《系统工程》课程教学资源（英文文献）Optimization of a Potential of Logistics System

2011 21st International Conference on Systems EngineeringOptimization of a potential of logistics systemMariusz WasiakDepartment of Logistics and Transportation Systems,FacultyofTransportWarsawUniversity of TechnologyKoszykowa75,00-662Warsaw,Polande-mail:mwa@it.pw.edu.plAbstract-This paper defines a potential of logistics systemlogisticswhichenablestheaforementionedsystem,with regard to appropriate criteria and provides originaloptimization.model of logistics system allowing optimization of its potential.By limiting the scope of logistics systems resources toModel maps logistics task, system resources, system structurethe technical and human resources, the logistics systemand characteristics of all elements. The results of staticpotential is determined by:optimization of potential of logistics system performed withnumber of various types of means of work requiredgiven approach are presented.to completethe cargo flowtransformation intheareas of logistics system (matrix Xws)andonKeywords-logistics system; system potential; optimization ofconnections between them (array XMs),apotentialnumber of employees of different work categoriesrequiredonsubsequentworkshiftstocompletethe1THEPROBLEMOFOPTIMIZATIONOFLOGISTICStransformation of cargo flows in the areas ofSYSTEM POTENTIALlogistics system(matrixXwL)and on connectionsLogistics systems deal with processes transforming cargobetween them (arrayXML),and information flows.These processes, according to thelabor consumption of transformationsaccording toscope of changes induced in cargo and informationflows canspace, time and shape for means of work (matrixbe divided into time,space and shape transformationsYRPS, YRTS and YRMS), employees realizing trans-(Fijalkowski,2003,p.168).formations without usage of any technical meansImplementation of processes transforming cargo and(matrix YRPL, YRTL and YRML), and employeesrealizing transformations with usage of technicalinformation flowsrequires logistics systemtodispose someresources.These resources are called logistics resources andmeans (matrix YRPO,YRTO and YRMO).enable realizing transformations of material and informationII.LOGISTICS SYSTEM MODELflows according to time, spaceandphysical form.Thus, theallocation of adequate logistics resources determines theA.Elementsofthemodelpossibility of performing thegiven tasks by logistics systemNo less important is right connection of these resources andRealization of cargo and information flows resultingensuring their proper usage. Thus, it is necessary to considerfrom logistics task ZL bylogistics system, requires systemresources due to the potential achieved through them.to dispose appropriate infrastructure Gs described with ade-Logistics system potential is defined as all its resourcesquate characteristics FS (Wasiak,2005, s.526-528).Chara-with relations between them and all work organizationalcteristics of structure elements of logistics system are theprinciples allowing transformations ofcargo and informationfunctions of disposed resources zo.Moreover,in eachflows.Potential of logistics system is its characteristiclogistics system it is possible to specify someprinciples ofdescribing thepossibility of operating.logistics task realization ZR. These principles define usedSo understood potential of logistics system is establishedtechnologies, sequences of operations, engaged technicalwithin designing process. Analysis of methods supportingmeans andwork forces aswell as strategic and operationalogistics systems design (eg.Brzezinski,2007; Fijalkowski,goals.Formal model embraces this aspects as constrains and1987,2003;Heragu,2008;Jacyna,2009;Korzen,1998;criteria of optimization logistics system potentialKusiak, 1990; Lambert, Stock, Eliram, 1998; Piasecki, 2000;Taking into account above, the model of logistics systemPowell,2008;Turban,Meredith,1991;VazacopoulosMSL was defined as follows (Wasiak, 2011):Verma, 2005; Wasiak, 2005, 2007, 2009) reveals that thismethodsarepartialandoverlysimplistic(oftencomputatioMSL =(ZL,ZO,GS, FS, ZR)(1)nally inefficient), and usually allows for finding only rationalsolutions.Thus, optimizing the potential of logistics systemsThe logistics task for a system can be performed inwith existing approaches is not possible.It is an essentialprerequisite to undertake research on developing a model ofdifferent ways.Starting with the selection of technicalIEEE446978-0-7695-4495-3/11 $26.00 2011 IEEE@computersocietyDOI 10.1109/ICSEng.2011.88

Optimization of a potential of logistics system Mariusz Wasiak Department of Logistics and Transportation Systems, Faculty of Transport Warsaw University of Technology Koszykowa 75, 00-662 Warsaw, Poland e-mail: mwa@it.pw.edu.pl Abstract — This paper defines a potential of logistics system with regard to appropriate criteria and provides original model of logistics system allowing optimization of its potential. Model maps logistics task, system resources, system structure and characteristics of all elements. The results of static optimization of potential of logistics system performed with given approach are presented. Keywords – logistics system; system potential; optimization of a potential I. THE PROBLEM OF OPTIMIZATION OF LOGISTICS SYSTEM POTENTIAL Logistics systems deal with processes transforming cargo and information flows. These processes, according to the scope of changes induced in cargo and information flows can be divided into time, space and