ENHANCING OPERATIONAL EFFICIENCY OF A CONTAINER OPERATOR: A SIMULATION OPTIMIZATION APPROACH. Santanu Sinha Viswanath Kumar Ganesan

Transcription

1 Proceedngs of the 2011 Wnter Smulaton Conference S. Jan, R.R. Creasey, J. Hmmelspach, K.P. Whte, and M. Fu, eds. ENHANCING OPERATIONAL EFFICIENCY OF A CONTAINER OPERATOR: A SIMULATION OPTIMIZATION APPROACH Santanu Snha Vswanath Kumar Ganesan Complex Decson Support Systems Tata Consultancy Servces Ltd. Mumba , INDIA ABSTRACT One of the key ssues n a typcal marne logstcs ndustry dealng wth contaner operatons s to maxmze proftablty subject to pre-specfed servce level complance(s) under uncertan and complex busness envronment. The problem becomes more complex n presence of heterogeneous customers, vared degree of demand prorty, supply restrctons, and other alled operatonal constrants. In ths paper, a typcal contaner busness operaton has been consdered where the servce provder deals wth dfferent types of customers. The problem has been modeled wth dscrete-event smulaton technques. A smulaton optmzaton technque has been deployed to analyze several opportuntes to mprove overall system performance n terms of ncreased proft, demand fulfllment rate, and dervng other contractual parameter(s) under vared scenaros. Trade-offs between dfferent KPIs ncludng fleet sze, unmet demand, servce level, and utlzaton have been analyzed and a senstvty analyss has been provded to brng n several manageral nsghts. 1 INTRODUCTION Globalzaton of world economy has accelerated the use of contaners n cargo transportaton through Thrd Party Logstcs Provders (3PL) and today over 60% of the world s martme cargo s transported n contaners, whle n some routes among the economcally strong countres the fgure has gone up to 100% (Steenken, Vob, and Stahlbock 2004). As an effectve mode of merchandse transportaton, use of contaners not only has reduced the handlng and transportaton costs, but also has been consdered as a faster and more effcent delvery opton to thousands of customers n a geographcally dstrbuted network (Bandera, Becker, and Borensten 2009). Issues related to contaner operatons have ganed sgnfcant attenton and have been extensvely studed under varous modelng contexts. The entre gamut of research can be captured nto two dmensons conceptual framework and soluton technology. In the perspectve of conceptual framework, the related models can broadly be categorzed nto two cost mnmzaton and proft maxmzaton. In the former, some authors have focused on cost mnmzaton models whch deal wth desgnng effcent reposton plan, forecastng, safety-stock determnaton, and tactcal fleet plannng problem (Erera, Morales, and Savelsbergh 2005; L et al. 2007). An excellent revew has been provded by Powell (2005). The other drecton consders the revenue maxmzaton aspects based on heterogeneous customer attrbutes. Ths stream of research merges the concept of both revenue management through dynamc prcng and cost mnmzaton through effcency enhancement. Not many of the revenue maxmzaton models have been developed for contaner ndustry. In the perspectve of soluton technology, a stream of research s based on mathematcal programmng where the authors have developed optmzaton models and soluton algorthms under dfferent modelng assumptons (Whte 1972, Turnqust and Jordan 1986). In all the cases, the authors have focused on de /11/$ IEEE 1727

