SAFETY STOCK ESTIMATION OF UNIT LOAD DEVICES FOR INTERNATIONAL AIRLINE OPERATIONS

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1 Joural of Marie Sciece ad Techology, Vol. 2, No. 4, pp (22) 43 DOI:.69/JMST SAFETY STOCK ESTIMATION OF UNIT LOAD DEVICES FOR INTERNATIONAL AIRLINE OPERATIONS Hua-A Lu ad Chie-Yi Che 2 Key words: bridge, corrosio, pier, reiforced cocrete, service life predictio. ABSTRACT Uit load devices (ULDs) are used to load air cargo ad passegers checked baggage for wide-bodied aircraft operatios. Sice ULDs are reusable at the destiatio, airlies ca ivest i a appropriate fleet size for their requiremets. The estimatio of safety stock levels for every operatig airport is a premeditated task because airlies must prepare eough devices for the outboud cosigmets of each flight. The variace of the umber of used devices for each arrival ad departure flight will ifluece the stock level of a airport. For scheduled iteratioal services, this study proposes a aalytic method based o a cyclically time-sequeced etwork that ca be used to express ULDs movig i ad out of a airport. The safety stock level is defied as the miimum quatity that ca support the utilizatio for the etire ext cycle at the period ed. The results of a case study o oe compay reveal that the airlie ormally establishes a high safety stock level. I. INTRODUCTION Uit load devices (ULDs) are the stadard equipmet for loadig air cargo ad checked baggage i wide-bodied aircraft operatios. Accordig to the defiitio of the Iteratioal Air Trasport Associatio (IATA), ULDs ca be may items [6]. I practice, ULDs are commoly defied as devices that ca be used to load freight, such as cotaiers ad pallets. The utilizatio of ULDs assists airlies i the stadardizatio ad uitizatio of loadig ad dischargig hadligs at airports. Airlies ca select customized types of ULDs for matchig the ier cotours of the mai ad lower decks of various aircraft Paper submitted 6/2/; revised 2/6/; accepted 3/22/. Author for correspodece: Hua-A Lu ( halu@mail.tou.edu.tw). Departmet of Shippig ad Trasportatio Maagemet, Natioal Taiwa Ocea Uiversity, Keelug, Taiwa, R.O.C. 2 Ta-Ho Maritime Corporatio, Hopig Brach, Hopig Village, Hualie Couty, Taiwa, R.O.C. sizes. Sice ULDs are also accommodated with a variety of aircraft, airlies ormally seek the beefit of commoality to purchase as may similar types of ULDs as possible. ULDs ca be reused after emptyig freight at the destiatio. Whe import shipmets are typically greater tha the export quatities, empty ULDs will accumulate at the airport. O the cotrary, a airport with greater export shipmets tha iboud freight will lack loadig equipmet. The airlie must appropriately repositio ULDs betwee airports i order to balace the differece of supply ad demad ad keep a sufficiet ad ecoomical fleet size. Therefore, it is importat for a airlie to properly estimate the safety stock level for each operatig airport i order to cope with its ULD repositioig operatio. The safety stock level is a crucial elemet i ivetory theory. Two alterative methods of determiig the safety stock level are used [8, 2]. The first techique is the aalytic method, which is always based o a computatio of the variace of demad. The secod method develops a simulatio processes. Zizka [2] used these two approaches to determie safety stock levels ad compared their quatified differece. Ta ad Tag [5] examied the demad variable as a Gauss fuzzy variable to estimate safety stock levels for a case without historical demad data. Cosiderig iteratioal air trasport services, ULDs are ormally moved with a fixed flight schedule ad without cosideratio of a better lead time for arbitrary supplemets. Marie cotaier trasport is aother idustry that follows the same decisio process regardig equipmet safety stock levels. The issue of safety stock levels i ports ormally appears i the discussio of empty cotaier repositioig [3, 9]. Sice cotaiers delivered through the marie system are coected with their origis ad destiatios by truck or rail systems, their buildup ad breakdow operatios are maily completed at depots or customers factories. This procedure leads to ucertaities of timig ad the quatities of empty cotaiers reused [2, 4,, 4]. Iteratioal air cargo services ormally execute buildup ad breakdow operatios at the air cargo termial. I the airlie busiess, several studies have dealt with various topics relative to air cargo operatio ad maagemet. Cargo load plaig is always viewed as a bi-packig prob-

