A SIMULATION-ILP BASED TOOL FOR SCHEDULING ER STAFF

Transcription

1 Proceedings of the 2003 Winter Simultion Conference S. Chick, P. J. Sánchez, D. Ferrin, nd D. J. Morrice, eds. A SIMULATION-ILP BASED TOOL FOR SCHEDULING ER STAFF Mrth A. Centeno Ronld Gichetti Richrd Linn Industril nd Systems Engineering Florid Interntionl University Mimi, FL 33199, U.S.A. Abdullh M. Ismil Informtion Technology Bptist Helth South Florid Corl Gbles, FL 33143, U.S.A. ABSTRACT Helthcre fcilities, especilly hospitls, re under finncil pressure to control cost. One element tht ffects cost significntly is stff. We hve developed tool tht integrtes simultion model nd n integer liner progrm (ILP). The simultion model estblishes the stffing requirements for ech period, nd the ILP produces n optiml clendr schedule for the stff, i.e. how mny stff members to strt t ech shift. The two models were fully integrted, under Visul Bsic interfce tht llowed non expert user of the heuristic to interct with it on repetitive plnning bsis. 1 INTRODUCTION Personnel or stff scheduling problems hve been studied for mny yers due to its importnce on the overll performnce of system in terms of qulity of service to the customer nd cost to the orgniztion. Different pproches hve been tken, including mthemticl models s well s computtionl ones. Some of these models hve been embedded in scheduling systems. A scheduling system hs two gols: 1) determine the minimum number of personnel to stisfy set of service level requirement, nd 2) build schedule tht specifies when person should strt his/her shift so tht ll periods in dy re covered, the stffing level requirement of ech period re met, nd lbor lws mndtes re preserved. With shrinking reimbursement rtes from the federl government (Medicre nd Medicid) nd Mnged Cre Compnies, hospitls must provide higher level of cre t lower cost in order to survive (Ismil nd Miville, 1999). Due to the Blnced Budget Act of 1997, the federl government hs cut Medicre nd Medicid spending by $70.1 billion; thus, producing negtive mrgins (Lewin Report, 1999, AHA sttistics). Over 60% of the cost of operting hospitl is in stffing (Hncock nd Chn 1988). Hospitls need to use scientific mngement tools, nd better scheduling systems, to reduce their stffing levels without ffecting qulity of services. Ptients become disstisfied with the service levels, especilly in the Emergency Room, when they hve to wit for long period of time to receive much needed cre. The ltter sitution occurs when stff is reduced rbitrrily. For the lst few yers, dministrtors nd mngers in helthcre hve turned to scientific methods to reduce cost nd improve their prctices. However, mngers in helthcre, especilly in ER, re clinicins not nlysts; thus, they need tools tht re esy to use nd flexible for their environment. We hve developed tool tht is simple to use, nd which embeds simultion nd mthemticl progrmming under VBA ppliction. With it, the ER dministrtion obtins the optiml number of nurses required per shift to stisfy predefined ptients length of sty (LOS) in the ER, bsed on demnd nd service times. Section 2 of this pper reviews literture pertinent to the stff scheduling problem. Section 3 provides description of the frmework under which the tool ws developed. Section 4, 5, nd 6 provide description of the simultion model, the ILP model, nd the integrtion respectively. Section 7 summrizes the findings nd lessons lerned out of this effort, nd it suggests some extensions to this work. 2 PREVIOUS WORK This section provides review of the literture orgnized in two prts: 1) focuses on mthemticl models nd 2) focuses on discrete event simultion for stff scheduling. 2.1 Opertions Reserch Bsed Scheduling Tools For decdes, reserchers hve used severl pproches to the stff scheduling problem including the use of sttistics, work mesurement, queuing models, nd integer progrmming. Isken nd Hncock (1998) discussed Tour Scheduling models s they pply to scheduling in hospitl

2 Centeno, Gichetti, Linn, nd Ismil ncillry units where demnd is vrible by dy of the week nd time of the dy; specificlly, the uthors introduced Tcticl Stffing Anlysis. This model ws written in AMPL lnguge nd solved using the CPLEX Optimiztion pckge. The output of the solution is text file tht lists ll the scheduling tours. However, s they point out mthemticl models seldom provide complete nswers to rel problems, but they provide prtil solutions, nd greter understnding of the problem. Khn (1991) presented solution tht ws network model to minimize the flow of resources through the network. The resource is the nursing stff tht needs to be ssigned to different deprtments in the hospitl. Khn used the miniml flow lgorithm to solve the problem. He proved tht