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![proven to ful®ll most goals comple-
tely. Moreover, faculties satisfaction
levelobtainedwereupto85.2and88.
8 for the two stages models respec-
tively. The overall satisfaction level
when combining the two results
reachedupto73.6%asfarasfaculties
getting their ®rst choices of prefer-
ences.Nonetheless,faculties'satisfac-
tionlevelreachedupto100%whenit
came to getting at least their second
choices of preferences.Itis important
to realize however, that faculties' sa-
tisfaction level is solely data depen-
dent.Thismeansthatifmostfaculties
prefer to teach the same course and
only one faculty could teach it at a
time, then not everybody who prefers
to teach that course could do so. On
the other hand, if it happens that
di€erent faculties prefer to teach dif-
ferentcourses,thenmostfacultieswill
be assigned to teach their preferred
courses. Work is underway to build a
three-stage model integrated within a
decision support system. The imple-
mentation and the results of the ex-
perimentationwithsuchsystemforall
majors at the College of Business
Administration will be reported in a
forthcoming paper.
References
Dinkel, J. and J.Mote. 1989. An Ecient
Decision Support System for Aca-
demic Course Scheduling. Opera-
tionsResearch,37(6): 853-864
Badri, M. A. 1996. A two-stage multi-
objective scheduling model for [fa-
culty-course-time] assignments. Eur-
opean Journal of Operational
Research,94(1): 16-28.
Badri, M. A., Davis, D. L., Davis, D. F.,
Hollingsworth, J. 1998. A multi-ob-
jective course scheduling model:
Combining faculty preferences for
courses and times. Computers and
OperationsResearch,25(4): 303-316.
Hinkin, T. R. and Thompson, G. M.
2002. SchedulExpert: Scheduling
Courses in the Cornell University
School of Hotel Administration. In-
terfaces,32(6): 45-57
Al-Yakoob, S. M. and Sherali, H. D.
2006. Mathematical programming
models and algorithms for a class-
faculty assignment problem. Eur-
opean Journal of Operational Re-
search,173:488-507.
Al-Yakoob, S. M. and Sherali, H. D.
2007. A mixed-integer programming
approach to a class timetabling pro-
blem: A case study with gender po-
licies and trac considerations an.
EuropeanJournalofOperationalRe-
search,180:1028-1044.
Anderson, D., Sweeney, D., Williams, T.
2008. An Introduction to Manage-
ment Science: Quantitative Ap-
proaches toDecision Making, 11e.
Lee, S. 1972. Goal Programming for De-
cision Analysis. Auberback Publish-
ers, Philadelphia, PA.
A.J.A.S,Vo1.17,No.1
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Mohamad K. Hasan received a degree of Bachelor of Science in
Mathematical Statistics from Alexandria University, Egypt, in
1978. He was awarded a degree of Master of Science in Mathe-
matics from Texas AM University, Texas, USA, in 1988, and a
degree of Doctor of Philosophy in Transportation Systems from
Texas AM University, Texas USA, in 1991. Currently, he works
as Associate Professor at Department of Quantitative Methods
and Information Systems, College of Business Administration,
A.J.A.S,Vo1.17,No.1
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Uploaded byAndrew Molina
A Sequential Two-Stage Goal Programming Mod-El For Faculty-Course-Time Slot Assignments
This paper proposes a two-stage sequential goal programming model for faculty-course-time slot assignments at Kuwait University. The first stage uses goal programming to assign faculty members to courses by maximizing faculty course preferences. The second stage then allocates assigned faculty-courses to time slots by maximizing faculty time preferences. The model decomposes the complex scheduling problem into more manageable stages. Testing showed the first stage fulfilled faculty course teaching preferences up to 85.2% and the second stage fulfilled faculty-course-time slot preferences up to 88.8%.
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Similar to A Sequential Two-Stage Goal Programming Mod-El For Faculty-Course-Time Slot Assignments
A Sequential Two-Stage Goal Programming Mod-El For Faculty-Course-Time Slot Assignments
- 1. MohamadK.Hasan RaedQ.Al-Husain HameedA.Al-Qaheri A SEQUENTIAL TWO-STAGE GOALPROGRAMMING MOD- EL FOR FACULTY-COURSE- TIME SLOT ASSIGNMENTS Kuwait University Kuwait Key Words Abstract Faculty Course Assignment; Goal Programming; Faculty Time; Solt Assignment; University Course Scheduling; Two-Stage Model Developing a model that could produce ecient and e€ective faculty-course schedules has been a challenging task in universities around the world. Di€erent systems have been designed and built in an attempt to come up with the "optimal" schedule, yet every system has its limitations and drawbacks. This paper utilizes zero-one goal programming technique to assign faculty members to courses as a ®rst stage and then to allocate courses- faculties to time-slots as the second stage. Through this two-stage optimization procedure, the model seeks to maximizethe faculty coursepreferences in the ®rst stage andmaximizefacultytimepreferenceinthesecondstage. The method used in satisfying goals is the priority sequenceapproach,wheregoalsaresatis®edaccordingto their order of importance based on some university, college, department, and major regulations and require- ments.Themodelhasbeentestedondi€erentassignment scenarios. The ®rst stage has proven to ful®ll most goals completely to optimality, and then ful®ll the faculty course teaching preferences up to 85.2%. The second stage ful®lls the faculty-course-time slot teaching prefer- encesupto88.8%. Introduction Theproblemofassigningfacultiesto di€erent courses, time-slots, and class rooms such that resources are fully utilized,facultiesarecompletelysatis®ed, and students are eciently progressed through their educational requirements has been a recurring problem in most universities around the world. In an at- tempt to solve this problem, di€erent universities have adopted di€erent ap- SubmittedJuly2008,acceptedDecember2008. Arab Journal of Administrative Sciences 2010,Vol. 17,No. 1,169-191 169