2 432 Joural of Marie Sciece ad Techology, Vol. 2, No. 4 (22) lem with either two dimesios [5] or three dimesios []. Mogeau ad Bes [3] formulated a optimizatio model for cotaier loads for a specific aircraft type, which cosidered the weight ad balace problems caused by the placemet of ULDs ad the capacity costraits of the aircraft. Kasiligam [7] explored the differece betwee cargo reveue maagemet (CRM) ad passeger yield maagemet (PYM). The complexity of CRM results from the ucertaity of available weights ad volumes of carried freight that must be cosidered whe balacig the estimated amout of passeger baggage ad cargo. Ya et al. [8] ad Ya et al. [9] examied the hub-ad-spoke system of FedEx i the Asia trasport etwork to formulate models for cargo loadig uder give demads ad stochastic demads, respectively. Wu [7] preseted a decisio-makig framework for air cargo forwarders to ret air cotaiers from carriers. A umber of studies have also discussed ULD hadligs iside airport termials. Verwijmere ad Tilaus [6] explored resource programmig ad task schedulig for ULD buildup ad breakdow operatios. McAree et al. [2] explored the optimal desig for a sort facility i a large hub termial to deal with iboud ad outboud palletized loads, likig together the breakdow ad re-buildup operatios of ULDs i a hub. Lau ad Zhao [] developed a evet framework approach for the joit schedulig of differet types of cooperatig material hadlig equipmet for a automated air cargo hadlig system. The required quatities of ULDs prepared at each airport will ifluece the ULD relocatio i short-term operatio as well as the ULD fleet scale i log-term plaig. Thus, the estimatio of safety stock levels for each operatioal airport is vital for airlies. aims to desig a aalytic tool for iteratioal airlies to estimate the safety stock level of ULDs. From a log-term perspective, the scheduled airlie services are cyclical with a fixed period, which is ormally a week. The defiitio of a safety stock level i this research is the miimum ULD quatities that ca support the utilizetio for the ext whole cycle. proposes a timesequeced etwork to express ULD moves at a airport. Based o the flow coservatio priciple, the aalysis method ca assess a appropriate safety stock level. A case study courtesy of a Taiwaese iteratioal airlie was coducted for real-world applicatio. II. DETERMINANTS FOR ULD SAFETY STOCK LEVELS The preparatio of ULDs is predomiatly cocered with the operatioal parameters ad the flight patter of a airport. The parameters reveal the efficiecy of airport groud hadlig for cargo, baggage ad ULD operatios. The flight patters ifluece the umber of ULDs ad the timig of movig ULDs i ad out of the airport.. Groud Hadlig of ULDs There are three mai stages for ULD hadlig at the airport. The first stage is the ramp operatio that icludes dischargig iboud ULDs from the aircraft, loadig outboud ULDs oto the aircraft, ad the trasportatio of ULDs betwee the aircraft side ad the stagig area. The secod stage is the buildup ad breakdow process at the baggage sortig/distributig area ad i the cargo termial. The fial stage is the serviceability ispectio of the ULDs. ) Ramp ad Termial Operatios Ramp operatios cosist of may activities to serve the aircraft o the groud. ULD loadig ad dischargig at the aircraft is oe of these activities. The trasportatio of ULDs from the baggage sortig area ad the cargo termial to the aircraft follows the completio of buildup operatios. Outboud ULDs, with the exceptio of last-miute chages, are ormally ready beside the aircraft s locatio for rush trasit ad turaroud flights. Iboud ULDs ca also be trasported to the distributio area ad to the termial for baggage claim ad cargo breakdow, respectively. Relatively, the operatioal performace of this sector is ot as critical as the ULD hadlig i the termial. Normally, the required workig time for this sector is embedded i the etire groud service time of the aircraft. For iteratioal operatios, airport cargo termials are desiged to facilitate the coversio hadligs betwee bulk freight ad uitized loads. Air freight that accesses the termial always accommodates the schedule of assiged departure or arrival flights. Shippers require the reservatio of a buffer time for deliverig outboud cosigmets to the termial, i