using the miniml flow lgorithm would yield the sme results s the simplex method. This study cn provide some insights into the stff scheduling problem of ER systems, but it does not provide complete methodology for stffing complex system such s n ER system. Hncock nd Chn (1988) ddressed the problem of stff scheduling where the worklod vries from dy to dy nd the dministrtors need to schedule stff weeks in dvnce. The vribility in demnd is ddressed by one of the following strtegies: Stffing t verge demnd levels with no considertion to work force cpbility. Stffing t constnt level, overtime permitted, nd considertions to work force cpbility. Stffing t constnt level, no overtime permitted, nd considertions to work force cpbility. Stffing t different level ech dy, no overtime, nd considertions to work force cpbility. Stffing t different level ech dy, limit on overtime nd demnd, work force cpbility considered. Stffing t different level ech dy, limit on overtime, workforce cpbility considered, nd work tsk my spn over two dys. For ech of these strtegies, the uthors clculted the lbor cost nd the productivity for the deprtment being stffed. Tine nd Rmyn (1982) provided review of the mnpower scheduling lgorithms from common frmework. This scheduling pproch is bsed on the ide tht the scheduling problem is composed of five stges or subproblems. These five stges re the determintion of temporl mnpower requirements, totl mnpower requirement, recretion blocks, recretion/work schedules, nd shift schedules. For ech of these stges, they suggested different lgorithms. They lso compred nd discussed the lgorithms nd solutions for ech stge. The uthors presented review of the vilble lgorithms to nlyze ech of the five stges of the scheduling problem. Bker (1976) surveyed the bsic mthemticl models for workforce scheduling. He discussed shift scheduling nd dy-off scheduling in generl, s well s the methods to solve such problems using mthemticl progrmming. He presented model for llocting overlpping shifts with demnd fluctutions (the Klein City Problem). He lso presented the service level policy for stff requirement in shifts scheduling. For the dy-off scheduling, he discussed the problem where n employee workweek does not mtch the service fcility operting week. For this sitution, he presented model tht provides equl ssignments by rotting individuls mong dy-off ptterns. 2.2 Scheduling Using Simultion Computer simultion cn be used to model nd nlyze rel-world problems tht cnnot be successfully pproched by other types of nlyticl techniques (Fitzptrick et. l, 1993). In the lst two decdes, the use of simultion s plnning nd decision mking tool hs been spreding rpidly in the helthcre ren. Mny simultion projects hve been done for hospitls round the world, primrily in Emergency Deprtments. Pitt (1997) reports on project tht uses simultion s resource plnning tool. The project is the PRISM project (Plnning Resources using Interctive Simultion Modeling). PRISM is generl frmework tht supports the nlysis of rnge of models nd vribles to test different scenrios in the resource nd strtegic plnning in hospitls. A simultion model of new one-stop pre-procedurl work-up nd ssessment re of the University of North Crolin Hospitls ws developed by Glick (1996) to evlute different scenrios (stffing levels versus ptient volume). For ech scenrio, the simultion predicted the utiliztion for nurses, nesthesiologists, nd other pertinent stff throughout the dy. The simultion lso produced ptient witing time, ptient time in the system nd the totl number of ptients processed throughout the dy. Using these results, schedule for the different required stff ws formulted bsed on the simultion results. Evns, Gor, nd Unger (1996) used simultion s well to investigte vrious schedules of nurses, ER technicins, nd doctors to reduce the verge ptient time in the system. The uthors creted simultion model of prticulr Emergency Room using ARENA simultion pckge softwre to evlute different personnel schedules. Five different schedules were evluted, nd decision ws mde bsed on the verge time in the system. Other reserchers hve used simultion in this sme mnner; For instnce, McGuire (1994) used simultion to reduce Length of Sty (LOS) in n emergency deprtment. One of the lterntives tht ws evluted is the introduction of dditionl stff to the emergency room. Hmmond nd Mhesh (1995) used simultion to test mnning heuristics for bnk tellers to meet the desired level of services in bnks. In this study, the reserchers used mnning model bsed on queuing theory to clcu-