shape transformations (Fijakowski, 2003, p. 168). Implementation of processes transforming cargo and information flows requires logistics system to dispose some resources. These resources are called logistics resources and enable realizing transformations of material and information flows according to time, space and physical form. Thus, the allocation of adequate logistics resources determines the possibility of performing the given tasks by logistics system. No less important is right connection of these resources and ensuring their proper usage. Thus, it is necessary to consider resources due to the potential achieved through them. Logistics system potential is defined as all its resources with relations between them and all work organizational principles allowing transformations of cargo and information flows. Potential of logistics system is its characteristic describing the possibility of operating. So understood potential of logistics system is established within designing process. Analysis of methods supporting logistics systems design (eg. Brzeziski, 2007; Fijakowski, 1987, 2003; Heragu, 2008; Jacyna, 2009; Korze, 1998; Kusiak, 1990; Lambert, Stock, Ellram, 1998; Piasecki, 2000; Powell, 2008; Turban, Meredith, 1991; Vazacopoulos, Verma, 2005; Wasiak, 2005, 2007, 2009) reveals that this methods are partial and overly simplistic (often computatio￾nally inefficient), and usually allows for finding only rational solutions. Thus, optimizing the potential of logistics systems with existing approaches is not possible. It is an essential prerequisite to undertake research on developing a model of logistics system, which enables the aforementioned optimization. By limiting the scope of logistics systems resources to the technical and human resources, the logistics system potential is determined by: • number of various types of means of work required to complete the cargo flow transformation in the areas of logistics system (matrix XWS) and on connections between them (array XMS), • number of employees of different work categories required on subsequent work shifts to complete the transformation of cargo flows in the areas of logistics system (matrix XWL) and on connections between them (array XML), • labor consumption of transformations according to space, time and shape for means of work (matrix YRPS, YRTS and YRMS), employees realizing trans￾formations without usage of any technical means (matrix YRPL, YRTL and YRML), and employees realizing transformations with usage of technical means (matrix YRPO, YRTO and YRMO). II. LOGISTICS SYSTEM MODEL A. Elements of the model Realization of cargo and information flows resulting from logistics task ZL by logistics system, requires system to dispose appropriate infrastructure GS described with ade￾quate characteristics FS (Wasiak, 2005, s. 526-528). Chara￾cteristics of structure elements of logistics system are the functions of disposed resources ZO . Moreover, in each logistics system it is possible to specify some principles of logistics task realization ZR . These principles define used technologies, sequences of operations, engaged technical means and work forces as well as strategic and operational goals. Formal model embraces this aspects as constrains and criteria of optimization logistics system potential. Taking into account above, the model of logistics system MSL was defined as follows (Wasiak, 2011): MSL= ZL, ZO,GS, FS, ZR (1) The logistics task for a system can be performed in different ways. Starting with the selection of technical 2011 21st International Conference on Systems Engineering 978-0-7695-4495-3/11 $26.00 © 2011 IEEE DOI 10.1109/ICSEng.2011.88 446

means, and ending with theprinciples of work organizationwithout depreciation charges Ks.,variable unit-cost cs, ofadoptedinthesystem.Theaimof theoptimizationof thetime consumed,investment expenditures Ns.,expected lifelogistics system potential is to determine the set of availabletime Tss,times of changeovers tps,technical readinessresources and possible principles of work organization thatAs.,work-timeutilization Hs.,a setRs,oftypes ofcargowill provide cost-effective logistics task realization at theappropriatelevel of service.streams handled by this type of technical mean, and setPPs,ofcargo streamtransformations.AdditionallyforeachB.Logistics tasktype of mean of work (se S) and all cargo streams handledThetypes of cargo streams moved in logistics system arebythis mean(reRs,)the setNo,of numbers of necessaryrepresented as a set R = (r:r =l,...R).Handling of theseemployees,and set(no,eNo,)Lo"of availablecate-streams means transformation according to time, space andshape.The set of possible cargo stream transformations isgories of human resources for no, -th workplace are defined.given P=(p: p=1,..,P). Set P can be decomposed toSimilar characteristics are defined for all means of workthreesub-sets:Pp(shapetransformations),PT(time（se)and possiblecargo streams transformationstransformations),and PM (space transformation).Each of(pe PPs,). They are denoted as NpP and Lpp..Chara-shape transformations is characterized by types RpP ands.npcteristics FzM of each work-shift（zme ZM）embracesvolumes Opp. of cargo streams on entrance and typesstart time tram and end time tz zmnRkP and volumes Qk Pr of cargo streams appearing on exitas a result of this transformation.D.System structureThe size oftasks that must be handled by logistics systemLogistics system embraces set of elements connectedbyresults fromboth:thenumber