2 velopng mathematcal models to manage dynamc fleet operatons. Specfc to contaner ndustry, several crucal research efforts have been carred out (Cranc, Gendreau, and Dejax 1993; Erera, Morales, and Savelsberg 2005). Further, a general model for managng dynamc fleets under varous transportaton modes has been descrbed by Powell (2005). Another stream of research on contaner operatons s based on computer smulaton. In ths sense, computer smulaton has been deployed to address several busness ssues such as, mprovng the performance of contaner termnal operatons (Yun and Cho 1999), lner shppng operatons (McLean and Bles 2008), empty contaner repostonng (Jula, Chassakos, and Ioannou 2006), and the problem of determnng optmal fleet sze under varous operatonal constrants (Donga and Song 2009). From the revew of lterature, t has been observed that though tradtonal mathematcal and optmzaton technques have been successfully appled to solve dverse busness problems n the doman of contaner operatons, these technques cannot capture system behavor n an uncertan and dynamc envronment where there are several nteractons among the system components (Sage and Rouse 2009). In a typcal 3PL busness model, there are several parameters wth sgnfcant varablty and uncertantes such as, customer arrval rate, customer demand, full-move transt tme, empty reposton tme, capacty allocaton, and reposton polcy. The complexty goes even hgher n presence of heterogeneous customers wth vared degree of contrbuton/proftablty and servce expectatons. In such stuatons, smulaton s consdered to be an mportant and effcent tool to analyze system varablty and randomness and capture system behavor under varous condtons through several what-f scenaros. Thus, we have been motvated to address the ssues of contaner operatons wth segmented demand. In ths effort, we merge both the aspects of revenue maxmzaton and cost mnmzaton together n a basc 3PL busness model wth two dfferent types of customers, vz., hgh and low prorty. A smulaton-based approach has been deployed to analyze the system behavor over the plannng horzon and determne the optmal control parameters. We have nvestgated the trade-off between segmented demand and servce-level and the ssue of determnng optmal fleet sze correspondng to target demand fulfllment rate for any type of customers. Further, we analyze a typcal practce of delayed delvery whch s very common n contaner/3pl ndustry where customer s asked to wat for sometme tll the contaners/equpments are avalable. A smulaton optmzaton technque has been appled to determne the optmal length of such watng tme consderng other factors such as overall demand fll rate, revenue, proft, and servce level complance. The remander of the paper s organzed as follows. The problem of contaner busness operaton has been brefly dscussed n secton 2. A smulaton model has been developed n secton 3. In secton 4, we brefly dscuss about smulaton optmzaton. We carry out several smulaton experments and elaborate the results n secton 5. Fnally, we summarze and conclude n secton 6. 2 PROBLEM DESCRIPTION In ths paper, the concepts of revenue management are evaluated for a contaner operator (a typcal 3PL) that transports materals for ts customers from one locaton to another n a geographcally dspersed supply chan network. The 3PL operaton conssts of the followng functons: 1. Management of customer orders for empty contaners 2. Servng customers by dspatchng empty contaners to the customer locatons subject to the avalablty of contaners at the respectve servce depots 3. Loadng of materals and shpment of contaners from customer locatons to destnatons 4. Reposton of empty contaners back to the approprate servce depot(s) to serve future customer demand theren Though the 3PL servce provder operates on hundreds of unque orgn-destnaton par, for the purpose of llustraton and tractablty, wthout losng generalty, we assume three major hubs or zones of operaton by aggregaton and 3x3 = 9 trade-lanes as shown n Fgure 1 where, d = demand at, v j, c j are 1728

3 revenue and cost respectvely between trade-lane to j. Here, λ [d ] represents the stochastc arrval rate of Customers along wth stochastc demand d ~ at locaton (=1,2,3). ~ λ 1 d 1 1 V j / C j (, j=1, 2, 3) v j / c j (, j=1, 2, 3) 1 1 ~ λ 2 d ~ λ 3 d Full move Empty move Fgure 1: Contaner busness operaton model wth 3X3 trade-lanes For smplcty of exposton, we consder that the operator manages a homogeneous fleet of contaners. We further consder that the servce provder faces two dfferent types of customers hgh prorty and low prorty dependng on ther margnal yeld per capacty. The order fulfllment happens on a frst-n-frst-out (FIFO) bass; but n case of a capacty shortage, we assume that the hgh prorty customers are gven hgher prorty governed by a contractual agreement {WT, P} whch guarantees a delayed order fulfllment wthn an addtonal WT days falng whch the servce provder s subjected to pay a penalty of P per ordered capacty to the respectve hgh prorty customer. The overall order fulfllment can be represented as shown n Fgure 2. In ths case, the ssue s to determne the optmal WT correspondng to a specfc penalty charge P under dynamc and uncertan busness envronment. Further, trade-offs between dfferent KPIs (fleet sze, unmet demand, servce level, utlzaton) have been analyzed and a senstvty analyss has been provded to brng n several manageral nsghts. 3 BUSINESS MODEL OVERVIEW The nputs, busness metrcs, and the control varables used for modelng the 3PL process operatons are elaborated n ths secton. 3.1 Input Parameters The followng nput parameters (factors) have been consdered n the busness model (, j =1,2,3): Customer arrval rate n locaton Percentage ( p ) of hgh-prorty customers n locaton Average demand for contaners n locaton Percentage of shpment between to j Revenue per contaner n trade lane to j, for hgh prorty customer Revenue per contaner n trade lane to j for low prorty customers Transt tme from to j for full load contaner Logstcs cost to move a sngle contaner from to j Reposton tme from to j for empty load contaner Reposton cost per contaner from to j. 1729