3 Centeno, Gichetti, Linn, nd Ismil lte the required number of employees to meet the level of service requirements. The second prt of this study is the utiliztion of simultion to test new mngement policies. The mnning model provided methodology to clculte the required number of employees while the simultion model tested for the corresponding service level. Grci et l. (1995) studied the flow of ptients t Mercy Hospitl in n effort to reduce the witing times of ptients. As result of this study, Fst Trck lne ws dded to the Emergency Room; thus, reducing the totl time in the system by 25% for ptients with low priority without ffecting the times of ptients with higher priority. This study ws performed using simultion where the uthors conducted the simultion of this system with nd without the Fst Trck to test the effect of implementing this Fst Trck on the system. Fitzptrick. Bker, nd Dve (1993) used simultion modeling to improve scheduling of the operting room of n 800 bed medicl center in the southestern United Sttes. In this study, three different block schedules were compred bsed on throughput, verge witing time, the distribution of witing time, queue chrcteristics, fcility utiliztion, nd cost effectiveness. The simultion model ws built using GPSS. 3 THE FRAMEWORK Simultion models cn provide sttisticlly ccurte nd insightful mens to nlyze nd predict the performnce of system such s hospitl s emergency deprtment, which is complex system formed by lrge number of units with strong interreltionships. On the other hnd, Integer Liner Progrmming is n optimiztion technique tht is concerned with finding the best possible nswer to problem. In the cse of n emergency deprtment, the schedule must meet certin conditions, such s those imposed by regultions nd/or to protect stff nd ptients, including mximum shift length, or mximum overtime hours. In order to mke the simultion nd the liner progrmming model useful to ED mngement, these two techniques hve been integrted under VBA for ARENA ppliction (Figure 1). The simultion model determines the stff requirements during ech of the predetermined periods in dy, given current conditions of demnd nd service times. The results, nmely the number of the RN s in ech of those periods, re then fed utomticlly to the ILP model to generte shift-bsed 24-hour schedule. Through User-Defined Conditions, the nlyst provides the current system s conditions such s the ptients rrivl pttern, the service ptterns of different servers in the ER system, nd the trget performnce level of the LOS. There re two different lterntives to get the dt into the simultion model. The first option is to hve the user input the dt mnully into the simultion model. The second option is to hve the user crete text files tht contin the dt for ech ctegory. For this effort, the second option ws chosen for User's Defined Conditions VBA for ARENA User Input ARENA Simultion Model Simultion outputs: Schedules Integrtion Routines (VBA for ARENA) Figure 1: System Integrtion Finl Results LINGO ILP no other reson thn to reduce the mount of progrmming needed for this prototype. The user simply cretes text files with predefined formt nd nmes. The ARENA Simultion Model mimics the temporl behvior of the ER, nd it clcultes the minimum number of stff required for ech of the nine periods identified. A set of VBA Integrtion Routines is embedded in the simultion model to support dt cquisition from the user, s well s the dt exchnge from the user to the simultion model, from the simultion model to the ILP model, nd bck to the user. A LINGO Integer Liner Progrm is used to determine the ctul lloction of personnel to meet the requirements of ech nd every time period. 4 THE ER MODEL Ptients rrive to the Emergency Deprtment by two different methods: 1) Fire rescue or n mbulnce, or 2) by their own men of trnsporttion. Ptients rriving by Fire Rescue or n mbulnce re given highest priority nd go to bed immeditely. All other ptients re triged nd ssigned n cuity level. There re four different cuity levels used t the model hospitl; Level I, II, III nd IV. When ptient rrives t the emergency room, the ptient hs to be first triged nd ssigned n cuity level. If the cuity level is not emergent, the ptient hs to be registered nd then would wit until bed becomes vilble. Once bed becomes vilble, the ptient is escorted to bed by registered nurse (RN). The RN performs the initil ptient evlution, strts tretment, nd document findings on the ptient chrt. After this evlution, the ptient is seen by physicin who will recommends the tretment nd will order ll the necessry tests, such s n X-ry, blood test, EKG, etc, nd documents finding on the ptient s chrt. The RN, cting on the physicin s orders, strts performing tests nd tretments. At this time, the RN stys in chrge of monitoring the ptient s tretment nd condition. The RN t this time could be ssisting other ptients s well.