- 2. proaches ranging frommanual schedul- ing, sophisticated mathematical models and computer programs, and decision support systems. Using either ap- proaches,however,theproblemofdevel- opingperfectschedulesstillpersist. Manual approaches have proven to cause an ine€ective course scheduling. Problems such as o€ering required courses at the same time on the same day,assigningthewrongclasssizetothe wrong class room, inevitable biased faculty-course assignment, and rela- tivelylongtimetocompletetheschedule have all been conventional results of using such approaches. In an attempt to eliminate or at least minimize such problems, researches have been devel- oping more sophisticated methods. Their attempts date back to the early 70s, where linearprogramming models, networkmodels,large-scaleintegerpro- gramming models were developed to solvethefaculty-courseschedulingpro- blem. Although such models have suc- cessfully produced satisfying faculty- courseassignments,someofthesemod- els have failed to include the time com- ponent factor to their models. On the otherhand,modelsthathaveaddressed the time components, have failed to consider the classroom availability as- pect (Dinkel and Mote, 1989). More recently,however,sophisticatedmathe- maticalprogrammingmodelshavebeen developed to solve the faculty-course scheduling problems, yet they have either failed again to include the room information, or could not been opti- mally solved (Al-Yakoob and Sherali, 2006; HinKin and Thompson, 2002; Badri et al., 1998; Badri, 1996) due to itslevelofcomplexity.Forexample,Al- Yakoob and Sherali (2006, 2007) have proposed a two-stage approach for sol- ving the faculty-course scheduling pro- blem. In their ®rst stage model (Al- yakoob and Sherali, 2007) an ecient class timetable that considers available facilityresourcessuchasclassroomswas developed. Then, the output of their ®rst-stage model was used as an input totheirsecondstagemodel(Al-Yakoob and Sherali, 2006), which is concerned with assigning faculty members to classes for individual departments. Although in their model the faculty- course scheduling problem has been taken one step further, in speci®c, it addresses a gender related policies, further enhancements to their model hadtobeimplementedbeforeasolution could be reached. When they tried to solve the model, they encountered out- of memory diculties before reaching any solution that was within 50% of optimality. To overcome these dicul- ties they developed a two-phase LP- based heuristic and the best perfor- mance they have obtained using this heuristic yielded a solution within 68% ofoptimality.Thetimeneededtoobtain this solution was still more than two days and in some other cases they A.J.A.S,Vo1.17,No.1 170
- 3. encountered out-of memoryproblem. They developed another complicated heuristic procedure,but their solution's optimality ranged from 55% to 73%. Themodelinge€ortsrequired,thecom- plexity and time necessary to develop utility function of faculty preference, andtheruntimerequiredforcompleting theheuristicbasedsolutionwasfarfrom optimality, which could limit their ap- plicationwhenusedonapracticalcase. Another approach that has been utilized to overcome the complexity of solving the faculty-course scheduling problem to optimality is the use of decision support system. Their use has played a signi®cant role in trying to come up with close to optimality solu- tions in relatively reasonable time. Thus,methodssuchasdevelopingspe- cialized computer programs to auto- mate the scheduling process have been a rectifying alternative. Software such as ScheduleExpert (Hinkin and Thompson, 2002) has been developed at Cornell University School of Hotel Administration, which made course scheduling more ecient and more e€ectivetobothstudentsandfaculties. Their software can determines what classes should be taught, what time they should be taught, and in what location. If desired, the software can also determine who will teach each class. However, in order to ®nd such a solution,acomplexheuristicprocedure had to be designed and run. The user thenmustpausetheprogram,examine the generatedschedules,and decideon thebestsolution.Thistakesusbackto the same old dilemma of running into possibleine€ectiveschedules. Goalprogrammingmaybeusedin somedecisionprocessestoassureleast possibledeviationfromgoals(Ander- son et al., 2008), Lee (1972), Lee and Schniederjans (1983), Schniederjans et al. (1982). The natural con¯ict in the course-faculty-time assignment problem between competing indivi- dual faculty members (i.e. faculty members wanting to teach certain courses or sections at certain times), represents an ideal application of the goal con¯icting resolution character- istics inherent in goal programming. ThemodelsofHarwoodandLaw- less (1975) and Schniederjans and Kim (1987) though did use goal pro- gramming to examine the con¯icting goalsinthefaculty-courseassignment problem. The major drawback with the ®rst model is that it may be very diculttoimplement.Theypresented a multitude of criteria that are strict requirements rather than goals. As a result,thesecriteriaaddneedlesscom- plication and data collection require- ments to the model. On the other hand, the proposed model of Schnie- derjans and Kim (1987) sought to overcome the possible implementa- tion limitations of the Harwood and MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 171