of different types of loadstransportation dependence.These objects are places,wheredescribed in matrix QZ and from the range of their trans-cargo streams are processed, e.g. produced, stored, sorted,formation (the P set).Therefore, the logistics task ZL forsold or consumed (Ghiani et all, 2004, s. 1). Thus, thelogistics systemisdefined asfollows:structure of a logistics system results from the location oflogistics objects being elements of this system and fromZL =(QZ, P)(2)functional areas separated within this objects. The logisticsfacilities,andfunctionalareasseparatedin themarelinkedwith adequate relations.Functional areas of logistics systemsWhere QZ-qz''e N : ze Z,re Rz,teT is a matrixrealizing cargo stream transformations according to theof volume of cargo entries to the system with elementsshape and time are organized to dedicated point-wise areas,qz interpreted as the volume of r-th type cargo entering towhile functional areas realizing space transformation arethe system in t-th moment from z-th sourceconnectionsbetweenthemLogistics system structure Gs was formally defined asC.Systemresourcesfollows:Assuming that technicalresources to be used in logisticssystemS-{s:s=l,.,s], types of human resourcesGS =(AS, RS)(4)L-1:/=1,.,), principles for work organization (e.g.number of work-shifts)ZM=zm:zm=1...ZM,andwhere:sets of characteristics of this resources FL, Fs,Fzm areAS - set of logistics system elements,known,the vector zo was defined as follows:RS - set of relations between the logistics system ele-mentsSet As contains elements representing:impact of theZO=(L,FL,S,Fs,ZM,FzM)(3)environment to the system, namely sources of cargoflowsZ={z:z=],.,z] and areas W-{w,w:w,w=],..wAmongst characteristics Fr of each human resourcescategory (le L) model includes: fixed annual cost of workinwhichcargo streamsaretransformed accordingto timeand shape.Moreover,the setof logistics system's areaswasKLy, variable unit-cost cL, of time consumed, recruitmentdecomposed to the sets WP of areas realizing shape transfor-and preliminary research costsNLy,expected lengthof em-mations and WTof areas realizing timetransformations:ployment TL,, operational readiness ALy,work-time utili-zation HL,.Within the set L of human resources categories.(5)AS=ZUW=ZUWPUWTthe sub-set LF of manual workers was distinguished andconnected to the set RL, of types of cargo streams whichThe set Rs was decomposed to the set of relationsmay be handled by worker of I-th category.betweencargostream sourcesand functional areasAmongst characteristics Fs of each mean of workRSzw=(z,w)e ZxW) , and set of relations between(se S) model includes: fixed annual cost of ownership447

means, and ending with the principles of work organization adopted in the system. The aim of the optimization of the logistics system potential is to determine the set of available resources and possible principles of work organization that will provide cost-effective logistics task realization at the appropriate level of service. B. Logistics task The types of cargo streams moved in logistics system are represented as a set R = {r : r = 1,., R} . Handling of these streams means transformation according to time, space and shape. The set of possible cargo stream transformations is given P = { } p : p =1,., P . Set P can be decomposed to three sub-sets: PP (shape transformations), PT (time transformations), and PM (space transformation). Each of shape transformations is characterized by types p Rp and volumes p r Qp , of cargo streams on entrance and types p Rk and volumes p r Qk , of cargo streams appearing on exit as a result of this transformation. The size of tasks that must be handled by logistics system results from both: the number of different types of loads described in matrix QZ and from the range of their trans￾formation (the P set). Therefore, the logistics task ZL for logistics system is defined as follows: ZL = QZ, P (2) Where = [q ∈ z ∈ Z r ∈ RZ t ∈T] z r t z Z , , , QZ N : is a matrix of volume of cargo entries to the system with elements r t z qZ , interpreted as the volume of r-th type cargo entering to the system in t-th moment from z-th source. C. System resources Assuming that technical resources to be used in logistics system S = { } s : s = 1,., S , types of human resources L= {l :l = 1,., L}, principles for work organization (e.g. number of work-shifts) ZM = {zm : zm = 1,., ZM } , and sets of characteristics of this resources FL , FS , FZM are known, the vector ZO was defined as follows: ZO = L,FL, S,FS, ZM,FZM (3) Amongst characteristics FL of each human resources category (l ∈ L ) model includes: fixed annual cost of work l KL , variable unit-cost l cL of time consumed, recruitment and preliminary research costs l NL , expected length of em￾ployment l TL , operational readiness l AL , work-time utili￾zation l HL . Within the set L of human resources categories, the sub-set LF of manual workers was distinguished and connected to the set l RL of types of cargo streams which may be handled by worker of l-th category. Amongst characteristics FS of each mean of work ( s ∈ S ) model includes: fixed annual cost of ownership without depreciation charges s KS , variable unit-cost s cS of time consumed, investment expenditures s NS , expected life￾time s TS , times of changeovers s tp , technical readiness s AS , work-time utilization s HS , a set s RS of types of cargo streams handled by this type of technical mean, and set s PPS of cargo stream transformations. Additionally