4 Centeno, Gichetti, Linn, nd Ismil Once the ptient is stble nd tretments re complete, the physicin decides on the ptient s disposition. The RN prepres nd rrnge for ptient s disposition documenting ll ctions on ptient s chrt. The rrivl pttern presented seven different distributions (Tble 1). The service times of the RN nd the MD were divided into two min stges since they do not service ptient from strt to finish nd then move on to the next ptient. For the RN, Phse 1 is from the time ptient occupies bed in the tretment re until the physicin sees the ptient, nd phse 2 is mde of the rest of the time until ll tretments re completed. For the MD, Phse 1 is the time of the ptient initil evlution by the MD, when tests nd tretments re ordered nd documented, nd Phse 2 is the time from the completion of tests until the ptient is stbilized nd decision on disposition of ptient is to be mde. In this mnner, the server (RN nd MD) is seized to perform the tsk nd then relesed once this tsk is completed. Ech service time for the RN s nd the MD s consisted of multiple distributions s given in Tbles 2 nd 3. To build model for the system being studied, it is necessry to know the properties of the ptients being treted. All ptients tht cme in to the emergency deprtment were logged in with ll their properties including their method of rrivl, disposition, nd the uxiliry procedure received (Tble 4). Times for other ncillry ctivities re in given in Tble 5. Tble 1: Distributions for Inter Arrivl Times Period Period Distribution 1 12:00 AM 3:00 AM Exponentil (0.73) 2 3:00 AM - 7:00 AM Exponentil (1.06) 3 7:00 AM - 8:00 AM Exponentil (0.54) 4 8:00 AM - 9:00 AM Exponentil (0.39) 5 9:00 AM - 10:00 AM Exponentil (0.30) 6 10:00 AM 1:00 PM Exponentil (0.26) 7 1:00 PM 12:00 AM Exponentil (0.36) Acuity Levels I II III IV Tble 3: MD Service Times MD Phse I Service Time MD Phse II Service Time Distribution % Distribution % Uniform (9,11) 0.34 Uniform (7,8) 0.67 Uniform (15,17) 0.33 Uniform (11,13) 0.33 Uniform (19,20) 0.33 Uniform (3,6) 0.60 Uniform (4,8) 0.40 Uniform (11,14) 0.40 Uniform (11,15) 0.60 Uniform (4,6) 0.80 Uniform (4,6) 0.50 Uniform (10,12) 0.20 Uniform (10,11) 0.33 Uniform (11,17) 0.17 Uniform (3,6) 0.33 Uniform (2,6) 0.50 Uniform (7,8) 0.67 Uniform (8,11) 0.50 Tble 4: Ptient Behvior Percentges Action Percentge Arrivl by fire rescue or 24 Arrivl mbulnce Arrivl by own trnsporttion 76 Ptients dmitted 46 Ptients dischrged 45 Deprture Ptients leve ginst medicl 3.3 dvice (AMA) Ptients leve without 5.7 being seen (LWBS) Ptients hve lb procedures 69 Ptients tht hve rdiology 55 Procedures procedures Ptients tht hve EKG 42 procedures Tble 5: Auxiliry Service Times Activity Distribution Registrtion Service Time Norml (11.1,4.2) Trige Time 2 + Weibull (7.37, 1.69) Lb Service Time 10 + Gmm (23.3, 2.56) Rdiology Service Time Weibull (18.2, 1.34) EKG Service Time Tringulr (15,21,30) Acuity Levels I II III IV Tble 2: RN Service Times RN Phse I Service Time RN Phse II Service Time Distribution % Distribution % Uniform (19,22) 0.33 Uniform (21,22) 0.33 Uniform (31,33) 0.50 Uniform (27,30) 0.50 Uniform (37,39) 0.17 Uniform (34,43) 0.17 Uniform (20,22) 0.5 Uniform (16,22) 0.33 Uniform (30,38) 0.5 Uniform (24,25) 0.33 Uniform (29,33) 0.34 Uniform (20,26) 0.4 Uniform (7,17) 0.6 Uniform (27,31) 0.4 Uniform (24,35) 0.4 Uniform (39,41) 0.2 Uniform (13,15) 0.33 Uniform (8,9) 0.33 Uniform (19,24) 0.50 Uniform (13,16) 0.50 Uniform (29,31) 0.17 Uniform (18,20) 0.17 Once the model ws verified nd vlidted, the conditions for the experiments were estblished. Initilly, the simultion model ws run for 10 replictions, nd the LOS for ech repliction ws recorded. These vlues were used to clculte the smple size required to chieve relibility level of ± 3.61 when building 95% confidence intervl. From these, it ws estblished tht the number of replictions required is ILP MODEL An optimiztion ILP model is used to find the optiml number of stff (RN s) needed to work ech shift. To build the ILP model, the first step ws to identify the shifts tht re used by the hospitl. In this cse, the shifts used re 12 hours in length, with strt nd end times s in Tble 6. Bsed on these shifts, period could hve nurses from