- 4. Lawlessmodel.Inadditiontosatisfy- ingdepartmentalgoalsonthenumber andtypesofcourseo€eringsrequired, as well asthe faculty teaching load requirements, their proposed model alsodealtwithfacultycourseteaching preferences. The major drawback with this second model is that it considered only one dimension of the departmental course scheduling, the faculty-course assignment problem. The second dimension dealing with the course-time assignment problem was not dealt with. Badri (1996) proposed two-stage goal programming model that over- came the possible implementation limitation of Harwood and Lawless model. The model maximizes faculty- coursepreferencesinassigningfaculty members to courses and then max- imizesfacultytimepreferencesinallo- cating sources to time blocks (slots).The results of the model appli- cation to the United Arab Emirates University demonstrate the model's capability to provide an assignment that satis®es departmental policies and procedures with regard to course o€erings, as well as recognizing the personalpreferencesofthefacultyfor teaching particular courses and dur- ing certain time blocks. Badri etal.(1998)proposed a goal programming model the can simulta- neouslyconsiderfacultypreferencesof courses and times. The application of the model illustrated how the faculty assignment problem could be struc- tured into relatively small model (i.e. relative to Badri (1996)). In this re- search paper Badri did not make a completecomparisonbetweenhistwo- stagemodelandthesimultaneousone basedonauniqueapplicationforboth models regarding the same problem. The focus of our research activity is to build a three-stage (sequential) goal programming model, inline with Badri(1996)butwithdi€erentmajor, department, and college and univer- sity policies. Rules and priorities are integrated in a decision support sys- tem that would allow the person in chargeoffaculty-courseschedulingto come up with the most ecient and e€ective schedule. Figure 1 shows a block diagram and information ¯ow of the three-stage (sequential) goal programming model under investiga- tion.Inthe®rststageofthemodel,the faculty-course assignment stage, the inputs to this stage would be faculty course preferences input (as shown in Table 1), university, college and de- partment assignment rules and regu- lations related to assigning courses to faculties. The output of this stage would be faculties with courses as- signed. The second stage, the faculty- course-time slot (timetabling) stage, would take faculties time preferences fortheirassignedcourses(asshownin Table 4), the university, college, and department timetabling requirements A.J.A.S,Vo1.17,No.1 172
- 5. as inputs inorder to generated the faculty-course-time slot assignment (timetabling). The third stage model, theroomassignmentstagewouldtake the faculty-course-time slot assign- ment result from the second stage along with the university, college, and department room assignment re- quirements as inputs in order to gen- erate a complete ®nal schedule. The decompositionofschedulingproblem into three distinct and interrelated stages, compared to a single (simulta- neously) stage solution, leads to an easeofuseandsigni®cantreductionin computation time. Work is underway to build the three-stage model integrated within a decision support system. The imple- mentation and the results of the ex- perimentation with such system for multimajorattheCollegeofBusiness Administration in Kuwait University will be reported in a forthcoming paper. As a result, in this paper we report the result of the implementa- tion of two stages of our three-stage model.Insection2wepresentthetwo- stage mathematical model, namely faculty-course-time slot assignment. In section 3 we present the results of our experimentation with the model and section 4 we present our conclu- sion and future research. The Mathematical Model Inthissection,wedescribethegoal linear programming model that is applied to the ®rst of the two stages of the model, namely the faculty- courseassignmentandthetimetabling assignment. An overview of goal pro- grammingmodelformulationisgiven ®rst, followed by a detailed descrip- tion of the two-stage model. General Goals Linear Programming (GLP) Model Formulation Agoalisadesiredresult.Itmaybe underachieved,fullyachieved,orover- Figure 1: Faculty Course Schedule Block Diagram and Information Flow Course Assignment Phase Course Assignment Phase Faculty Course Preference Input Timetabling Phase Timetabling Phase Room Assignment Phase Room Assignment Phase Faculty Course Assignment Course Schedule Faculty Course Preference Input Assignment Rules, Regulations And Requirements Input Faculty Time Preference Input Timetabling Rules, Regulations And Requirements Input Room Assignment Rules, Regulations And Requirements Input Faculty-Course timetabling MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 173
- 6. achieved. Relative emphasisapplied throughmanagerialactioncontributes to the degree of goal achievement. Symbolically, 1 unit of e€ort applied to activity xj might contribute an amount aij toward the achievement of theith goal. Thetargetlevelfortheith goal,bi , is fully achieved if X n jˆ1 aijxj ˆ b To allow for underachievement or overachievement, let dÿ i = negative deviation from the ith goal (underachievement) d‡ i = positive deviation from the ith goal (overachievement) From this, for the ith can be stated in general terms as X n jˆ1 aijxj ˆ dÿ i ‡d‡ i ˆ bi iˆ 1; 2; ::::; m It is required that one or both of the deviational variables (dÿ i ; d‡ i ) be zero in the solution, since it is not possible for both underachievement and overachievement to occur at the same time. The goal programming model must be able to incorporate goal at- tendant with both ranking and weighting as appropriate. Let pk= Ranking coecient for all deviationshavingkth priorityofbeing avoided. wÿ ik= Relativeweightofthedÿ i in the kth rank w‡ ik= Relativeweightofthed‡ i in the kth rank With mgoals, the goal linear pro- gramming model may be formulated mathematically as requiring the mini- mization of the linear weighted rank- ing function X n jˆ1 X k pk wÿ ikdÿ i ‡wÿ ikd‡ i † Subject to the linear constraints P n jˆ1 aijxj ‡dÿ i ÿd‡ i ˆ bi iˆ 1; 2; ::::; m xj; dÿ i ; d‡ i 0 iˆ 1; 2; :::m; jˆ1; 2; :::; n Goal programming seeks satisfac- tory level of goal attainment that represents the best possible overall outcome. This aim can be realized if theseveralgoalarestatedandformu- latedmathematicallyinamannerthat permit appropriate consideration in the goal programming model. There- fore, the decision maker must deter- mine which goal are most important andassignanordinalvalue(priority), Pk , to each goal or group of goals, Further, within a given goal, there A.J.A.S,Vo1.17,No.1 174