for each type of mean of work (s ∈ S ) and all cargo streams handled by this mean ( s r ∈ RS ) the set r Nos of numbers of necessary employees, and set ( r s r s no ∈ No ) r s nor s , Lo of available cate￾gories of human resources for r s no -th workplace are defined. Similar characteristics are defined for all means of work ( s ∈ S ) and possible cargo streams transformations ( s p ∈ PPS ). They are denoted as p Nps and p s np p s , Lp . Chara￾cteristics FZM of each work-shift ( zm ∈ ZM ) embraces start time trzm and end time tzzm . D. System structure Logistics system embraces set of elements connected by transportation dependence. These objects are places, where cargo streams are processed, e.g. produced, stored, sorted, sold or consumed (Ghiani et all, 2004, s. 1). Thus, the structure of a logistics system results from the location of logistics objects being elements of this system and from functional areas separated within this objects. The logistics facilities, and functional areas separated in them are linked with adequate relations. Functional areas of logistics systems realizing cargo stream transformations according to the shape and time are organized to dedicated point-wise areas, while functional areas realizing space transformation are connections between them. Logistics system structure GS was formally defined as follows: GS = AS, RS (4) where: AS – set of logistics system elements, RS – set of relations between the logistics system ele￾ments. Set AS contains elements representing: impact of the environment to the system, namely sources of cargo flows Z = {z : z =1, ., Z} and areas W = {w,w': w,w'=1,.,W} in which cargo streams are transformed according to time and shape. Moreover, the set of logistics system’s areas was decomposed to the sets WP of areas realizing shape transfor￾mations and WT of areas realizing time transformations: AS = Z ∪W = Z ∪WP ∪WT (5) The set RS was decomposed to the set of relations between cargo stream sources and functional areas RSZW = {(z,w)∈ Z ×W} , and set of relations between 447

thetype of performed transformation ptw,thenumber ofRSww=(w.w)eWxW:w?wfunctionalareascargo streamtransformations(reRs,QRww)implementedMoreover, the set RS was divided to the set RM containingatthesametimewithusageofavailablemeansofworkrelationsbetweensystemselements,namelytransformationsaccording to space and set RFof formal links between(se Sww)Nrsw.sand their realization times trsw.s,and thesystem elements.For afixed structure of relationsbetweennumberofcargo streamstransformations(reRL,Rw)system elements, for each element the sets Il of predeces-implemented at the sametimeby manual workers ofeach ca-sor and I..consequents areknown.tegory(le Fww)Nrw./with realization times trLw/ Elements of the set of the links between logistics systemE.Characteristics of elementsofsystem structureareas representing cargo streams shape transformationsThe set of characteristics of elements of logistics system((w,w)eRM)are described by characteristics FrM em-structureisasum of set ofcharacteristicsofcargo streamsbracing: the set of handled cargo streams types RRw.w,sourcesFz,thefunctional areas in which the transforma-probabilities of directing to them different cargo streamstions accordingto shapeFwp,timeFw and space FrM areperformedandsetofcharacteristicsofformallinksbetween(reRRw.w）Pwwthe capacities of awaiting placestheareasFRF:expressed inanumberof unitsof differenttypes(re RRw.w)Pmw.w,the set of availablemeans ofworkFS-FZUFWPUFWTUFRMUFRF(6)Smw.w,the set of human resources categories Lw.w,theThe characteristics Fz of each cargo stream sourceset of manual workers Fmw.w, the set of available work-(zeZ)include types of generated cargos Rz,and theshifs ZMw.w, the type of performed transformation pmw.wvolume of cargo stream entering to the system in followingThe setFrmembraces the numberofcargostreammoments qz'transformations(re Rs,Rrw.w)implemented at the sameCharacteristics Fwp of elements of the set of the logisticstime with usage of available means of work (se Smw.w)system areas engaged in shape transformations of cargoNws,andtheirrealizationtmswwandthenumstream(weWP)consistof:set of types of handled cargostreams Rww,the capacities of awaiting places expressed inber of cargo streams transformations (re RL,RRw.w)im-plemented at the same time by manual workers ofeach cate-a number of units of different types (re Rww) Pw, the setgory (leFMw.w)NMw.w./with realization times tMw.w. -of availablemeansof workSww,thesetof categoriesofThe elements of the set of formal links between logisticshuman resources Lww,the set ofmanual workers Fww,thesvstemelements((ww)eRF)aredescribedwithcharacteset of available work-shifts Zwwthe set of transformationristics Fr embracing:the set oftypes of cargo streamspossible PPwwand sets Pwsw.and PwLw. of transforma-RRw.w moved on them and transition probabilities for thistion possible to provide with this means of work(se Sww)streams(reRRw.w)pw.wand workers of each categories (le Fww).IILSTATICOPTIMIZATIONFORRAILWAY-ROADLOADINGMoreover set Fwp gives probabilities pp of shapeTERMINALtransformation(pePPww)oncargostreams（reRpP)With regard to formal notation of a logistics systemThe number of transformations（pePwsw.s)implementedmodel,thetask of static optimization of logistics systemat the same time with usage of available means of workpotential was developed.Above constrains were consider:(seSww)Npsw.s,appropriaterealizationtimestpsw.s,theconstrainforcargoflowsbetweensystemelements,number