4 Fgure 2: Order fulfllment process wth hgh and low prorty customers 3.2 Busness Metrcs The followng parameters (responses) have been consdered to measure the performance of the busness model: Gross proft Operatng cost Revenue Unmet demand (UMD) Contaner utlzaton 3.3 Control Varables The followng control varables havng a drect nfluence on any of the above mentoned busness objectve, have been consdered n the model: Servce level (SL k ), where k = 1, 2 ndcatng the hgh and low prorty customers, respectvely Reposton polcy Contractual watng tme for premum customers n case of nventory shortage (WT) Fleet sze (FS) Safety-stock level at locaton has been calculated as follows: 1730

5 SS 2 k 1 SL k LT 2 2 D dk k 2 LT (1) where, LT and (σ LT ) represent the average and standard devaton of supply lead-tme whle D k and (σ dk ) ndcate the average and standard devaton of demand for customer type k at locaton. Thus, f the safety-stock level at a locaton falls below the expected level SS, the reposton polcy ensures the earlest replenshment of empty contaners from other sources havng excess capacty. Further, we assume that the contractual back order lead tme (WT),.e., the watng tme of the hgh prorty customers to be served n case of a capacty shortage, s a varable and can have sgnfcant mpact on the overall performance of the system. Wth smulaton optmzaton, we have shown how an optmal WT can be derved for a specfc fleet sze (FS), and other nput parameters. We also nclude a senstvty study wth the varous nput parameters. The contaner utlzaton s calculated as follows: The objectve s to measure the system performance wth the help of the followng KPIs: gross proft, operatng cost, revenue, unmet demand, and utlzaton. The typcal questons that could help mprovng busness performance are: What should be the optmal WT for a specfc fleet sze (FS), and other nput parameters to mnmze unmet demand or maxmze revenue? What are the trade-offs between fleet sze and other key performance ndcators (KPIs)? Wth all the complextes mentoned above, the proposed model seems to be complex and mathematcally ntractable. In such stuatons, smulaton s an mportant and popular tool that consders varablty and randomness n the busness processes and captures the system behavor under varous condtons by analyzng several what-f scenaros. 4 SIMULATION OPTIMIZATION Recently, wth the ncreasng power of computng devces, smulaton optmzaton has become an effectve way to merge the benefts of both smulaton and optmzaton to fnd a set of model specfcatons (.e., nput parameters and/or structural assumptons) that leads to optmal performance (Aprl et al. 2005). More specfcally, smulaton optmzaton s an optmzaton technque where the performance s measured on the bass of the output of a smulaton model. The problem settngs contans the usual optmzaton components, such as, decson varables (x), objectve functon f(x), and the assocated constrants (Q) (Ólafsson and Km 2002). The objectve functon s estmated usng a functon of the stochastc smulaton output say, g(x) defned n a real space,.e., f: Q R. The objectve functon typcally mght be an unbased estmate of the true objectve functon, that s, f(x) = E[g(x)]. More detals are avalable n Ólafsson and Km (2002), Aprl et al. (2003), and Fu, Glover, and Aprl (2005). Accordngly, n smulaton optmzaton, the optmzaton engne chooses a set of values for the controllable nputs and these are used as nputs to the smulaton engne. Based on the performance of the smulaton output, the optmzer selects the next tral soluton untl the termnaton crtera s acheved or a desred level of mproved output s obtaned. A detaled revew of varous technques has been provded by Azadvar (1999). A typcal example of such applcaton n a 3PL ndustry has been llustrated n Snha and Ganesan (2009). 1731

