Solutions for the port facilities development

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IOP Coferece Series: Materials Sciece ad Egieerig PAPER OPEN ACCESS Solutios for the port facilities developmet To cite this article: V Dragu et al 018 IOP

1 IOP Coferece Series: Materials Sciece ad Egieerig PAPER OPEN ACCESS Solutios for the port facilities developmet To cite this article: V Dragu et al 018 IOP Cof. Ser.: Mater. Sci. Eg View the article olie for updates ad ehacemets. This cotet was dowloaded from IP address o 19/1/018 at 00:1

2 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 Solutios for the port facilities developmet V Dragu, E Rosca, F. Rusca, A Rusca ad E A Roma Uiversity Politehica of Bucharest, Faculty of Trasports, Trasport, traffic ad logistics Departmet, Splaiul Idepedeţei, No. 313, 06004, Bucharest, Romaia v_dragu@yahoo.com Abstract. The developmet of the port facilities must be carried out i cocordace with the ships flows size so that the sum of waitig costs for demads arrived for service ad also for the service statios is miimal. I actual operatig coditios this miimum is difficult to obtai due to varyig demads faced by ports. The solutios for the port facilities developmet are based o the criterio that aims maximizig the social beefit obtaied usig the mathematical models of queuig theory. The paper aims to idetify models for developig port facilities by which a ratioal dimesioig of istallatios subjected to time variable demads will be achieved (hadlig facilities at berth, covered / ucovered storage areas).cosiderig the multitude of mathematical models of the differetiated queuig theory accordig to the umber of chaels, distributio of arrival times ad distributio of service time or the umber of places i the waitig strig / system, there is a problem of choosig the model to approximate as accurately as possible the future operatio of the port system. The model validatio is doe through a case study which solve a problem of ratioal developmet of the ecessary port facilities at a operative berth. The proposed model use the miimum ecoomic cost criterio (cost of ships waitig for service ad cost of berth iactivity) kowig that the ratio of these costs i most cases exceeds 4/1. 1. Geeral cosideratios The optimal sizig, developig ad exploitatio of the port facilities problems have always bee subjects of may techical papers due to its difficulty stemmig from the multitude of factors, parameters, operatig hypotheses, restrictios ad coectios ivolve [1-4]. The port is a typical example of a itermodal termial i which, for the smooth ruig of the trasport process the followig coditios must be met: the trasport process cotiuity, the accordace of trasfer ad storage capacities, a logical successio of system occupacy times i the techological flow, [5]. The simultaeous fulfilmet of these coditios becomes difficult, maily due to exogeous factors of the port system (weather coditios, differet ship capacities ad capabilities, iteratioal political situatio) leadig to variable exploitatio demads of the istallatios. This ted to disturb the rhythm of lad trasport thus trasferrig cogestio to aother area or trasport termial. The variable demads i port operatio are udesirable as they lead to the maiteace of additioal capacities that are oly used durig peak periods of traffic, so ivestmets for additioal techical edowmets are ot recovered[6]. It follows that it s beig searched the criterio o which to determie the optimal structure of port techical edowmets is sought. The criterio is adopted accordig to the iterests of the decisio-maker but i may techical papers [5, 4, 11, 15] it is metioed as a ecoomic criterio. Cotet from this work may be used uder the terms of the Creative Commos Attributio 3.0 licece. Ay further distributio of this work must maitai attributio to the author(s) ad the title of the work, joural citatio ad DOI. Published uder licece by Ltd 1