of transformations(pePwLw))implemented at theconstrainfortransformations of cargo streams accor-ding to shape, time and place,same time by manual workers of each category(leFw.)constrain for maintenance of technical means reali-NpLw, and realization times tplwj for this operations arezing transformations of cargo streams,given.constrain for the number of means of work and theThe set of logistics system areas in which transforma-number of employees in functional areas of the sys-tions of cargo streams accordingtotime(weWT)areper-tem,formed is described by characteristics FwT embracing:theconstrain for not exceeding acceptable level of in-set of handled cargo streams types Rww,the capacities ofvestmentexpendituresonsystem,awaitingplaces expressed inanumber of units of differentconstrain for integer values of decision variables fortypes(reRww)Pw,the setofavailablemeansofworknumberofmeansofworkandnumberofemployeesaswell as workburdenformeans of workand em-Sww,the setofhuman resources categories Lww,the setofployees.manual workers Fww,thesetofavailablework-shiffs Zww448

functional areas RS W W WW = ∈× ≠ {( ', ) ' ww w w : }. Moreover, the set RS was divided to the set RM containing relations between systems elements, namely transformations according to space and set RF of formal links between system elements. For a fixed structure of relations between system elements, for each element the sets −1 w of predeces￾sor and w consequents are known. E. Characteristics of elements of system structure The set of characteristics of elements of logistics system structure is a sum of set of characteristics of cargo streams sources FZ , the functional areas in which the transforma￾tions according to shape FWP , time FWT and space FRM are performed and set of characteristics of formal links between the areas FRF : FS = FZ ∪ FWP ∪ FWT ∪ FRM ∪ FRF (6) The characteristics FZ of each cargo stream source ( z ∈ Z ) include types of generated cargos z RZ and the volume of cargo stream entering to the system in following moments r t z qZ , . Characteristics FWP of elements of the set of the logistics system areas engaged in shape transformations of cargo stream ( w∈WP ) consist of: set of types of handled cargo streams RWw , the capacities of awaiting places expressed in a number of units of different types ( w r ∈ RW ) r PWw , the set of available means of work SWw , the set of categories of human resources LWw , the set of manual workers FWw , the set of available work-shifts ZWw , the set of transformation possible PPWw and sets PWSw,s and PWLw,l of transforma￾tion possible to provide with this means of work ( w s ∈ SW ) and workers of each categories ( w l ∈ FW ). Moreover set FWP gives probabilities p r wp , of shape transformation ( w p ∈ PPW ) on cargo streams ( p r ∈ Rp ). The number of transformations ( w s p ∈ PWS , ) implemented at the same time with usage of available means of work ( w s ∈ SW ) p w s NPS , , appropriate realization times p w s tPS , , the number of transformations ( w l p ∈ PWL , ) implemented at the same time by manual workers of each category ( w l ∈ FW ) p w l NPL , and realization times p w l tPL , for this operations are given. The set of logistics system areas in which transforma￾tions of cargo streams according to time ( w∈WT ) are per￾formed is described by characteristics FWT embracing: the set of handled cargo streams types RWw , the capacities of awaiting places expressed in a number of units of different types ( w r ∈ RW ) r PWw , the set of available means of work SWw , the set of human resources categories LWw , the set of manual workers FWw , the set of available work-shifts ZWw , the type of performed transformation w pt , the number of cargo stream transformations ( s w r ∈ RS ∩ RW ) implemented at the same time with usage of available means of work ( w s ∈ SW ) r w s NTS , and their realization times r w s tTS , , and the number of cargo streams transformations ( l w r ∈ RL ∩ RW ) implemented at the same time by manual workers of each ca￾tegory ( w l ∈ FW ) r w l NTL , with realization times r w l tTL , . Elements of the set of the links between logistics system areas representing cargo streams shape transformations ( (w',w)∈ RM ) are described by characteristics FRM em￾bracing: the set of handled cargo streams types w',w RR , probabilities of directing to them different cargo streams ( w w r ', ∈ RR ) r w w p ', , the capacities of awaiting places expressed in a number of units of different types ( w w r ', ∈ RR ) r PM w',w , the set of available means of work SM w',w , the set of human resources categories LM w',w , the set of manual workers FM w',w , the set of available work￾shifts ZM w',w , the type of performed transformation w w pm ', . The set FRM embraces the number of cargo stream transformations ( s w w r ', ∈ RS ∩ RR ) implemented at the same time with usage of available means of work ( w w s ∈ SM ', ) r NMSw',w,s , and their realization times r MSw w s t ', , , and the num￾ber of cargo streams transformations ( l w w r ', ∈ RL ∩ RR ) im￾plemented at the same time by manual workers of each cate￾gory ( w w l ∈ FM ', ) r NMLw',w,l with realization times r MLw w l t ', , . The elements of the set of formal links between logistics system elements ((w',w)∈ RF ) are described with characte￾ristics FRF embracing: the set of types of cargo streams w',w RR moved on them and transition probabilities for this streams ( w w r ', ∈ RR ) r w w p ', . III. STATIC OPTIMIZATION FOR RAILWAY-ROAD LOADING TERMINAL With regard to formal notation of a logistics system model, the task of static optimization of logistics system potential was developed. Above constrains were consider: • constrain for cargo flows between system elements, • constrain for transformations of cargo streams accor￾ding to shape, time and place, • constrain for maintenance of technical means reali￾zing transformations of cargo streams, • constrain for the number of means of work and the number of employees in functional areas of the sys￾tem, • constrain for not exceeding acceptable level of in￾vestment expenditures on system, • constrain for integer values of decision variables for number of means of work and number of employees as well as work burden for means of work and em￾ployees. 448