6 In ths paper, the varous aspects of operatonal and tactcal plannng n the scope of the above mentoned model are evaluated wth smulaton optmzaton and several nsghts have been provded n scope of manageral decson makng under dverse contexts. 5 SIMULATION EXPERIMENTS AND RESULTS Three dfferent busness cases have been consdered heren to provde varous nsghts on applcaton of revenue management prncples and operatons plannng wth smulaton optmzaton technques. A popular smulaton tool ARENA 10 (refer ARENA Smulaton Software; Source: has been deployed to model, smulate, and optmze the busness operaton process dscussed above. 5.1 Base Case Ths case has been used as a reference to compare the benefts of mplementng Revenue Management (RM) practces usng smulaton and optmzaton engnes. The base case consders unform customer arrval rate and dspatch volume across all lanes. Reposton of empty contaners s assumed to follow the smple rule: If current nventory at locaton s more than the desred safety stock SS AND (Current Inventory + Planned recept) at locaton j s less than safety stock SS j, Then Move empty contaners from locaton to j. For any locaton, the safety stock level S can be estmated from (1) where the servce level for both type of customers have been consdered as 80%,.e. SL1 SL Further, for the fleet sze of 150 ntally dstrbuted unformly, the trade-off between back order tme and the correspondng proft can be shown n Table 1. Table I: Results of the base case smulaton (p = 0.5) Sr. WT (hr) Proft Overall SL SL 1 SL 2 Utlzaton % 79.5% 79.5% 39.0% % 87.0% 74.6% 39.7% % 92.2% 70.3% 39.8% % 95.2% 70.5% 39.8% % 95.0% 69.6% 39.8% % 97.3% 66.2% 40.5% % 99.1% 66.0% 38.8% % 99.8% 68.8% 39.3% % 99.8% 63.7% 39.7% % 100.0% 66.2% 40.2% % 100.0% 66.2% 40.1% Ths shows that the maxmum proft s acheved wth WT = 100. However, t s tedous to generate large number of scenaros to fnd out the optmal WT *. The next model establshes the beneft of smulaton optmzaton n such cases to derve optmal parameter value. 1732

7 5.2 Optmzaton of Base Case Model The earler base case model has been optmzed wth smulaton optmzaton wth OptQuest embedded n ARENA. The optmzaton engne deploys varous algorthms based on Tabu search, scatter search, nteger programmng, and neural networks to mprove performance objectves. In ths case, the back order tme WT has been consdered as a varable and the optmal WT * has been found at hrs. The varaton of net proft wth back order duraton (WT) s shown n Fgure Proft WT (Hr) Fgure 3: Optmzaton of base case model Ths shows a further 0.65% ncrease of proft as compared to the earler case. The mpact of the optmal WT on servce levels on two dfferent types of customers has been shown n Fgure 4. Servce Level 100% 90% 80% 70% 60% 50% WT*= WT (Hr) Fgure 4: WT vs. Servce level Overall SL SL1 SL2 5.3 Base Case Model wth Optmzaton under Vared Proportons of Customer Types Next, we derve the optmal WT under vared proporton p of hgh-prorty customers n locaton. The results are tabulated n Table Capacty Plannng The demand fulfllment rate for hgh prorty customers drops at ncreased servce levels. Ths s attrbuted to the fact that hgher safety stock level results n less free contaners. However, demand fulfllment rate for low prorty customers ncreases at ncreased servce levels - ths s due to the fact that addtonal fleet base ncreases the chance of possble fulfllment of low prorty orders after servng the hgh prorty ones. The mpact of fleet szes and servces levels across the two types of customers s demonstrated n 1733

8 the followng fgures. Fgure 5a and 5b demonstrates the performance at 100% SL and 85% SL for hgh and low prorty customers respectvely when servng dfferent proportons of demand among two types of customers. Table 2: Optmal * WT vs. p Optmal WT Proft Overall SL SL 1 SL 2 Utlzaton 0% % -- 79% 39.0% 10% % 98% 76% 39.3% 25% % 99% 72% 39.9% 50% % 100% 64% 40.7% 75% % 99% 44% 43.5% 100% % 95% % p 120% Demand fullflment (%) 100% 80% 60% 40% 20% 0% Fleet Sze Prorty I: 25% Prorty I: 50% Prorty I: 75% Prorty I: 100% Fgure 5a: Fleet sze vs. demand fulfllment (P1 Customers) 100% Demand fulfllment (%) 75% 50% 25% Prorty II: 25% Prorty II: 50% Prorty II: 75% Prorty II: 100% 0% Fleet Sze Fgure 5b: Fleet sze vs. demand fulfllment (P2 Customers) 1734

9 Dervng optmal fleet sze: Fgure 5c demonstrates how to arrve at an optmal fleet sze correspondng to gven Servce Levels and expected demand fulfllment rate. As an example, n order to meet 90% and 70% servce level for hgh and low prorty customers respectvely and to mantan an aggregate 92% demand fulfllment rate, the optmal fleet sze s 120. Fgure 5c: Fleet sze vs. demand fulfllment Fleet sze vs. Net Proft: Followng the experments, t has been found that net proft ncreases wth ncrease n P 1 type of customers because of hgher contrbuton. However, though hgher fleet sze ntally results n hgher proft, further ncrease reduces the net proft due to hgh captal expendture. Ths observaton s qute evdent from fgure 6. Fgure 6: Fleet sze vs. net proft 1735