5 Centeno, Gichetti, Linn, nd Ismil different shifts; for exmple, period 1 (12:00AM-3:00 AM) hs nurses from shift 3 (3:00 PM - 3:00 AM) nd nurses from shift 4 (7:00 PM - 7:00 AM). Tble 7 shows ech period with its corresponding shifts coverge. The ILP objective function seeks to minimize the lbor cost for RN s. For this model the cost of one RN per shift is given in Tble 6. A minimum of one RN is required t ll times. Then the ILP model is Subject to n i= 1 Where X i = c i = = j X i Minimize z = c i X n i=1 j = 1, 2,, m j X i 1 nd integer i = 1, 2,, n Number of nurses working shift i Slry cost for nurse during shift i Number of RN s required per period s determined in the simultion model i = Index for shifts j = Index for periods n = Mximum number of shifts m = Mximum number of periods The ILP model with ctul dt (Tble 6 nd Tble7) is s follows: Min Z = X Subject to: X1 X 2 X 3 X 4 5 X 3 + X 4 1 (Period 1) X 4 + X 5 2 (Period 2) X 1 + X 5 3 (Period 3) X 1 + X 5 4 (Period 4) X 1 + X 5 5 (Period 5) X 1 + X 2 + X 5 6 (Period 6) X 1 + X 2 + X 3 7 (Period 7) X 1 + X 2 + X 3 + X 4 8 (Period 8) X 2 + X 3 + X 4 9 (Period 9) i Tble 6: Shifts Dt Shift # Strt Time End Time Lbor Cost 1 7:00 AM 7:00 PM $ :00 AM 11:00 PM $ :00 PM 3:00 AM $ :00 PM 7:00 AM $ :00 AM 3:00 PM $ Tble 7: Period nd Corresponding Shifts Time Period Time Period Covered Shifts :00 AM 3:00 AM X X 3:00 AM 7:00 AM X X 7:00 AM 8:00 AM X X 8:00 AM 9:00 AM X X 9:00 AM 10:00 AM X X 10:00 AM 1:00 PM X X X 1:00 PM - 6:00 PM X X X 6:00 PM 8:00 PM X X X X 8:00 PM 12:00 AM X X X Minimum Number of Nurses Needed In the bove ILP model, there re three equtions tht re similr, (Period 3, 4, nd 5) differing only in the right hnd side (RHS) constnt ( ). The constrint with the mx{ 3, 4, 5} will render the other two constrints redundnt. These equtions re left in the ILP model becuse the vlues of 3, 4, nd 5 my chnge due to chnges in the input prmeters of the simultion model. Any chnge to the input prmeters of the simultion model will result in chnges to the results of the simultion model, which in turn will ffect the vlues. Since this model is ment to be reusble, these similr constrints hve been left in to llow the model to choose its own redundnt constrints, depending on current conditions. It is lso worth noting tht lbor costs chnge over time. Therefore, the vlues of (slry cost for nurse during shift) re red from text file, llowing flexibility in the constrint equtions s well s in the objective function of the ILP model. Every time the ILP model is run, the lbor cost text file is red by the ILP model ssigning vlues to ech c. The LINGO Model is given in Figure 2. j c j 6 VBA INTEGRATION j j The tool is the integrtion of severl commercil of the self (COTS) softwre. As shown in Figure 1, the two min

6 Centeno, Gichetti, Linn, nd Ismil SETS: Nurses_Periods/ RN1 RN2 RN3 RN4 RN5 RN6 RN7 RN8 RN9/ : Demnd; Nurses_Shifts/ SH1 SH2 SH3 SH4 SH5/ : Requirement; Cost_shifts/C1 C2 C3 C4 C5/ : Cost; End Sets DATA: Demnd 'Finlschedules.txt' ); Cost 'ShiftCost.txt' = Requirement; ENDDATA [OBJECTIVE] MIN = Cost(C1)*Requirement(SH1) + Cost(C2)*Requirement(SH2) + Cost(C3)*Requirement(SH3) + Cost(C4)*Requirement(SH4) @GIN(Requirement(SH5)); Requirement(SH3) + Requirement(SH4) >= Demnd(RN1); Requirement(SH4) + Requirement(SH5) >= Demnd(RN2); Requirement(SH1) + Requirement(SH5) >= Demnd(RN3); Requirement(SH1) + Requirement(SH5) >= Demnd(RN4); Requirement(SH1) + Requirement(SH5) >= Demnd(RN5); Requirement(SH1) + Requirement(SH2) + Requirement(SH5) >= Demnd(RN6); Requirement(SH1) + Requirement(SH2) + Requirement(SH3) >= Demnd(RN7); Requirement(SH1) + Requirement(SH2) + Requirement(SH3) + Requirement(SH4) >= Demnd(RN8); Requirement(SH2) + Requirement(SH3) + Requirement(SH4) >= Demnd(RN9); END! Terse