in Table 2 ha he number of supermare s employees is enough o be scheduled in a normal woring day (negaive means employee's surplus). Bazaar has he bigges employees surplus afer Deparmen Sore. The number of cashiers is no enough he firs wee in every monh. Informaion abou employees defici or surplus can be considered in employee recruimen plan. The ineger programming model can be used o deermine he opimal numbers of employees required, bu in pracice, all of he available employees have o be assigned so ha he opimal soluions for ineger programming is almos impossible o be applied. In he proposed scheduling sysem, he defici or surplus will be allocaed equally as shown in Table 3. Five woring days employees surpluses for supermare are allocaed equally on Wednesday, Thursday, Friday, Saurday and Sunday. Whereas in Deparmen sore, 50 woring days employees surplus for his deparmen are leveled by allocaing 7 more people on he Monday o Saurday and 8 more people on Sunday. Only for cashiers, wo persons lac are allocaed on he Monday and Tuesday Implemenaion of model and Sofware o schedule he employees The number of employees assigned in he real schedule and he new schedule for deparmen sore is shown in Table 4. Table 4. The number of deparmen sore s employees, Monday Augus Real New Opimal Shif Shif Shif The schedule resuled by new scheduling sysem should be in he form of: Proceedings of he Inernaional Conference on Compuer and Indusrial Managemen, ICIM, Ocober 29-30, 2005, Bango, Thailand 13.3

4 1. The overall employee s schedule in one wee. 2. The employee's schedule of a deparmen in one day. 3. The employee's schedule of a deparmen in one shif in a day. 4. An employee s schedule in one wee. The real schedule did no arrange he employee s brea ime. I caused employee's empiness in brea ime. The gap analysis for he deparmen sore schedule on Monday, Augus is shown in Table 5 and Figure 4. From his gap, i is seen ha he new schedule is beer han he real schedule. The example of he real employee assignmen is shown in Figure 3. Table 5 The gap analysis Descripion Real Opimal Model Gap-Real Gap-Model The employees' surplus in his deparmen is very large, bu Figure 4 showed ha real schedule sill has ime inerval wih lac of employees ( ). The bigges employee surplus is in In he new schedule, he lac of employee did no happen in any inerval and he employee surplus in each inerval of ime is well allocaed. In real scheduling, he employee's res was no arranged, on he oher hand he new schedule considered he employees breaing ime. Therefore he new model and scheduling sysem is beer han real scheduling used by he company. Ja m Shif I Shif II Shif III G A P Figure 3. The shif and he number of employees assigned D E P A R T M E N T S T O R E G A P T IM E IN T E R V A L R e a l M o d e l Figure 4 The Deparmen sore gap analysis0 Monday, Augus Model compaibiliy wih he Real Condiion. Model compaibiliy wih he real condiion depends on he parameer used in modeling. If here are oo many idle in cerain ime and on he oher hand, oo many deficis in anoher inerval, his is an indicaion ha he parameer model mus be observed again. The condiion changes resuling in he change of he parameers model are able o be accommodaed by he sysem and Sofware. So ha his sysem and sofware is sill be applied by changing he defaul of he parameers model. 4. Conclusion The Conclusions from he whole research are as follows: 1. Scheduling wih he proposed model and sysem is beer han he real scheduling, ha is: a. Real schedule does no arrange he employee's breaing ime. b. In idle ime, , oo many employees scheduled in real schedule caused a very high cos o he company. 2. The new model and scheduling sysem is suiable for company using muliple shifs and having he paern 6 woring days for 7 service days a wee. In new sysem, he employee's brea is no carried ou simulaneously in brea window so as he employee's empiness in he breaing ime will no be available. Therefore his scheduling model can fulfill he opimal number of employees assigned in he busy/idle period and he employee's righ o mae use of his brea. 3. The new model and scheduling sysem suppored by Sofware faciliaes he human resources deparmen o schedule he available employees. The sofware made have several advanages: a. Faciliaes employees scheduling. b. Flexible in accommodaing he employee's reques for day-off in cerain day, or being no scheduled o cerain shif in cerain day. c. Flexible in accommodaing various model parameer change, including he change in he period of planning, he lengh of he res, woring hours in one day, shif, he parameer from ineger programming consrain. d. Knowing he opimal number of employees needed for a Deparmen could suppor a beer recruimen planning. e. The employee s defici/surplus is leveled each day, aferwards is leveled again during every shif so as o he dump/he lac of employee will no happened oo wors. Noaions used: K T C The se of all shif The se of planning periods ha he schedule covers The cos of assigning an employee in shif, K b The number of employees needed in every period. a is equal o one if period is woring period for shif Special Issue of he Inernaional Journal of he Compuer, he Inerne and Managemen, Vol. 13 No.SP2, Ocober,

5 X is equal o zero if period is no woring period for shif An ineger decision variable for he number of employees in shif M The number of employees in shif and sar his lunch brea in period BM The se of planning periods where employee in shif TM can sar for lunch brea. The se of shif where period is saring period for lunch brea. 5. References Ayin,T. (1996). Opimal Shif Scheduling wih Muliple Brea Windows. Managemen Science, Insiue for Operaions research and The Managemen Science, 42, 4, Ayin, T (1998). A Composie Branch and Cu Algorihm for Opimal Shif Scheduling wih Muliple Breas and Brea Windows. Journal of he Operaional Research Sociey, 49, 6, Baer, K.R.(1976), Worforce Allocaion in Cyclical Scheduling Problems. Operaion Research Quarerly, 27, Danzig, G.B.(1954), A commen on Edie s Traffic Delays a Toll Boohs. Operaions Research, 2, 3, Proceedings of he Inernaional Conference on Compuer and Indusrial Managemen, ICIM, Ocober 29-30, 2005, Bango, Thailand 13.5

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