- 7. may be subgoals of unequal impor- tance which must be given di€erent weights, wÿ ik w‡ ik. Solving any goal programming model involves achieving highest priority goal, ®rst, before any of the lower priority goals are considered. Once the highest priority goal is at- tained to fullest extent possible, the goal programming model proceeds to ®ndasatisfactoryleveltonexthighest prioritygoal,andsoon.However,itis not always possible to achieve every goal to the extent desired by the decision maker. But the advantage of goal linear programming over ordin- ary linear programming is that it seeks, within the given set of con- straints, to minimize the deviation from the established goals targets, while the ordinary linear program- ming seeks to minimize or maximize certain goal directly. Stage I: Faculty-Course Assignment Goal Linear Programming Model In this section we formulate the goal programming model that repre- sents the rules and regulations of Kuwait University, College of Busi- ness Administration, and the require- ments of Management Science major at department of Quantitative Meth- ods for assigning courses to faculty. Suppose we have m faculty mem- bersandncourses.Eachfacultymem- ber ihas a speci®c maximum number of course sections load Li (some fa- cultymemberhasamaximumloadof three course sections and some has maximum load of two) to teach, and each course jcould have one or more di€erent sections Nj that should be cover by faculty members. Someofthecoursesaredesignated as College Level Courses (CLC) and others are designated as Major Level Courses (MLC) (core or elective courses). LetXijbethenumberofsectionsfor coursejthatwillbeassignedtofaculty memberi,andRij bethepreferencefor faculty member ito teach course j. Rij takesvalues1,2,3,4,and5.Where5is themostfavoriteonecourse/section.If Rij= 0 then Xij = 0, which means that the faculty member idoes not want to teach coursejatall. The required rules for this assign- mentcanberepresentedbythefollow- ing goals and priorities: Goal1: Eachfacultymemberishouldtake exactly his maximum load Li. This goal has a priority P1 and is repre- sented by the following formula: X n jˆ1 Xij ‡dÿ 1i ÿd‡ 1i ˆ Li iˆ 1; 2; ::::; m theobjectiveistominimizebothof dÿ 1iand d‡ 1i 8i: MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 175
- 8. Goal2: The number ofcourse sections Nj for course j should all be covered by faculty members. This goal has a priority P1.This goal is represented by the following formula: X n jˆ1 Xij ‡dÿ 2jÿd‡ 2j ˆ Nj jˆ 1; 2; ::::; n theobjectiveistominimizebothof dÿ 2i and d‡ 2j 8j. Goal3: Each faculty member should take at lease one of the CLC course sec- tions. This goal is a department level requirement and is given a priority level P2 . This goal is represented by the following formula: X j2CLC Xij‡dÿ 3iÿd‡ 3i ˆ 1 iˆ 1; 2; ::::; m theobjectiveistominimizedÿ 3i 8i. Goal4: Each faculty member should take at lease one of the MLC course sec- tions. This goal represent another department level requirement and is given a priority level P3 . This goal is represent by the following formula: X j2CLC Xij‡dÿ 4iÿd‡ 4i ˆ 1 iˆ 1; 2; ::::; m theobjectiveistominimizedÿ 4i 8i. Goal5: Maximize the total preference for each faculty member i that has a load Li . This goal has a priority P4 and is represented by the following formula: X n j RijXij‡dÿ 5iÿd‡ 5i ˆ5Li iˆ1; 2; ::::; m theobjectiveistominimized‡ 5j 8i. Finally we have one more hard constrain that does not allow any faculty member i to take more than two sections for the same course j . This constraint is represented by the following formula: Xij 2 iˆ 1; 2; :::; m andjˆ 1; 2; :::; n Satisfying the above goals with their priorities and the other require- ments, the ®rst stage GLP can be written as following: First Stage GLP: Minimize P1w‰P m iˆ1 dÿ 1i ‡d‡ 1i†‡ P n jˆ1 dÿ 2j ‡d‡ 2i†Š‡ P2 P m i dÿ 3i ‡P3 P m i dÿ 4i‡ P4 ‡P m i dÿ 5i A.J.A.S,Vo1.17,No.1 176
- 9. Subject to: P n jˆ1 Xij‡dÿ 1iÿd‡ 1i ˆLiiˆ1; 2; :::; m P n iˆ1 Xij‡dÿ 2jÿd‡ 2j ˆNj jˆ1; 2; :::; n P n j2CLC Xij‡dÿ 3iÿd‡ 3i ˆ1 iˆ1; 2; :::; m P n j2MLC Xij‡dÿ 4iÿd‡ 4i ˆ1 iˆ1; 2; :::; m P n j RijXij‡dÿ 5iÿd‡ 5i ˆ5Li iˆ1; 2; :::; m Xij ˆ 0 if Rij ˆ 0 2 otherwise; iˆ 1; 2; :::; m and j ˆ 1; 2; :::; n d‡ 1i; dÿ 1i; d‡ 2j; dÿ 2j; d‡ 3i; dÿ 3i; d‡ 4i; dÿ 4i; d‡ 5i; dÿ 5i; 0 foriˆ 1; 2; ::::; mand jˆ 1; 2; ::::; n Where wis very big value to force the values of the deviations d‡ 1i; dÿ 1i; d‡ 2j; dÿ 2j 8iand 8jto be zeros. Stage II: Faculty-Course-Time As- signment Goal Linear Programming Model In this section we formulate the goal programming model that repre- sents the rules and regulation of Ku- wait University, College of Business Administration requirements for as- signing time slots to Faculty-Course assignment resulting from stage I. First, we de®ne the following new notations: Notations: tdp ˆ f1; 2g,Timeslotnumberina day dand period p, where dˆ f1; 2g; days of the week. Such that 1 ={Sunday, Tuesday, Thures- day} and 2={Monday, Wednesday} and p ={m, a}, such that m = morningtime anda= afternoontime Xijkijtdp ˆ 1 iffaculty iassignedto coursejsectionkij during timeslottof daydinperiodp 0 Otherwise 8 : Otdp= Numberofroomsavailable at time slot number tdp. The required rules for this assign- mentcanberepresentedbythefollow- ing goals and priorities: Goal1: Total number of courses assigned inaspeci®ctimeslotcannotexceedthe number of rooms available for that time slot. This goal has a priority P1 and is represented by the following formula: X i X j X kij Xijkij tdp ÿd‡ 1tdp ‡dÿ 1tdp ˆotdp 8tdp theobjectiveistominimized‡ 1tdp8tdp. MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 177