output mode SET TERSEO 1! Open file DIVERT Shifts.TXT! Send solution to the file SOLUTION! Close solution file RVRT! Quit LINGO QUIT Figure 2: The LINGO ILP Model components of the tool re: simultion model nd n integer liner progrm. The tools used to develop these two components re ARENA nd LINGO. These tools hve mster-slve reltionship, with ARENA retining the mster role becuse of its VBA cpbility. Figure shows the mcro steps of the heuristic tht enble the communiction between the user nd ARENA nd ARENA nd LINGO. The user never intercts directly with LINGO, only with ARENA through simple nd friendly interfce. Figure 3 shows the steps in the VBA integrtion. It required the progrmming of severl ARENA model events: RunBegin RunEndRepliction RunEnd. The code for gthering dt nd implementing Reyes (1998) gol driven simultion heuristic is very extensive, but since the interesting prt ws the embedding of the ILP model, Figure 4 provides the subset of the VBA code tht triggers nd controls LINGO. 1 Get the gol (LOS) from user 2 Lod files (schedules) Chnge = 0 3 Run Simultion 4 At end of Simultion run, For = 1 Clculte 95% CI on LOS for i to n (Number of periods per dy) n periods If Gol < MAX( los ) then RN i RN + Chnge = 1 Next i = 1 i = i 1 5 If Chnge i, then Stop Simultion Updte physicl model (SCHEDULES) Go to step 3 Else Export RN from SCHEDULES to file i End If 6 Trigger Lingo ILP model RN i Lod Files (cost, ) Get solution, trnsfer to file 8 Puse simultion execution, retin control 9 Trigger Lingo ILP model RN i Lod Files (cost, ) Solve ILP model, trnsfer results to n ASCII file 10 Red ILP results file 11 Disply finl Results. Figure 3: Steps in the Integrtion Process At the conclusion of the simultion run, the number of nurses is exported from the SCHEDULES element to text file. A VBA routine (LingoControl) triggers LINGO to run the pre-formulted LINGO ILP model. The LINGO model is progrmmed to red the text file contining the number of nurses required per time period. VBA for ARENA runs the ILP model, vi the DDE fcility of Sendkeys. The results re then exported to text file tht is in turn red by VBA for ARENA to exhibit the finl results through user form.

7 Sub LingoControl() Dim LingoConnector, thefile, Strt DIm PuseTime Dim TotlCost, TotlHours As Integer ' ' Triggering Lingo ' thefile = stffing.lg4 LingoConnector=Shell( lingo.exe,1) AppActivte LingoConnector SendKeys %Fo, True ' ALT+F nd O SendKeys thefile, True ' sending file nme to be opened SendKeys {tb 2}{enter}, True 'click on OPEN in dilog box SendKeys %LS, True ' running the model ' 'pusing to llow solver to finish ' PuseTime = 3 ' Set durtion. Strt = Timer ' Set strt time. Do While Timer < Strt + PuseTime DoEvents ' Loop 'Resume control from Lingo SendKeys C, true SendKeys %FX, True 'Close Lingo Open Shifts.txt For Input As #15 I = 0 While Not EOF(15) Input #15, My I = I + 1 Wend Close #15 ObsNum = I ReDim m(obsnum) As Integer Open Shifts.txt For Input As #15 file. Do While Not EOF(15) For I = 1 To ObsNum Input #15, z m(i) = z Next I Loop Close #15 Centeno, Gichetti, Linn, nd Ismil ' Open RNSH1 = m(1) : RNSH3 = m(3) : RNSH2 = m(2) RNSH4 = m(4) : RNSH5 = m(5) TotlCost = 300 * RNSH * RNSH * RNSH * RNSH * RNSH5 TotlHours = 12 * (RNSH1 + RNSH2 + RNSH3 + RNSH4 + RNSH5) Lod ResultForm ResultForm.Shift1.Text = RNSH1 ResultForm.Shift2.Text = RNSH2 ResultForm.Shift3.Text = RNSH3 ResultForm.Shift4.Text = RNSH4 ResultForm.Shift5.Text = RNSH5 ResultForm.Hours.Text = TotlHours ResultForm.Objective.Text = TotlCost ResultForm.Show 7 CONCLUSIONS This work presents tool tht integrtes two proven tools, simultion nd integer liner progrmming to help ER mngements to stff their deprtments correctly without over-spending. The vlue of this