The discounted sum of operational costs and capitalComputations performed with OPoSLog software revealexpenditure revisedbyincomesfrom theresaleof means ofthat for considered terminal because of economic reason it isworkafterthelifetimeisacriterionof staticoptimizationofbettertodoloading operations with usage of gantry craneslogistics systempotential.that other types of equipment.The optimal potential for con-Formulated taskof static optimization of logistics systemsidered terminal is presented in Table 1.potential was used to optimize potential of railway-roadtransshipment terminal (Fig. 1)'.Loaded and empty highTABLELTHE OPTIMALPOTENTIALFOR CONSIDERED TERMINALcapacity trucks are entering to the considered terminal fromMaterial streamNumber and categorysource Z1. The source Z2 is origin for loaded and emptyNumber and typetransformationof employeesfreight trains.Terminal realizes loading operations (loading,ofmeans of workCodeDescriptionShift#！Shift#2unloadingdirect transshipment)and bulk storage of looseVehicle control on3 control points onT14 workers3 workersmaterials insensitive for weather conditions (front A)andentranceentranceI control point onpacked materials insensitive (front B) and sensitive forT2vehicle control on exit1 workerentranceweatherconditions(frontC).TheMito M7andM14toHardened not-M20 transformations accordingto space areperformer byBulk storage of looseT3covered yard with-materialsself-propelled means of external transport,and transforma-net area 16635m2tions M9,M10, M12 and M13 are part of shape transforma-Storage of insensitiveLack of appropria-T4packed materialsleneedstions No. P3 and P4 (storage is realized within a range ofHardened coveredtransshipment equipment).Storage of sensitiveT5yard with net areapacked materials3 621 m23controlpointsonT6Vehicle control on exit4workers3workersexit[D1controlpointonT7Train controlonexitI workerexitDividing trains intoP1I arrival truck2 workersworker合groupsofrail cars10 gantrycranes1 operators1operatorsLoading operations onP2Aloosematerialswith crane tracks4workers3workersLoading operations onpacked materials in-1 gantry crane with I operator,P3NM7sensitivefor weathercranetracks2workersconditionsLoading operations on雪packed materials sen-4 gantry cranes4 operators,4 operators,M9P4sitive for weather con-with crane tracks4 workers4workersditions?P5Forming trainsi departure trackworkerIworkerMM1Moving loose mate-M8,rials from/to the stora-9 wheel loaders10 workers9 workersM1ige place to the area ofMI9antrycranesrangOoTransformations according to time (T):IV.CONCLUSIONSTI - vehicle control on entrance,Literature review presents problems of designing of dif-T2 -preliminary vehicle control on entrance,ferent classes of logistics systems.The methods supportingT3- bulk storage of loose materials,T4- storage of insensitive packed materials,selection of technical equipment appropriate for performedT5-storage of sensitive packed materials,tasks for the logistics systems are known as well as methodsT6-vehicle control on exit,for assigning workers to the workplaces. However, there isT7-train control on exit.no complexanalysis of problemsof optimizationof logisticsTransformations according to shape (P):systems potential. In consequence there is no approaches todetermining logistics systems potential allowing its optimalP1-dividing trains into groups of rail cars,P2 -loading operations on loose materials,forming.The model of logistics system presented in the pa-P3-loading operations on packed materials insensitivefor weatherper allows formulation of decision problems of optimizingconditions,potential of logistics systems of different classes (for diffe-P4-loading operations on packed materials sensitive for weatherrent assumptions within the area of technology and evalua-Figure 1.The structure of considered transshipment terminaltioncriteria).Itcanbeabaseforamodelofstaticoptimi-zationoflogistics systemspotentialandamodel ofdynamicoptimization.Detailed example data are discussed in M. Wasiak (2010, s. 82-89)449