- 10. Goal2: Elimination of timingcon¯ict of courses that can be taken at the same time for similar college level courses (CLC). Total number of similar CLC as- signed during a speci®c time slot in morning-time cannot exceed 2 sec- tions for the same course. This goal hasapriorityP2 andisrepresentedby the following formula: X i X kij Xi j kij tdm ÿd‡ 2jtdm ‡dÿ 2jtdm ˆ 2 8j2 CLC andtdm The objective is to minimize d‡ 2jtdm8j2 CLC and tdm. Goal3: Total number of similar CLC as- signed during a speci®c time slot in afternoon-time cannot exceed 1 sec- tionforthesamecourse.Thisgoalhas apriorityP3 andisrepresentedbythe following formula: X i X kij Xi j kij tda ÿd‡ 3jtda ‡dÿ 3jtda ˆ 1 8j2 CLC andtdm The objective is to minimize d‡ 3jtdm8j2 CLCand tda. Goal4: Reduce the gaps between ULC. The ULC courses should be 4 times more condensed during the morning- time than they are during the after- noon-time,where4isjustanynumber thatthedepartmentwishestochoose. This goal has a priority P4 and is representedbythefollowingformula: P i P j2ULC P kij P tdm Xijkij tdmÿ 4P i P j2ULC P kij P tda Xijkij tda ÿd‡ 4 ‡dÿ 4 ˆ 0 The objective is to minimize dÿ 4 . Goal5: Thisismorelikeaguideline,where 60% of courses should preferably be o€ered during the odd days and 40% during the even days. This goal has a priority P5 and is represented by the following formula: P i P j P kij P t1p Xijkij t1pÿ 1:5 P i P j P kij P t2p Xijkij t2p†ÿd‡ 5 ‡dÿ 5 ˆ 0 The objective is to minimize dÿ 5 . Goal6: Thisismorelikeaguideline,where 70% of courses should preferably be o€ered during the morning-time and 30%duringtheafternoon-time.These goals have a priority P6 and is repre- sented by the following formula: A.J.A.S,Vo1.17,No.1 178
- 11. P i P j P kij P tm1 Xijkij t1mÿ 2:3 P i P j P kij P ta1 Xijkijta1†ÿd‡ 6 ‡dÿ 6 ˆ 0 P i P j P kij P tm2 Xijkij t2mÿ 2:3 P i P j P kij P ta2 Xijkij ta2†ÿd‡ 7 ‡dÿ 7 ˆ 0 Theobjectiveistominimized6 , d7 Goal7: Maximize the professor prefer- ences on their class times. This goal hasapriorityP7 andisrepresentedby the following formula: P j P kij P tdp Rijkij tdp: Xijkijtdp ÿd8i‡dÿ 8i ˆM 8i; such that M is a large number The objective is to minimize dÿ 8i 8i HardConstrains 1 - Sum of sections taught for every professor in every speci®c time slot must be at most equal to 1. X j X kij Xi j kij tdp 1 8i2 I; 8tdp 2 - Sum of ULC o€ered during a speci®c time slot during same day must equal at most 1. X i X j2ULC Xi j1 tdp 1 8tdp 3 - Sum of time slots for each section for every professor, every course, and every section must equal 1. X tdp Xi j kij tdp ˆ 1 8i; j; klij Satisfying the above goals with their priorities and the other require- ments, the second stage GLP can be written as following: Second Stage GLP: Minimize P1 P tdp d‡ 1tdp ‡P2 P j P tdm ‡dÿ 2jtdm†‡ P3 P j P tda d‡ 2jtda†‡P4dÿ 4 ‡P5dÿ 5 ‡ P6 dÿ 6 ‡dÿ 7 †‡P7 P i dÿ 8i Subject to: P i P j P kij Xijkij tdp ÿd‡ 1tdp ‡dÿ 1tdp ˆOtdp 8tdp P i P kij Xijkij tdm ÿd‡ 2jtdm ‡dÿ 2jtdm ˆ2 8j2CLCandtdm P i P kij Xijkij tda ÿd‡ 3jtdm ‡dÿ 3jtda ˆ1 8j2CLCandtda P i P j2ULC P kij P tdm Xijkij tdmÿ 4P i P j2ULC P kij P tda Xijkij tda ÿd‡ 4 ‡dÿ 4 ˆ0 P i P j P kij P t1p Xijkij t1pÿ 1:5 P i P j P kij P t2p Xijkij t2p†ÿd‡ 5 ‡dÿ 5 ˆ0 MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 179
- 12. P i P j P kij P tm1 Xijkij t1mÿ 2:3 P i P j P kij P ta1 Xijkijt1a†ÿd‡ 6 ‡dÿ 6 ˆ0 P i P j P kij P tm2 Xijkij t2mÿ 2:3 P i P j P kij P ta2 Xijkij t2a†ÿd‡ 7 ‡dÿ 7 ˆ0 P j P kij P tdp Rijkij tdp: Xijkij tdp ÿd‡ 8i‡dÿ 8i ˆM 8i; suchthatMisalargenumber P j P kij Xijkij tdp 1 8i2I; 8tdp P i P j2ULC Xij1 tdp 1 8tdp P tdp Xijkij tdp ˆ1 8i; j; kij allXijkijtdp arebinary,andalld0s 0 Experimentation The experimentation was per- formed in two parts re¯ecting the two-stage model under investigation as described earlier. Section 3.1 fo- cuses on the faculty-course assign- ment stage: its collection date and its analysisandresult.Section3.2focuses onthesecond,thefaculty-course-time slot(timetabling)assignmentstage:its collection date and its analysis and result.Section3.3presentsandoverall assessment. Stage I: Faculty- Course Assignment Data Collection A form consisting of courses to be taught by the Department for the fall 2008 semester was presented to each faculty member as shown in Table 1. Faculty members were instructed to insert a value between 1 to 5 for each desired course section, where 1 and 5 Table 1 Faculty - Courses Preference Table Preferences Table (Fall 2008) Faculty Courses Faculty 205 210 310 316 318 415 410 412 493 428 473 532 Load Faculty1 3 5 4 2 1 0 0 0 0 0 0 0 3 Faculty2 2 5 1 0 3 4 0 0 0 0 0 0 3 Faculty3 5 4 0 2 0 0 3 0 2 0 0 0 3 Faculty4 5 4 0 0 0 1 0 3 0 0 0 3 3 Faculty5 4 5 0 0 0 0 0 0 3 1 0 2 3 Faculty6 5 4 2 3 1 0 0 0 0 0 0 0 3 Faculty7 5 4 0 3 0 2 0 0 0 0 2 0 3 Faculty8 4 5 3 2 1 0 0 0 0 0 0 0 3 Faculty9 5 4 1 2 3 0 0 0 0 0 0 0 3 Course sections 9 8 1 1 1 1 1 1 1 1 1 1 A.J.A.S,Vo1.17,No.1 180
- 13. represent the lowestand highest pre- ferences respectively. A value of zero was also requested to be inserted to indicate no preference for that parti- cular course and to force SOLVER not to assign the course for that faculty member. Other important in- put data such as number of faculties, the maximum load assigned to each faculty, number of courses and the numbers of sections for each course were also collected as part of the required data for the model. Upon the completion of the data collection, the model was run and results that indicate the course assignment for each faculty member was obtained as shown in Table 2. Analysis and Assessment The course assignment model was able to successfully distribute all fa- cultymemberstotheircoursesaccord- ing to the college level requirements (goals 1 and 2), department level requirements (goals 3 and 4), and faculties' preferences (goal 5). The percentages of achievement for each goal are shown in Table 3. Case 1 represents the situation where the total faculties' load, gener- ally 3 loads per faculty, equals to the total sections o€ered. Di€erent sce- Table 2 Faculty - Courses Assignment Table Assignment Table Courses Faculty 205 210 310 316 318 415 410 412 493 428 473 532 Faculty1 0 2 1 0 0 0 0 0 0 0 0 0 Faculty2 0 2 0 0 0 1 0 0 0 0 0 0 Faculty3 1 0 0 0 0 0 1 0 1 0 0 0 Faculty4 1 0 0 0 0 0 0 1 0 0 0 1 Faculty5 0 2 0 0 0 0 0 0 0 1 0 0 Faculty6 2 0 0 1 0 0 0 0 0 0 0 0 Faculty7 2 0 0 0 0 0 0 0 0 0 1 0 Faculty8 1 2 0 0 0 0 0 0 0 0 0 0 Faculty9 2 0 0 0 1 0 0 0 0 0 0 0 MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 181