10 Senstvty analyss: The followng fgure shows the trade-off between Fleet sze (FS), Servce level (SL) and net proft. The followng varatons have been consdered: Large FS: 210 Contaners Low FS: 60 Contaners Hgh SL: SL1= 99%, SL2=80% Low SL: SL1= 80%, SL2=60%. The results for P1 Customer demand are shown n Fg. 7. The results for P2 Customer demand has been found to be a mrror mage of Fg. 7 due to the fact that P1 and P2 demand always equal to 100% when added Low FS (60)_ Hgh SL {99, 80} Low FS (60)_Low SL {80, 60} Large FS (210)_Hgh SL (99, 80} Large FS (210)_Low SL {80,60} Net Proft P-I customer demand (%) Fgure 7: Fleet sze, net proft and P1 customer demand It has been observed that servce level does not have much mpact on net proft f fleet sze s low as due to small fleet sze, mantanng the safety stock level becomes dffcult due to capacty shortage. Other observatons related to the system behavor are as follows: For a gven fleet sze: As p1 ncreases, gross revenue ncreases, smultaneously unmet demand for prorty customer (UMD-I) ncreases wth hgher penalty cost, Thus, net proft (NP) decreases. However, f p1 ncreases beyond a certan level, dependng on the margnal revenue and unt penalty charge, addtonal penalty charge may be offset by addtonal revenue leadng to ncreased net proft. For larger fleet sze: Wth larger fleet sze, UMD-1 decreases. As a result, penalty decreases. But because of hgher cost related to procure addtonal fleets (Capex), net proft decreases. However, f p1 ncreases gross revenue also ncreases. Thus, sometmes, the addtonal Capex s offset by addtonal revenue. In such cases, net proft ncreases. If fleet sze s small and safety stock (SS) s hgh, contaners reman dle at some places and capacty utlzaton decreases. However, f fleet sze ncreases up to a certan level, utlzaton ncreases because of more free/avalable contaners beyond whch utlzaton agan starts decreasng due to hgh safety stock levels or surplus capacty. 1736

11 6 CONCLUSION Managng contaner busness operatons wth heterogeneous customer demand and servce prorty under uncertan and complex busness envronment has been a key challenge for the practtoners. In order to address the ssue, ths paper has studed a typcal contaner operaton process and appled dscrete-event smulaton technque to mprove overall system performance n terms of ncreased proft, demand fulfllment rate, and dervng other contractual parameter(s) under vared scenaros. The problem has been modeled n the perspectve of revenue management practces assumng dfferent types of customers wth vared levels of prorty to mprove proftablty and servce level agreement. The proposed model has shown how smulaton and optmzaton can be appled to decde the optmal order/servce lead tme for the hgh prorty customers to maxmze proft. Further experments have been conducted to provde several nsghts on system behavor wth nput parameters such as, fleet sze, servce level, and proporton of hgh prorty customers. Impact of such nput parameters on the key performance ndcators such as, demand fulfllment rate, proft, utlzaton, and operatng cost, has also been dscussed followng a senstvty study. It has fnally been shown how smulaton and optmzaton can help takng more nformed decsons to sgnfcantly mprove the overall performance level of a contaner busness process and also help n takng varous strategc decsons such as fleet sze and servce level agreements under dverse busness envronments. ACKNOWLEDGMENT We sncerely acknowledge Dr. Sddhartha SenGupta, Head, Complex Decson Support Systems (CDSS) group for hs nvaluable nputs and constant gudance throughout the work. We are also thankful to Dr. Sumt Raut, Dr. Sudhr Snha, Dr. Sharadha Ramanan, and Mr. Shrpad Salsngkar, Tata Consultancy Servces, for ther crtcal comments and helpful suggestons durng the research and preparaton of the earler manuscrpts. REFERENCES Aprl, J., F. Glover, J. Kelly, and M. Laguna Practcal Introducton To Smulaton Optmzaton. In Proceedngs of 2003 Wnter Smulaton Conference, edted by S. E. Chck, P. J. Sanchez, D. M. Ferrn, and D. J. Morrce, Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers, Inc. Aprl, J., M. Better, F. Glover, J. P. Kelly, and M. Laguna Enhancng Busness Process Management wth Smulaton Optmzaton. BP Trends January 2005, Accessed March %20Aprl%20et%20al.pdf. Azadvar, F Smulaton Optmzaton Methodologes. In Proceedngs of the 1999 Wnter Smulaton Conference, edted by P.A. Farrngton, H.B. Nembhard, D.T. Sturrock, and G.W. Evans, Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers, Inc. Bandera, D. L., J. L. Becker, and D. Borensten. A DSS for Integrated Dstrbuton of Empty and Full Contaners. Decson Support Systems 47: Cranc, T. G., M. Gendreau, and P. Dejax Dynamc and Stochastc Models for the Allocaton of Empty Contaners. Operatons Research 41(1): Donga, J., and D. Song Contaner Fleet Szng and Empty Repostonng n Lner Shppng Systems. Transportaton Research Part E: Logstcs and Transportaton Revew 45(6): Erera, A. L., J. C. Morales, and M. Savelsbergh Global Intermodal Tank Contaner Management for the Chemcal Industry. Transportaton Research Part E: Logstcs and Transportaton Revew 41:

12 Fu M. C., F. W. Glover, and J. Aprl Smulaton optmzaton: A revew, new developments, and applcatons, In Proceedngs of the 2005 Wnter Smulaton Conference, edted by M.E. Kuhl, N. M. Steger, F. B. Armstrong & J. A. Jones, Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers, Inc. Jula, H., A. Chassakos, and P. Ioannou Port Dynamc Empty Contaner Reuse. Transportaton Research Part E: Logstcs and Transportaton Revew 42(1): L, J-A., S. C. H. Leung, Y. Wu, and K. Lu, Allocaton of empty contaners between mult-ports. European Journal of Operatonal Research 182(1): McLean, A. A., and W.E. Bles A Smulaton Approach to the Evaluaton of Operatonal Costs and Performance n Lner Shppng Operatons, In Proceedngs of the 2008 Wnter Smulaton Conference, edted by S. J. Mason, R. R. Hll, L. Mönch, O.Rose, T. Jefferson, and J. W. Fowler, Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers, Inc. Ólafsson S., and J. Km Smulaton Optmzaton. In Proceedngs of the 2002 Wnter Smulaton Conference, edted by E. Yücesan, C. H. Chen, J. L. Snowdon, J. M. Charnes, Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers, Inc. Powell, W. B Dynamc Models of Transportaton Operatons. In Supply Chan Management: Desgn, Coordnaton and Operaton, Handbooks n Operatons Research and Management Scence, 11: Elsever. Sage, A. P., and W. B. Rouse Handbook of Systems Engneerng and Management. John Wley & Sons, Inc. Snha S. and Ganesan V Dynamc Modellng of Busness Process Flows and Transformatons usng Smulaton Optmzaton. In Proceedngs of the 7 th AIMS Internatonal Conference on Management, IIM Bangalore, Inda. December, Steenken, D., S. Vob, and R. Stahlbock Contaner Termnal Operaton and Operatons Research: a Classfcaton and Lterature Revew. OR Spectrum 26: Turnqust, M. A., and W. C. Jordan "Fleet Szng Under Producton Cycles and Uncertan Travel Tmes." Transportaton Scence 20(4): Whte, W Dynamc Transshpment Networks: An Algorthm and ts Applcaton to the Dstrbuton of Empty Contaners. Networks 2(3): Yun, W. Y., and Y. S. Cho A Smulaton Model for Contaner-Termnal Operaton Analyss usng an Object Orented Approach. Internatonal Journal of Producton Economcs 59: AUTHOR BIOGRAPHIES SANTANU SINHA obtaned hs Ph.D from the Indan Insttute of Technology Kharagpur, Inda and s currently workng as Assstant Consultant n the appled research group Complex Decson Support Systems at Tata Consultancy Servces Ltd., Mumba. Hs current research nterests are n the areas of supply chan management, logstcs, nventory management and optmzaton. The author has already publshed papers n nternatonal journals ncludng, Mathematcal and Computer Modelng, Computers & Industral Engneerng, Internatonal Journal of Operatonal Research, etc. Hs emal address s <santanu.snha@tcs.com>. VISWANATH KUMAR GANESAN obtaned hs Ph.D from the Indan Insttute of Technology Madras, Inda and s currently workng as Consultant n the appled research group Complex Decson Support Systems at Tata Consultancy Servces Ltd., Mumba. Hs current research nterests are n the areas of supply chan management, logstcs, nventory management and optmzaton. The author has already publshed papers n nternatonal journals ncludng, European Journal of Operatonal Research, Computers & Industral Engneerng, Computers & Operatons Research, Internatonal Journal of Producton Economcs, etc. Hs emal address s <vswanath.ganesan@tcs.com>. 1738