tool hd to be scertined by nswering one question: Is the heuristic t lest s good s the empiricl method currently used? This implies tht even if the heuristic is s good s the empiricl pproch there is n intrinsic vlue in using it, nmely tht the process of generting the schedule is utomted; hence, the schedules re less prone to errors nd cn be generted fster. Since this heuristic ws estblished for stff scheduling in ER, the totl nurse-hours per dy for the empiricl pproch nd the heuristic were clculted t different demnd levels. Tble 8 shows the totl nurse hours for ech of the two methods. For the empiricl method, n ER mnger ws consulted to perform the stffing of nurses t the different ptients levels. As cn be seen in Tble 8, the schedule is fixed between 40 nd 80 ptients, the totl of nurse-hours re then incresed proportionlly bsed on the number of ptients. Trils Tble 8: Totl Nurse-Hours (Number of ptients) TH TE Trils (Number of ptients) TH TE A t-test ws used to nswer the question. The hypothesis test is set up s follows: H : T < T 1 0 E H H : T T, where, T = Totl person-hours for Heuristic T E = Totl person-hours for Empiricl End Sub Since the resulting confidence intervl (24.67, 44.13) Figure 4: VBA Code to Control LINGO does not contin zero, nd the two til significnce level is less thn 0.005, we reject the null hypothesis. Thus, there H E H

8 Centeno, Gichetti, Linn, nd Ismil is sufficient evidence to conclude tht there is difference between the two popultions. Furthermore, becuse the difference T E - T H is positive (34.4), schedules generted using the heuristic requires less person hours thn the schedules generted using the empiricl method. Therefore, the heuristic is better thn the empiricl pproch. The men improvement in the totl person-hours is hours per dy, tht is 28% improvement. Estimting nursing hourly rte to be t $35.00, the 28% improvement, for 15 beds emergency room, will result in n nnul svings of pproximtely hlf million dollrs (34.4 hours/dy*$35.00/hour * 365 dys/yer = $439,460). If hospitl decides to implement this heuristic, they must own ARENA nd LINGO softwre pckges, which implies n investment of pproximtely $25, Given the expected svings, investing in the softwre is profitble. This tool will id ER mngement in determining the exct number of stff required to chieve specific gol, which is the time in the system tht ptient spends in ER. With this tool, ER mngement would be ble to determine the number of nurses by shift bsed on specific time tht they would like to hve the ptients out of the system. They would lso be ble to clculte bsed on their lbor rtes, the cost ssocited with specific time in the system. They lso cn use this tool to experiment with three different importnt fctors; lbor cost, time in the system, nd number of nurses. REFERENCES Bker, K. R., 1976, Workforce Alloction in Cyclicl Scheduling Problems: A Survey, Opertionl Reserch Qurterly, 27(1), Corre, D., 1999, A Study of Response Surfce in Simultion of Emergency Room Systems, Mster s Thesis, Florid Interntionl University, Evns, G. W., T. B. Gor, nd E. Unger, 1996, A Simultion Model for Evluting Personnel Schedules in Hospitl Emergency Deprtment, Proceedings of the 1996 Winter Simultion Conference, J.M. Chrles, D. J. Morrice, D. T. Brunner, nd J. J. Swin (eds.), Fitzptrick, K. E., J. R. Bker, nd D. S. Dve, 1993, An Appliction of Computer Simultion to Improve Scheduling of Hospitl Operting Room Fcilities in the United Sttes, Interntionl Journl of Computer Applictions in Technology, 6 (24), Grci, M. L., M. A. Centeno, C. River, N. DeCrio, 1995, Reducing Time in n Emergency Room Vi Fst-Trck, Proceedings of the 1995 Winter Simultion Conference, C. Alexopoulos, K. Kng, W. R. Lilegdon, nd D. Goldsmn (eds), Glick, N. D., 1996, Predicting Stff Levels for New Service Using Animted Simultion Softwre, Quest for Qulity nd Productivity In Helth Services 1996 Conference