- 14. nariosofdi€erentpreferencesofinput were tested forcase 1, where total faculties' load were equal to the total loadofcourseso€ered,themodelwas ableto satisfygoals1through 4upto 100% in most scenarios. Depending on the level of competition over the courses being o€ered, however, the satisfying goal 5, that is giving each faculty exactly the courses of his ®rst choicetoteach,rangedfrom73.3%up 85.2%. This indicates that the more competition there is over the same course the harder it is to satisfy every faculty's desire. Cases 2 and 3 represent the situa- tion where total faculties' load either greater than or less than the total sections o€ered. Di€erent Scenarios that represent the percent increase or decrease between the faculties' loads andthesectionso€eredbythedepart- ment were tested for each case as shown in Table3. In case 2, where faculties' load is greater than the total sections o€ered by the department, results indicate thatthegreaterthedi€erencebetween the two, the lower the percentage met of some goals such as 1, and 5. This Table 3 Percentage of Goal Achievement for Di€erent Cases and Scenarios Percentage Met Case Description Scenario Goal1 Goal2 Goal3 Goal4 Goal5 1 Faculties' Load= Sections O€ered 1 100 100 100 88.9 82.9 2 100 100 100 100 85.2 3 100 100 100 100 73.3 4 100 100 100 100 84.4 5 100 100 100 100 77 2 Faculties' Load Sections O€ered 8% 92.6 100 100 88.9 77 17.4% 85.2 100 100 88.9 69.6 19% 77.8 100 100 88.9 62.2 21% 70.4 100 100 88.9 54.9 3 Faculties' Load Sections O€ered 8% 100 92.6 100 88.9 85 12.5% 100 88.9 100 88.9 85.5 17.4% 100 85.2 100 88.9 86 22.7% 100 81.5 100 88.9 86.4 A.J.A.S,Vo1.17,No.1 182
- 15. means that theless sections there are to o€er, the lower the chances that every faculty will be assigned his full load and the more the competition is overthosecourse.Hence,themodel's ability to meet the ®rst choice of course to teach for the faculties is reduced. Figure 2 shows the decline in the percentage of satisfying every faculties' ®rst choice. Similarly, in case 3, where facul- ties'loadislessthanthetotalsections o€ered by the department, results indicatethatthegreaterthedi€erence betweenthetwo,thelowerthepercen- tage met of some goals such as 2, and 5. This means the less faculties there are to teach the courses in which the department is intend to o€er, the less the chances that every course will be Figure 2: Percentage of Meeting Faculties' First Choice Case 2 Figure 3: Percentage of Meeting Faculties' First Choice Case 3 MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 183
- 16. assigned a facultyto teach it and, based on the competition, there more chancesforeveryfacultytogethis®rst choice of courses. Figure 3 shows increaseinthepercentageofsatisfying every faculty's ®rst choice. Stage II: Faculty-Course-Time Slot Assignment Data Collection After assigning faculties to their preferredcoursesasindicatedinstage I, faculties were then asked to ®ll in their preferable time slots for their courses as shown in Table 4. Faculty members were instructed to insert a value between 1 to 4 for each desired time slot, where 1 and 4 represent the lowestandhighestpreferencesrespec- tively. Faculty members were also asked to insert the value of zero for absolutely undesirable time slot. Those undesirable time slots were translatedtohardconstraintsinorder to ensure that faculties will not be assignedanyoftheirundesirabletime slots.Otherimportantinputdatasuch as the number of rooms assigned by the collegeto the department in every timeslot,requirednumberofsections forCLCineverytimeslot,theratioof courses to be o€ered during morning sessionsversusafternoonsessions,the ratio of courses to be o€ered during Day 1 (Sunday, Tuesday, and Thurs- day)versusDay2(MondayandWed- nesday),andtheamountofdispersion of ULC. Upon the completion of the datacollection,themodelwasrunand results that indicate schedule for each faculty member was obtained as shown in Table 5. Analysis and Assessment The faculty-Course-time slot as- signment model was able to success- fullydistributeallfacultymembersto theirpreferredtimeslotsbasedonthe goalsandrulesexplainedinsection2.3 asshowninTable6.Resultsshowthat mostgoalsweremetupto100%.The only goal that was underachieved is goal 4, which is the goal that require ULC to be 4 times more condensed during the morning than they are duringtheafternooninordertoelim- inate the dispersion of courses for students, were 4 is just any constant that the department sees appropriate. ThesumofULCo€eredduringmorn- ing time came up to be 7 courses, where the number of ULC o€ered during afternoon time came up to be 3. This means the model was not able tocondensetheULCduringmorning time as desired, which is what lead to the underachievement of goal 4 by 42%. Goal 8 indicates that about 90%ofthefacultiesgotthetimeslots they wished for of their ®rst choice. Overall Assessment Sincethemodelhasbeendesigned to®ndthelocaloptimaforeverystage A.J.A.S,Vo1.17,No.1 184