The discounted sum of operational costs and capital expenditure revised by incomes from the resale of means of work after the lifetime is a criterion of static optimization of logistics system potential. Formulated task of static optimization of logistics system potential was used to optimize potential of railway-road transshipment terminal (Fig. 1)1 . Loaded and empty high capacity trucks are entering to the considered terminal from source Z1. The source Z2 is origin for loaded and empty freight trains. Terminal realizes loading operations (loading, unloading direct transshipment) and bulk storage of loose materials insensitive for weather conditions (front A) and packed materials insensitive (front B) and sensitive for weather conditions (front C). The M1 to M7 and M14 to M20 transformations according to space are performer by self-propelled means of external transport, and transforma￾tions M9, M10, M12 and M13 are part of shape transforma￾tions No. P3 and P4 (storage is realized within a range of transshipment equipment). Figure 1. The structure of considered transshipment terminal 1 Detailed example data are discussed in M. Wasiak (2010, s. 82-89). Computations performed with OPoSLog software reveal that for considered terminal because of economic reason it is better to do loading operations with usage of gantry cranes that other types of equipment. The optimal potential for con￾sidered terminal is presented in Table 1. TABLE I. THE OPTIMAL POTENTIAL FOR CONSIDERED TERMINAL Material stream transformation Number and type of means of work Number and category of employees Code Description Shift # 1 Shift # 2 T1 Vehicle control on entrance 3 control points on entrance 4 workers 3 workers T2 Vehicle control on exit 1 control point on entrance 1 worker – T3 Bulk storage of loose materials Hardened not￾covered yard with net area 16 635 m2 – – T4 Storage of insensitive packed materials Lack of appropria￾te needs – – T5 Storage of sensitive packed materials Hardened covered yard with net area 3 621 m2 – – T6 Vehicle control on exit 3 control points on exit 4 workers 3 workers T7 Train control on exit 1 control point on exit 1 worker – P1 Dividing trains into groups of rail cars 1 arrival truck 2 workers 1 worker P2 Loading operations on loose materials 10 gantry cranes with crane tracks 11 operators, 4 workers 11 operators, 3 workers P3 Loading operations on packed materials in￾sensitive for weather conditions 1 gantry crane with crane tracks 1 operator, 2 workers – P4 Loading operations on packed materials sen￾sitive for weather con￾ditions 4 gantry cranes with crane tracks 4 operators, 4 workers 4 operators, 4 workers P5 Forming trains 1 departure track 1 worker 1 worker M8, M11 Moving loose mate￾rials from/to the stora￾ge place to the area of gantry cranes range 9 wheel loaders 10 workers 9 workers IV. CONCLUSIONS Literature review presents problems of designing of dif￾ferent classes of logistics systems. The methods supporting selection of technical equipment appropriate for performed tasks for the logistics systems are known as well as methods for assigning workers to the workplaces. However, there is no complex analysis of problems of optimization of logistics systems potential. In consequence there is no approaches to determining logistics systems potential allowing its optimal forming. The model of logistics system presented in the pa￾per allows formulation of decision problems of optimizing potential of logistics systems of different classes (for diffe￾rent assumptions within the area of technology and evalua￾tion criteria). It can be a base for a model of static optimi￾zation of logistics systems potential and a model of dynamic optimization. T1 Z1 T6 Front A Front B Front C M9 M4 M12 M16 M5 M17 T4 P3 M10 M6 M13 M18 M7 M19 T5 P4 P1 P5 P2 M8 M2 M11 M14 M3 M15 T3 M1 T2 Z2 M20 T7 Transformations according to time (T): T1 – vehicle control on entrance, T2 – preliminary vehicle control on entrance, T3 – bulk storage of loose materials, T4 – storage of insensitive packed materials, T5 – storage of sensitive packed materials, T6 – vehicle control on exit, T7 – train control on exit. Transformations according to shape (P): P1 – dividing trains into groups of rail cars, P2 – loading operations on loose materials, P3 – loading operations on packed materials insensitive for weather conditions, P4 – loading operations on packed materials sensitive for weather 449

Z. Korzen, Logistyzne systemy transportu bliskiego imagazynowaAccording to described model, the assumptions for static[6]nia, Tom I Infrastrukura, Technika, infomacja", Instytut Logistykioptimization of logistics system potential are presented.TheiMagazynowania,Poznan,1998optimization task constrains and evaluation criteria are given.A, Kusiak"Intligent Manufacturing Systems, Prentice Hall, En-71Withregard to presented approach to static optimization, theglewood Cliffs,New Jersey,1990.optimal potential for selected railway-road transshipmentD. M. Lambert, J. R. Stock, L. M. Ellram, "Fundamentals of logistics[8]terminal was found.management", McGraw-Hill Irwin, Boston, 1998.The verification confirms regularity of proposed appro-S. Piasecki, .Sieciowe modele symulacyjne do wyznaczania strategii[9]ach.Moreover, simulation models of logistics systems lea-rozwoju przedsiebiorstw (teoria i praktyka)", instytut Interfakcjding to optimization of their potential can be interestingWarszawa,2000.direction of research with usage of proposed formal notation.[10] W. B. Powell, "Real-Time Dispatching for Truckload Motor Car-riers", in G. D. Taylor (ed.), "Logistics Engineering Handbook", CRCSuch a models allows for representing stochastic and dyna-Press, Taylor & Francis Group, Boca Raton, Chapter 15, 2008.mic character of processes of cargo streamtransformations[] E. Turban, J. R. Meredith, "Fundamentals of management science",performed in logistics systemsFifth edition, Irwin,Homewood,Boston,1991.[12] A. Vazacopoulos, N. Verma, "Hybrid MIP-CP techniques to solveACKNOWLEDGMENTa multi-machine assignment and scheduling problem in XPRESS-Researches financed from funds for science in the yearsCp", in P. Pardalos M., D. W. Heam (ed.), "Supply chain optimi-2010-2012 as a research project No.NN509 478138zation",Springer, New York, Chapter 12, 2005Project coordinator: Mariusz Wasiak.