3 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 Specific models for the sizig ad developmet of port facilities have bee developed usig the priciple of maximizig the social beefit. A ecoomically correct sizig ca be achieved by usig the mathematical models of mass-service waitig theory where ships are system users waitig for service ad service statios may be berths or hadlig facilities o the quay [1-14]. There are a multitude of mathematical models of the queuig theory, differetiated by the time arrivals distributio or time service distributio, the umber of servig statios, the servig disciplie, or the umber of places i the queue/strig. Thus, it appears the problem of choosig a model that approximates more accurately the operatio of the port system. [15]. It is also emphasized that models that do ot use elemetary flows (Poisso distributio of arrival times) lead to complicated ad difficult to use mathematical expressios, which limits the scope of applicability of the models. The mathematical theory of mass service allows the processig ad iterpretatio of waitig issues so as to improve their egative effect ad at the same time offers the possibility to make predictios o which to achieve optimal operatio of the port system i terms of cost. The issue of optimal sizig is ot so simple for berths where ships loadig/uloadig is carried out with itermediate storage (idirect trasfer). However, by itroducig some simplifyig assumptios, the operatio of such a trasfer system ca be assimilated with two series-coected waitig systems. (Problems arise i harmoizig the processig capacity of the two systems, sice capacity costraits may come from either of the two itercoected systems) [14]. Whe usig the multichael direct trasfer model (with multiple servig statios workig i parallel), it ca be oticed that the average waitig time for service decreases if the average arrivals itesity ad average service itesity icreases to the same extet. So, for high-capacity istallatios, higher demads ca be accepted [6,7]. t sv ; 1 t sv1 t sv. (1) If t 1 t sv, sv 1 where λ, μ represet the average arrivals itesity ad the average service itesity; the service itesity factor of the system or the umber of demads arrivig i the system while a uit is i service; t the average time of servig a demad. The values of the service itesity factor accordig to the umber of istallatios of the same type, takig ito cosideratio a ratio betwee the cost for ship operatio ad the cost for of port istallatios operatio of 4/1, are preseted i the table 1. sv Table 1. Recommeded values of the service itesity factor [10]. The umber of the same type istallatios Service itesity factor As ca be see from Table 1, for small umbers of istallatios also the service itesity factor is low, this traslates ito a high degree of iactivity, which i may cases is ot accepted by the port admiistratios. Problems arise whe aalyzig multi-chael servig models if the port has a sigle dock with successive berths because the umber of servig statios ca ot be determied rigorously. Oe hypothesis would be that a berth be defied by a certai quay legth so that a represetative type of ship could be accommodated ad the umber of berths will be give by the umber of ships that could be hauled simultaeously alog the quay. This hypothesis is ot always suitable because i the case of cotaier termials, the trastaier craes are cosidered as service statios because they determie

4 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 the area where service ca be doe. If the quay is fully occupied by the ships, the umber of craes may be isufficiet to serve all moored ships ad therefore the defiitio of berths accordig to their legth is iappropriate. I other cases ships with self-hadlig facilities may be moored, i which case the umber of berths ca be defied accordig to the legth of the quay. The questio arises: how may craes are i a servig statio? It is assumed that there are craes that ca be used simultaeously for a ship ad that the margial productivity of the craes is costat regardless of whether they work for the same ship or for differet ships. Uder these circumstaces, for a system cosistig of 3 craes, it is cosidered that the total waitig time i the system is miimal if all craes are used for a sigle ship. [10]. So the distributio of craes by a crae for each of the three ships, two craes for a ship ad oe crae for aother ship is disadvatageous. For clarificatio, it is assumed that three idetical ships arrive at the same time i the port ad that service time will be oe day if 3 craes are allocated to a ship, 1,5 days if craes are allocated to a ship ad 3 days if oe crae is allocated to each ship. The solutio is preseted i table. Allocatio of craes Table. The total time i the system [14]. Total service time [days] Total waitig time [days] , , ,5 7, ,0 Total waitig time i the system [days] Table shows that the most efficiet policy is to allocate all three craes to operate o each ship.. Models based o miimizig the waitig costs The problem of reducig the waitig time of vessels i ports is of particular ecoomic importace, due to the eed to reduce or eve elimiate demurrage resultig from failure of the operatio times provided i the charter cotracts. The use of the multimodal direct trasfer model for port equipmet sizig aims to optimize some fuctios or system parameters. I this sese, we try to optimize the ecoomic fuctio of the system, which is the sum of the waitig costs, both o the part of the ships arrivig for operatio ad o the port istallatios (ofte there are restrictios i additio to the ecoomic fuctio). Port istallatio costs cosist of: a) a quasi-fixed cost comprisig the equipmet of the quay, warehouses, craes, etc., b) a variable cost comprisig hadlig costs, fuel cost, taxes of various kids. Their variatio is show i the figure 1, [10] Whe the traffic volume icrease, the quasi-fix cost decrease, while the variable cost remais costat util the port istallatios have to meet a higher traffic volume. At this poit it teds to grow because more expesive hadlig methods must be used. The cost of ships waitig time i the port also has two compoets (figure ): a) the cost of operatig time (the waitig time at berth), b) the cost of waitig for operatio at berth. As traffic icreases, the cost of waitig times icreases greatly, eve expoetially. The total cost is the sum of the port facilities cost ad the cost of ships waitig time i the port. These are show i figure 3. It is show i figure 3 that the graph represetig the total cost for port system curve has a miimum i poit B. This miimum is at a traffic volume lower tha the miimum cost for port facilities (poit A). If port plaig / sizig oly takes ito accout the miimizatio of port facilities cost, the quatity ad quality of services provided to shipowers will decrease which will lead to to port cogestio ad implicitly etail additioal costs ad ecoomic iacceptability. The size of the various cost elemets, determies ways to reduce total port costs. The miimum amout of 3