- 17. Table 4 Faculty-Course-Time SlotPreference Table PREFERENCE TABLE SUNDAY/ TUESDAY/ THURSDAY (D1) MONDAY/ WEDNESDAY (D2) Morning Afternoon Morning Afternoon Faculty i Course j Section kij 8:00 - 9:00 9:00 - 10:00 10:00 - 11:00 11:00 - 12:00 1:00 - 2:00 2:00 - 3:00 3:00- 4:00 8:00 - 9:15 9:30 - 10:45 11:00 - 12:15 2:00 - 3:15 3:30 - 4:45 Faculty 1 210 1 4 3 2 1 0 0 0 0 0 0 0 0 210 2 0 4 3 2 1 0 0 0 0 0 0 0 310 1 2 3 4 1 0 0 0 0 0 0 0 0 Faculty 2 210 3 4 3 2 1 0 0 0 0 0 0 0 0 210 4 0 4 3 2 1 0 0 0 0 0 0 0 415 1 0 0 4 3 2 1 0 0 0 0 0 0 Faculty 3 205 1 4 3 2 1 0 0 0 0 0 0 0 0 410 1 0 4 3 2 1 0 0 0 0 0 0 0 493 1 0 0 4 3 2 1 0 0 0 0 0 0 Faculty 4 205 2 0 0 0 0 0 0 0 4 3 2 1 0 412 1 0 0 0 0 0 0 0 0 4 3 2 1 532 1 0 0 0 0 0 0 0 1 2 4 3 0 Faculty 5 210 5 0 0 0 0 0 0 0 4 2 3 1 0 210 6 0 0 0 0 0 0 0 3 4 2 1 0 428 1 0 0 0 0 0 0 0 2 1 4 3 0 Faculty 6 205 3 3 4 2 1 0 0 0 0 0 0 0 0 205 4 4 3 2 1 0 0 0 0 0 0 0 0 316 1 1 2 4 3 0 0 0 0 0 0 0 0 Faculty 7 205 5 0 0 0 0 0 0 0 4 3 2 1 0 205 6 0 0 0 0 0 0 0 0 4 3 2 1 473 1 0 0 0 0 0 0 0 3 2 4 0 1 Faculty 8 205 7 0 4 3 2 1 0 0 0 0 0 0 0 210 7 4 3 2 1 0 0 0 0 0 0 0 0 210 8 3 2 4 1 0 0 0 0 0 0 0 0 Faculty 9 205 8 1 2 3 4 0 0 0 0 0 0 0 0 205 9 2 3 4 1 0 0 0 0 0 0 0 0 318 1 4 3 2 1 0 0 0 0 0 0 0 0 MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 185
- 18. Table 5 Faculty-Course-Time SlotAssignment Output Table PREFERENCE TABLE SUNDAY/ TUESDAY/ THURSDAY (D1) MONDAY/ WEDNESDAY (D2) Morning Afternoon Morning Afternoon Faculty i Course j Section kij 8:00 - 9:00 9:00 - 10:00 10:00 - 11:00 11:00 - 12:00 1:00 - 2:00 2:00 - 3:00 3:00- 4:00 8:00 - 9:15 9:30 - 10:45 11:00 - 12:15 2:00 - 3:15 3:30 - 4:45 Faculty 1 210 1 1 0 0 0 0 0 0 0 0 0 0 0 210 2 0 1 0 0 0 0 0 0 0 0 0 0 310 1 0 0 1 0 0 0 0 0 0 0 0 0 Faculty 2 210 3 0 0 1 0 0 0 0 0 0 0 0 0 210 4 0 1 0 0 0 0 0 0 0 0 0 0 415 1 0 0 0 0 1 0 0 0 0 0 0 0 Faculty 3 205 1 1 0 0 0 0 0 0 0 0 0 0 0 410 1 0 1 0 0 0 0 0 0 0 0 0 0 493 1 0 0 0 0 0 1 0 0 0 0 0 0 Faculty 4 205 2 0 0 0 0 0 0 0 1 0 0 0 0 412 1 0 0 0 0 0 0 0 0 1 0 0 0 532 1 0 0 0 0 0 0 0 0 0 0 1 0 Faculty 5 210 5 0 0 0 0 0 0 0 1 0 0 0 0 210 6 0 0 0 0 0 0 0 0 1 0 0 0 428 1 0 0 0 0 0 0 0 0 0 1 0 0 Faculty 6 205 3 0 1 0 0 0 0 0 0 0 0 0 0 205 4 1 0 0 0 0 0 0 0 0 0 0 0 316 1 0 0 0 1 0 0 0 0 0 0 0 0 Faculty 7 205 5 0 0 0 0 0 0 0 0 0 1 0 0 205 6 0 0 0 0 0 0 0 0 1 0 0 0 473 1 0 0 0 0 0 0 0 1 0 0 0 0 Faculty 8 205 7 0 1 0 0 0 0 0 0 0 0 0 0 210 7 1 0 0 0 0 0 0 0 0 0 0 0 210 8 0 0 1 0 0 0 0 0 0 0 0 0 Faculty 9 205 8 0 0 0 1 0 0 0 0 0 0 0 0 205 9 0 0 1 0 0 0 0 0 0 0 0 0 318 1 1 0 0 0 0 0 0 0 0 0 0 0 A.J.A.S,Vo1.17,No.1 186
- 19. separately, it isimportant to ®nd overall all satisfaction level for facul- ties for the two stages combined. Taking Case 1/Scenario 1 into con- sideration,theoverallfacultysatisfac- tion level of the two stages combined was found to be 82.9% x88.8% = 73.6%. However, this result should notbemissinterpretedforitmeasures thesatisfactionlevelasfarasfaculties getting their ®rst choices. Results in- dicate that the overall satisfaction level for faculties reached up to 100% when it came to getting at least their second choices of preferences. Moreover, the model's simplicity in formulation, its promptness when reaching local optimal solution, and its overall goals' ful®llment over- whelms the need for combining the two stages into one complex model and solving it at once (i.e., Simulta- neously). Conclusion and Future Research Developing a model that could produce an e€ective faculty-course scheduling solution is no easy task. Di€erent systems have been designed and built in di€erent universities around the world in an attempt to comeupwiththe``optimal''schedule, yeteverysystemhasitslimitationsand drawbacks. This paper utilizes the goal programming technique and the idea of breaking (decomposing) the problem into smaller sub problems in order to simplify formulation and swiftly reach a satisfying solution to theoverallproblem.Themethodused in satisfying goals is the priority se- quence approach, where goals are satis®ed according to their order of importancebasedonsomeuniversity, college, and department regulations andrequirements.Themodelhasbeen tested on di€erent scenarios and has Table 6 Percentage of Goal Achievement for Faculty-Course-Time Slot Assignment Model Goals Percentage Met Goal 1 100 Goal 2 100 Goal 3 100 Goal 4 58 Goal 5 100 Goal 6 100 Goal 7 100 Goal 8 88.8 MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 187
- 20. proven to ful®llmost goals comple- tely. Moreover, faculties satisfaction levelobtainedwereupto85.2and88. 8 for the two stages models respec- tively. The overall satisfaction level when combining the two results reachedupto73.6%asfarasfaculties getting their ®rst choices of prefer- ences.Nonetheless,faculties'satisfac- tionlevelreachedupto100%whenit came to getting at least their second choices of preferences.Itis important to realize however, that faculties' sa- tisfaction level is solely data depen- dent.Thismeansthatifmostfaculties prefer to teach the same course and only one faculty could teach it at a time, then not everybody who prefers to teach that course could do so. On the other hand, if it happens that di€erent faculties prefer to teach dif- ferentcourses,thenmostfacultieswill be assigned to teach their preferred courses. Work is underway to build a three-stage model integrated within a decision support system. The imple- mentation and the results of the ex- perimentationwithsuchsystemforall majors at the College of Business Administration will be reported in a forthcoming paper. References Dinkel, J. and J.Mote. 1989. An Ecient Decision Support System for Aca- demic Course Scheduling. Opera- tionsResearch,37(6): 853-864 Badri, M. A. 1996. A two-stage multi- objective scheduling model for [fa- culty-course-time] assignments. Eur- opean Journal of Operational Research,94(1): 16-28. Badri, M. A., Davis, D. L., Davis, D. F., Hollingsworth, J. 1998. A multi-ob- jective course scheduling model: Combining faculty preferences for courses and times. Computers and OperationsResearch,25(4): 303-316. Hinkin, T. R. and Thompson, G. M. 2002. SchedulExpert: Scheduling Courses in the Cornell University School of Hotel Administration. In- terfaces,32(6): 45-57 Al-Yakoob, S. M. and Sherali, H. D. 2006. Mathematical programming models and algorithms for a class- faculty assignment problem. Eur- opean Journal of Operational Re- search,173:488-507. Al-Yakoob, S. M. and Sherali, H. D. 2007. A mixed-integer programming approach to a class timetabling pro- blem: A case study with gender po- licies and trac considerations an. EuropeanJournalofOperationalRe- search,180:1028-1044. Anderson, D., Sweeney, D., Williams, T. 2008. An Introduction to Manage- ment Science: Quantitative Ap- proaches toDecision Making, 11e. Lee, S. 1972. Goal Programming for De- cision Analysis. Auberback Publish- ers, Philadelphia, PA. A.J.A.S,Vo1.17,No.1 188