[13] M. Wasiak, ,Symulacja procesow logistycznych z wykorzystaniemprogramu SymProLog I", in Systemy Logistyczne. Teoria i Praktyka,Oficyna wydawnicza Politechniki Warszawskiej, Warszawa, 2005,REFERENCESpp.525-532.M. Brzezinski, Systemy w logistyce", Wojskowa Akademia Tech[1] [14] M. Wasiak, "A queuing theory approach to logistics systems mode-niczna,Warszawa,2007.ling", in Archives of Transport, Vol. 19, Iss. 1-2, Warszawska Dru-[2] G., Ghiani G. Laporte, R. Musmanno, "Introduction to Logisticskamia Naukowa PAN, Warszawa, 2007,s.103-120.Systems Planning and Control', John Wiley & Sons Ltd, Chichester,Wasiak, "Simulation model of logistic system", in Archives of[15] M. 2004.Transport,Vol._21,Iss.3-4,Warszawska Drukamia Naukowa PAN[3] J. Fijaikowski, ,Transport wewnetrzny w systemach logistycznych.Warszawa, 2009, s.189-206.Wybrane zagadnienia",Oficyna Wydawnicza Politechniki Warszaw-[16] M.Wasiak,The problem ofcargo stream transformations in logisticskiej, Warszawa 2003.system optimization", in M. Fertsch, K. Grzybowska (ed.),"Logistics[4]S. S. Heragu, "Material Handling System", in: G. D. Taylor (ed.).in the enterprises - selected aspects", Publishing House of Poznan"Logistics Engineering Handbook", CRC Press, Taylor & FrancisUniversity of Technology, Poznan, 2010, s. 67-90.Group, Boca Raton, Chapter 11,2008[17] M. Wasiak, "Formal notation of a logistic system model taking into[5] M. Jacyna, .Wybrane zagadnienia modelowania systemow transpor-consideration cargo stream transformations", in Archives of Trans-towych", Oficyna Wydawnicza Politechniki Warszawskiej, Warsza-port, Vol. 23, Iss.1, Warszawska Drukamia Naukowa PAN,wa, 2009.Warszawa,2011450

According to described model, the assumptions for static optimization of logistics system potential are presented. The optimization task constrains and evaluation criteria are given. With regard to presented approach to static optimization, the optimal potential for selected railway-road transshipment terminal was found. The verification confirms regularity of proposed appro￾ach. Moreover, simulation models of logistics systems lea￾ding to optimization of their potential can be interesting direction of research with usage of proposed formal notation. Such a models allows for representing stochastic and dyna￾mic character of processes of cargo stream transformations performed in logistics systems ACKNOWLEDGMENT Researches financed from funds for science in the years 2010 – 2012 as a research project No. N N509 478138 – Project coordinator: Mariusz Wasiak. REFERENCES [1] M. Brzeziski, „Systemy w logistyce”, Wojskowa Akademia Tech￾niczna, Warszawa, 2007. [2] G., Ghiani G. Laporte, R. Musmanno, “Introduction to Logistics Systems Planning and Control”, JohnWiley & Sons Ltd, Chichester, 2004. [3] J. Fijakowski, „Transport wewntrzny w systemach logistycznych. Wybrane zagadnienia”, Oficyna Wydawnicza Politechniki Warszaw￾skiej, Warszawa 2003. [4] S. S. Heragu, “Material Handling System”, in: G. D. Taylor (ed.), “Logistics Engineering Handbook”, CRC Press, Taylor & Francis Group, Boca Raton, Chapter 11, 2008. [5] M. Jacyna, „Wybrane zagadnienia modelowania systemów transpor￾towych”, Oficyna Wydawnicza Politechniki Warszawskiej, Warsza￾wa, 2009. [6] Z. Korze, „Logistyczne systemy transportu bliskiego i magazynowa￾nia, Tom I – Infrastruktura, Technika, Informacja”, Instytut Logistyki i Magazynowania, Pozna, 1998. [7] A., Kusiak “Intelligent Manufacturing Systems”, Prentice Hall, En￾glewood Cliffs, New Jersey, 1990. [8] D. M. Lambert, J. R. Stock, L. M. Ellram, “Fundamentals of logistics management”, McGraw-Hill Irwin, Boston, 1998. [9] S. Piasecki, „Sieciowe modele symulacyjne do wyznaczania strategii rozwoju przedsibiorstw (teoria i praktyka)”, Instytut Interfakcji, Warszawa, 2000. [10] W. B. Powell, “Real-Time Dispatching for Truckload Motor Car￾riers”, in G. D. Taylor (ed.), “Logistics Engineering Handbook”, CRC Press, Taylor & Francis Group, Boca Raton, Chapter 15, 2008. [11] E. Turban, J. R. Meredith, “Fundamentals of management science”, Fifth edition, Irwin, Homewood, Boston, 1991. [12] A. Vazacopoulos, N. Verma, “Hybrid MIP-CP techniques to solve a multi-machine assignment and scheduling problem in XPRESS￾CP”, in P. Pardalos M., D. W. Heam (ed.), “Supply chain optimi￾zation”, Springer, New York, Chapter 12, 2005. [13] M. Wasiak, „Symulacja procesów logistycznych z wykorzystaniem programu SymProLog 1”, in Systemy Logistyczne. Teoria i Praktyka, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa, 2005, pp. 525-532. [14] M. Wasiak, “A queuing theory approach to logistics systems mode￾ling”, in Archives of Transport, Vol. 19, Iss. 1-2, Warszawska Dru￾karnia Naukowa PAN, Warszawa, 2007, s. 103-120. [15] M. Wasiak, “Simulation model of logistic system”, in Archives of Transport, Vol. 21, Iss. 3-4, Warszawska Drukarnia Naukowa PAN, Warszawa, 2009, s. 189-206. [16] M. Wasiak, “The problem of cargo stream transformations in logistic system optimization”, in M. Fertsch, K. Grzybowska (ed.), “Logistics in the enterprises – selected aspects”, Publishing House of Poznan University of Technology, Pozna, 2010, s. 67-90. [17] M. Wasiak, “Formal notation of a logistic system model taking into consideration cargo stream transformations”, in Archives of Trans￾port, Vol. 23, Iss. 1, Warszawska Drukarnia Naukowa PAN, Warszawa, 2011. 450