5 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 these costs depeds o the ratio of the specific ships waitig time i port cost ad port facilities cost, which has commo values of 4/1 [10]. Cost per toe Ports cost Variable Cost Quasi-fix cost A Traffic volume Figure 1. Variatio of port istallatio costs. Cost per toe Cost of ships waitig time i the port Cost of waitig for operatio at berth Cost of operatig time Traffic volume Figure. The cost of ships waitig time i the port. The form of the total cost curve ad its miimum is determied by the complex mathematical relatioships that exist i the queuig theory for the average waitig ad servig times. The optimal solutio is obtaied by calculatig the umerical value of the fuctio F (s), for differet umbers of berths (s). I most cases, this fuctio is expressed as the statistical mea of waitig time costs (ships ad berths waitig times) over a time period T [16]: s c a c T c t a c s T, F 1 1 () where c 1 is the time uit cost for waitig demad; a - average umber of uits withi the queue; c time uit cost for service statios dowtimes; - average umber of uoccupied statios; 4

6 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/ average arrivals itesity; - average service itesity; t a - average queue waitig time. Total cost Total cost Cost of ships waitig time i the port Cost for port facilities t a Figure 3. The variatio of the total cost for port system. Withi F(s), ad must be determied. The value is quite simple to be determied, while requires thorough calculatio ad a comprehesive study of the waitig pheomeo kowig that this size is determied by the arrivals ad the service time distributios, the umber of servig statios, the arrival ad service disciplie ad the umber of uits i the queue. I moo-chael models, attetio is directed to determiig a ecoomically optimal value of. This value ca be determied by kowig the uitary waitig costs of icomig ships for operatio (c 1) ad the uitary cost of service statio iactivity, both with service persoel ad without (e a, e r). The optimal value of the service itesity factor is obtaied by calculatig the miimum cost for servig a uit [6,7]. For the optimal service statio demad o the followig expressio is obtaied: 1 o (3) c1 1 e e oly valid whe c1 e a er, which correspods to the situatios ecoutered i practice. If we cosider the itervals betwee arrivals ad service times correspodig to a expoetial distributio it results that the optimal service statio demad is eve smaller as the ratio betwee the uitary cost of ships waitig time i the port ad the uitary cost of remueratio of the servicig of the craes ea e r is higher. It is therefore atural that, i a ratioal exploitatio, the time use of the ship's operatig equipmet is much lower tha time use of similar equipmet used for loadig or uloadig wagos or trucks. The maximum value of is obtaied for c 0 what is impossible i practice. Table 3 shows variatio o 1 a r the o o f c1 / ea er. To study the multi-chael mass-servig system, you eed to go through the followig steps: B A Traffic volume t a 5