- 21. Lee, S. andSchniederjans, M. 1983. Mu- ticriteria Assignment Problem: A goal programming approach. Inter- faces,13: 75-81. Schniederjans, M., Kwak, N. and Hel- mer,C. 1982. Anapplication of goal programming to resolve a site loca- tion problem. Interfaces,12: 65-72. Harwood, G. and Lawless, R. 1975. Op- timizing organizational goals in as- signing faculty teaching schedules. DecisionScience,6: 513-524. Schniederjans, M. and Kim, G. 1987. A goal Programming Model to opti- mize departmental preference in course assignments. Computers and OperationsResearch,14 (2):87-96. MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 189
- 22. G _ l _ M [ F l a P L = Q l G ? C J O G q A A 9 = g d P a l Q J _ A c H _ l W t _ ? A M Z c [ C f ] 9 A J c 8 ? G _ A O Q c U _ _ l a G O G _ O Q G T c ? a C a r 9 B G _ A O Q c U l J l O t l 9 c J T H Q G 8 O r Q = 9 H G _ J T c H J l c O C J l O G _ r 9 J Q j G 9 l g ? G _ t a c B c g O A a a c Q F l a P L c T A a c h C H c F A H f F G O a _ ? A A Z q = 9 _ t p 9 A I a G _ p g 9 _ c ? F f ] 9 A J c 8 ? G _ A O Q c U _ _ l a G O G _ O Q G T c ? a C a r 9 B G _ A O Q c U , a G J O G k l H C J m G _ A J O c 9 B G _ A d A a G G l g d m G _ G 9 l g 9 B p d G l c h C F J 9 A G _ g 9 _ m . a r O A m A Z l c m a = F 9 A f O I C F d l ? p d J P G G _ l G 9 c _ _ J Z a c f _ b G _ G O a c G _ l D 9 _ d _ P _ u , a _ t H l g d m J P g G F F d l ? t 9 F B A g 9 F d l H = g ^ G a G F G _ r Z a Q a G _ g G R . p d J P G G _ = J E A m G T A M O G m a Q c r ? G _ = Q l G ? G _ K O p c ? G _ D F 9 8 c ? ( Z p Q - 1 ) = J c E A m A M Z c [ C f ] 9 A J c 8 ? G _ A O Q c U _ _ l a G O G _ O Q G T c ? p d G _ l Q J _ ? G F a _ b , D m A M Z c [ t c f ] a J c 8 ? A O Q c U l h G _ l 9 O I G _ l M Z Z ? _ _ _ p A Q G B G _ R l F c ? G _ l M Z Z ? _ t c c a m O Q G T d p d G _ l Q J _ ? G _ D 9 F c ? . M ; c J 9 A c H G _ l Q J _ A c H c g l c G _ F l a P L f _ b A g d c m C p ] _ c ? C f ] 9 A J c 8 ? G _ A O Q c U _ _ l a G O G _ O Q G T c ? p d G _ l Q J _ ? G F a _ b , D m A g d c m C p ] _ c ? C f ] 9 A J c 8 ? G _ A O Q c U _ I a r 9 B G _ R l F c ? _ A O Q c U t c l 9 O I A m A M Z c Z K 9 _ p d G _ l Q J _ ? G F a _ b . A r a m G _ a Q c r ? G _ l T A M O l ? p d J P G G _ = J E = A J r c s f O I C J O G q J T C a _ a c 9 B l J O O I , = J c E c A m A J r c s t c J O q J T C J l c A = 9 _ F T = ? E _ b G _ r a G f O a G _ r a G F c H G _ l a _ a = ? a G _ M 9 Z ? = 9 _ G 9 l g ? a G _ t _ c ? a G _ r T m a G _ A M Z [ , a A m G _ r c 9 m = T c F 9 Q c a J 9 B l M A _ p ? : M A = 9 Q Z J ? G _ F l a P L . a _ r O C D = A B G _ l Q J _ ? G F a _ b l H G _ F l a P L r O Q I f _ b A J r c s l g d m G F J O G q t 9 l _ ? , a A J r c s E G l 9 _ d C p ] _ c ? C f ] 9 A J c 8 ? G _ A O Q c U E _ b G _ l a G O G _ A d c Q i = a H p d A O Q c T K 9 = F T = ? 85,2 % a p d G _ l Q J _ ? G _ D 9 F c ? G T A a 9 Y G _ F l a P L C H c J r s C p ] _ c ? C f ] 9 A J c 8 ? G _ A O Q c U E _ b G F a r 9 B G _ R l F c ? _ A O Q c U G _ l a G O G _ l M Z Z ? _ K m = F T = ? E G l 9 _ c ? A Z c E _ b 88,8 % . Mohamad K. Hasanreceived a degree of Bachelor of Science in Mathematical Statistics from Alexandria University, Egypt, in 1978. He was awarded a degree of Master of Science in Mathe- matics from Texas AM University, Texas, USA, in 1988, and a degree of Doctor of Philosophy in Transportation Systems from Texas AM University, Texas USA, in 1991. Currently, he works as Associate Professor at Department of Quantitative Methods and Information Systems, College of Business Administration, A.J.A.S,Vo1.17,No.1 190
- 23. Kuwait University, Kuwait.His research interests include: Trans- portation Systems Analysis, Transportation Planning, Transporta- tion Network Modeling, Freight Transpiration Modeling, Travel Demand Modeling, Logistics, Supply Chain management, Net- work Optimization, Production and Operations Management, Scheduling, Simulation, Queuing and Mathematical Programming. NumericalAnalysis,MathematicalStatistics,StatisticalAnalysis. Raed Q. Al-Husain received his Bachelor of Science in Electrical Engineering and his Master of Science in Operations Research Engineering, from the University of Southern California, Los Angeles, in 1999 and 2000 respectively. He received his Doctor- al of Philosophy degree in Business Operations Management from the University of Houston, Texas, in 2005. Currently, he works as Assistant Professor in the Department of Quantitative Methods and Information Systems, College of Business Admin- istration, Kuwait University, Kuwait. His research interests include: Modeling Logistics and Supply Chain Networks, speci- ®cally in the petroleum industry, Production Planning and Scheduling Models, Health Care Operations Management, and Simulation Models. Hameed A. Al - Qaheri is Associate Professor of Information Systems and Chairperson, of the Department of Quantitative Methods and Information Systems, College of Business Admin- istration, Kuwait University. He has a PhD in Information System from the University of Pittsburgh. His research interests focus on Intelligent DSS, Web Intelligent, Intelligent Arabic Text Processing and Language Engineering Including Arabic Information Retrieval, Information Extraction, Text Categor- ization and Text Understanding and QA Systems and Intelli- gent Social Network. MohamadHasan, RaedAl-Husain, HameedAl-Qaheri 191
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