Proceedings, Institute of Industril Engineers, Hmmond, D. nd S. Mhesh, 1995, A Simultion nd Anlysis of Bnk Teller Mnning, Proceedings of the 1995 Winter Simultion Conference, C. Alexopoulos, K. Kng, W. R. Lilegdon, nd D. Goldsmn (eds), Hncock, W. M. nd T. J. Chn, 1988, Productivity nd Stffing of Hospitl Units with Uncertinty in the Demnd for Service, IIE Trnsctions, 20(4), Hospitl Sttistics, 2000 Edition, Helth Forum LLC, n ffilite of the Americn Hospitl Assocition. Isken, M. W. nd W. Hncock, 1998, Tcticl Stff Scheduling Anlysis for Hospitl Ancillry Units, Journl of the Society for Helth Systems, 5(4), Ismil, A. M. nd N. D. Miville, 1999, Flexible Stffing for Ancillry Deprtments in Hospitls, Industril Engineering Solutions 99 Conference Proceedings, B. Bopy, nd P. H. Cohen (eds), Khn, Z. A., 1991, A Note on Network Model for Nursing Stff Scheduling Problems, Informtion nd Decisions Technologies, 17 (1991), Klein, R. W., M. A. Dme, R. S. Dittus, nd D. J. DeBrot, 1990, Using Discrete Event Simultion to Evlute Housestff Work Schedules, Proceedings of the 1990 Winter Simultion Conference, O. Blci, R. P. Sdowski, nd R. E. Nnce (eds), Lewin Report, 1999, The Blnced Budget Act nd Hospitls: The Dollr nd Cents of Medicre Pyment Cuts, <http// (October 10, 1999). Mson, A. J., D. M. Ryn, nd D. M. Pnton, 1998, Integrted Simultion, Heuristic nd Optimiztion Approches to Stff Scheduling, Opertions Reserch, 46 (2), McGuire, F. 1994, Using Simultion to Reduce Length of Sty in Emergency Deprtments, Proceedings of the 1994 Winter Simultion Conference, J. D. Tew, S. Mnivnnn, D. A. Sdowski, nd A. F. Seil (eds.), Pitt, M., 1997, A Generlised Simultion System to Support Strtegic Resource Plnning in Helthcre, Proceedings of the 1997 Winter Simultion Conference, S. Andrdottir, K. J. Hely, D. H. Withers, nd B. L. Nelson (eds), Reyes, F., 1998, A Heuristic for On-Line Assessment of Simultion Output for Gol Driven Simultion, Mster s Thesis, Florid Interntionl University, Tine, H. M. nd A. Rmyn, 1982, On Mnpower Scheduling Algorithms, SIAM Review, Society for Industril nd Applied Mthemtics, 24(3),

9 Centeno, Gichetti, Linn, nd Ismil AUTHOR BIOGRAPHIES MARTHA A. CENTENO is n ssocite professor in the Deprtment of Industril nd Systems Engineering t Florid Interntionl University. She hs B.S. in Chemicl Engineering from I.T.E.S.O. (Gudljr, Mexico), M.S. in Industril Engineering from L.S.U. (Bton Rouge, LA), nd Ph.D. in Industril Engineering from Texs A&M University (College Sttion, TX). Her current reserch interests re in the design nd development of integrted simultion systems, on-line gol driven simultion, nd engineering eduction. She is member of ΤΒΠ, ΑΠΜ, ΦΗΣ, ASEE, IIE, INFORMS, nd SCS. Her emil ddress is <centeno@fiu.edu>,nd her web site is <risecenter.eng.fiu.edu>. RONALD GIACHETTI is n ssistnt professor here t Florid Interntionl University in the deprtment of Industril nd Systems Engineering. Dr. Gichetti received his Ph.D. in Industril Engineering in 1996 t North Crolin Stte University. He received his msters in Mnufcturing Engineering t Polytechnic University in Brooklyn, New York. He hs served s ssistnt professor since RICHARD J. LINN is n ssocite professor here t Florid Interntionl University in the deprtment of Industril nd Systems Engineering. He received his Ph.D. from Pennsylvni Stte University in 1987 His teching interests re Inventory Theory, Production Plnning nd Control, Simultion, Opertions Reserch, Design of Experiments, Informtion Systems, Logistics Mngement, Automtion, nd CAD/CAM/CIM. He hs been involved with the deprtment since ABDULLAH M. ISMAIL is business systems nlyst II t Bptist Helth South Florid. He hs over 10 yers experience in mngement engineering, project mngement, nd systems implementtion. He hs BS in industril nd systems engineering nd n MS in industril engineering from Florid Interntionl University. He is member of MIMSS nd Alph Pi Mu.