7 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/ the observatio, based o a sample, of the empirical distributios of arrivals ad ships service time, as well as the determiatio of the system solicitatio degree; - establishig the theoretical distributio of arrivals ad of service times, correspodig to the observed distributios; - determiatio of system parameters ad the aalytical study of the problem to determie the chages to be made to the system (variatio of s) i order to icrease profitability. t a Table 3. The o variatio. c 1 e a e r o 1 1,5,5,5 3 3,5 4 4,5 5 5,5 6 0,5 0,45 0,41 0,4 0,38 0,36 0,34 0,33 0,3 0,31 0,9 0,8 The variatio coefficiet (ratio betwee the dispersio ad the average) provides a useful idicatio of the theoretical distributio that could approximate the observable empirical distributio of the arrival ad service of ships i the port. Table 4 presets the theoretical distributios with which the empirical distributios ca be approximated, depedig o the value of the variatio coefficiet. Variatio coefficiet Name of distributios Table 4. Theoretical distributios of radom variables depedig o [5]. = 0 0< < 0,33 0< <0,71 0,71< <1 Uiform (costat) Normal Erlag Erlag distributio with differet itesities 1 ad 1 Expoetial >1 Hyperexpoetial I coclusio, obtaiig a rigorous miimum value of the objective fuctio is a difficult issue because waitig time (ships waitig time ad istallatios waitig time) is a parameter depedig o may elemets, some of them exogeous to the system. 3. Case study For the model developmet the arrivals of ships i the port were first studied (for a period of 30 days). The situatio is preseted i Table 5. Table 5. Ships arrivig i port. Day Number of ships arrived Day Number of ships arrived The umber of ships arrived per day varies from 0 to 7. The cocordace betwee the empiric repartitio ad the theoretical oe cosidered is verified ((M/M/s( /FIFO) Poisso distributio for arrivals ad Expoetial distributio for service time, with s umber of parallel servers/servig statios, places i the system ad FIFO disciplie queueig system). 6

8 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 Average ad dispersio for the empirical radom variable is ( m ad 1 m f 3, 37 N ). (4) 1 m f 3, 37 (5) N I order to check the cocordace betwee the empirical ad the theoretical radom variable, the test is used. If calculat tabelat, the the coclusio that a good cocordace exists betwee the two radom variables ca be draw: As we ca see i the distributio table of f NP calculat 3, 056 (6) NP P m m e (7)! 6 its value is i the cofidece iterval correspodig to the P = 0,05, 1, 59 ad it is higher tha calculat. It ca be cocluded that the observed frequecy regardig ships arrivals i port correspods to a Poisso distributio. Similarly, based o observatio, the ships service o berths was studied, determiig that the service time also follows a Poisso repartitio, checked with test. The average service time for a ship, determied by statistical study, is 18 hours, ad so, the average umber of service i the time uit (4 hours a day) is: 1.34 ad So, ρ=λ/μ=.5>1. For oe berth the queue icreases to ifiite ad the system does ot work i statioary regime. For the system to eter the statioary mode the service itesity factor of the system must be subuitary, ρ < 1. This happes for a umber of berths (s) equal to 3. Verifyig that the umber of berths is appropriate will be achieved by calculatig the mai elemets of the model for s = 3, 4, 5, 6, 7 ad 8. t sv t a P s s! 1 / s 0 s! s s 1 1 / s k P s k k! (8) (9) The iactivity time for service statios D i ad medium waitig time of the ships for service (D a) are: D D i s 4 t sv ad a a t (10) The waistig time of the ships waitig for service ad berths iactivity cost (c) is: C c1 Da c D i (11) 7

9 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 The calculated values of the system parameters ad the associated ecoomic fuctio are show i table 6. Form table 6 it is oticed that the miimum iactivity cost ad ships waitig time cost of the is obtaied for 5 berths, which is equivalet to a service itesity factor 0, 5. For may port admiistratios it is uacceptable. So other orgaizatioal solutios have to be foud. Table 6. The berth iactivity cost ad ships waitig time cost. Iactivity costs ad waitig time costs s P (0) t a D i D a (C) [zile] [h/zi] [h/zi] c 1 = 400 c 1 = 500 c 1 = 600 c = 100 c = 100 c = ,048 1,109 11,34 89, , ,00 4 0,071 0,165 35,34 13, , ,00 5 0,0784 0, ,34 3, , ,00 6 0,0799 0, ,34 0, , ,5 7 0,0803 0, ,34 0, , ,54 8 0,081 0, ,34 0, , ,6 4. Coclusio The developmet of port facilities ca be achieved through models based o miimizig waitig costs of both port istallatios ad for ships arrivig i port. Eve whe these elemets are kow, the practical applicatio of mass-servig theory models ca create problems i terms of complicated ad difficult to hadle mathematical expressios that ca be achieved i modelig the system. It is kow that today may ships are equipped with their ow loadig / uloadig facilities which makes it difficult to defie the servig characteristics. Whe desigig port equipmet sizes, it is difficult to determie the umber of service statios. Whe the waitig costs are ukow, the the ratioal dimesioig of the port equipmet ca be achieved usig models based o the levels harmoizatio, give that these models compare the parameters of the system. The problem with these models is the choice of the upper limits of the parameters that are harmoized. These ca be adopted by compariso with other similar ports i terms of size ad activity, ports that are recogized as operatig at maximum profitability. The usig of mass servig theory models leads to a ratioal dimesioig of port facilities with direct implicatios i reducig the ships ad port istallatios costs of waitig times. Policies applied deped o the costs ivolved i the sizig process, which may vary from oe area to aother ad eve i time. Ackowledgemet This work has bee fuded by Uiversity Politehica of Bucharest, through the Excellece Research Grats Program, UPB GEX 017. Idetifier: UPB- GEX017, Ctr. No. 65/ (GEX017). 5. Refereces [1] Rusca A, Popa M, Rosca E, Rosca M., Dragu V ad Rusca F 016 Simulatio model for port shutig yards, IOP Coferece Series: Materials Sciece ad Egieerig [] Diu O, Roşca E ad Ruscă F 016 Ilad waterway ports characteristics relevat for classificatio methodology purpose Proc. of the 3rd It. Cof. o Maritime Techology ad Egieerig (MARTECH 016) eds. C G Soares ad T A Satos (Lodo: CRC Press Taylor & Fracis Group) pp

10 ModTech 018 IOP Cof. Series: Materials Sciece ad Egieerig (018) doi: / x/400/8/08007 [3] Dekker S ad Verhaeghe R 006 A Modellig Approach for Itegrated Plaig of Port Capacity - Trade-Offs i Rotterdam Ivestmet Plaig, Promet - Traffic&Trasportatio 18() [4] Gudelj A, Krčum M ad Twrdy E 010 Models ad methods for operatioal i port cotaier termials Promet - Traffic&Trasportatio, (1) [5] Ruscă F, Popa M, Roşca E, Roşca M ad Ruscă A 016 Capacity aalysis of storage area from a maritime cotaier termial Proc. of the 3rd It. Cof. o Maritime Techology ad Egieerig (MARTECH 016) eds. C G Soares ad T A Satos (Lodo: CRC Press Taylor & Fracis Group) pp [6] Raicu Ş ad Maşală G 1981 Railway trasportatio. Fuctioig. Developmet. Efficiecy (i Romaia: Trasportul feroviar. Fuctioare. Dezvoltare. Eficietă) (Bucharest: EDP Publishig House) [7] Raicu Ş 007 Trasport Systems (i Romaia: Sisteme de trasport) (Bucharest: AGIR Publishig House) [8] Raicu Ş ad Popa Mihaela 1996 Some Difficult Problems i Usig the Models of Queuig Theory for the Real Systems Study Proc. of the 9 th Symp. o Modellig, Simulatio ad Idetificatio Systems (Uiv. "Duărea de jos" Galaţi) [9] Dragu V 006 Port equipmet with variable usage sizig (i Romaia: Dimesioarea istalatiilor portuare cu solicitari de exploatare variabile) Cocepte itermodale i trasporturi, (Bucharest: AGIR Publishig House) [10] *** L améagemets des ports, Mauel a l usage des plaificateurs des pays e developpemet-natio Uies, New York, 1984 [11] Page E 197 Queuig Theory i OR (Lodo: Butterworths) [1] Jurevic M ad Hess S 016 The operatioal plaig model of trashipmet processes i the port Promet- Traffic&Trasportatio, 8() [13] Hess M, Kos S ad Hess S 007 Queuig System i Optimizatio Fuctio of the Port's Bulk Uloadig Termial Promet- Traffic&Trasportatio 19() [14] Jasso J O 1984 Trasport system optimizatio ad pricig (Lodo: Joh Wiley ad Sos) [15] Kempa W M, Paprocka I, Kaliowski K, Grabowik C 015 O ifluece of model parameters o time-depedet queue-size distributio i a productio model with failures ad batched arrivals, Iter. J. of Moder Maufacturig Techologies VII() [16] Dragu V, Diu O, Ruscă A., Burciu Ş ad Roma E A 017 Queuig theory models used for port equipmet sizig IOP Coferece Series: Materials Sciece ad Egieerig

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