order to accommodate a series of procedures for customs declaratio ad ispectio for iteratioal trade. Sice export shipmets might be evetually set to the cargo termial, the buildup tasks ormally begi from a specific time prior to the flight departure. ULDs that are to be used for the departure flights must be ready before startig buildup. For imports, the breakdow performace cocers the availability of reusig ULDs. The higher the quatities of ULDs for a flight, the loger the fiish time for the breakdow tasks of the whole flight. Much more time is ormally required to breakdow a pallet tha a cotaier with the same umber of pieces i a shipmet. Therefore, a passeger flight eeds less time to empty the ULDs tha the same aircraft type used for combiatio (combi) ad freight flights, because it carries more cotaiers but less pallets. 2) Serviceability Ispectio for ULDs For esurig flight safety, o-time operatios, ad the prevetio of damage to the loads, ULDs must be kept i a serviceable status. Airlies defie the serviceability of ULDs accordig to the specificatios of Natioal Aerospace Stadard (NAS) 36 issued by the Aerospace Idustries Associatio (AIA) [6]. Based o the ULD maiteace practices of the airlies, the serviceable coditios for cotaiers ad pallets are differet. The former are more complicated tha

3 H.-A. Lu ad C.-Y. Che: Safety Stock Estimatio of Uit Load Devices for Iteratioal Airlie Operatios 433 the latter because of their differet structures, but cotaiers are easier to ispect tha pallets. Serviceable coditios for a cotaier iclude the base, body, door, ad the techical stadard order (TSO). Damage to cotaiers is ormally idetified by visualizatio. A serviceable pallet ca oly be checked at the base; its detoured level must be ispected ad calibrated by a specialized machie. The time expediture for ispectig oe pallet is loger tha for checkig oe cotaier; however, repairig damaged cotaiers ca require much more time tha the calibratio of a pallet. The ULD must be ispected for serviceability after emptyig its load to esure it is serviceable for reuse. However, iteratioal airlies caot afford to set up ispectio bases at all operatig airports. The compay studied i this paper oly built a serviceable ispectio ceter at the home airport because all aircraft depart ad retur there for the ext duty assigmet. Whe aircraft arrive, all retur ULDs are staged to execute a batch ispectio after breakig dow. Thus, it ca be esured that all set-out ULDs from the home airport are serviceable. Ay ULD that is questioable or has kow damage icurred from overseas statios must be set back to the home airport. Ituitively, the time spet for ULD ispectio ad calibratio will affect the timig of reuse. 2. Flight Patter The flight patter of a airport ca be represeted by the arragemet of timig ad sequeces for departure ad arrival flights, as well as the deployed aircraft type of each flight. The umber of flights withi a specific time widow represets the itesity durig this period. The itersectio of arrival ad departure flights stads for the complexity of a airport schedule. Sometimes, the airport schedule also reveals its role to the airlie. The itesity ad complexity of a airport schedule combied with ULD hadlig performace will affect its ULD stock level. ) Itesity ad Complexity of Flights For a airlie operatig iteratioal services, its route structure ormally forms a radial flight etwork. The home airport is the ceter of this etwork, while overseas statios are the spoke airports, which are liked with the hub by various routes. Each route cosists of two flights departig from the home airport to a turaroud airport ad the turig back from the opposite directio to the home airport. Each flight may be arraged to trasit to additioal airports i order to gather more passegers ad freights. Turaroud airports require loger groud time to repleish the provisio of the whole aircraft service. Trasit airports are always arraged with shorter groud time for hadlig fewer passegers ad freight tha the etire aircraft s capacity. The itesity of the home airport s schedule is aturally higher tha that of other airports because it is the origi ad also the ed of all routes. The airlie s schedule must cosider may criteria, which iclude the prefereces of passegers ad shippers for flight departures ad arrivals. The home airport s schedule always has peaks durig certai time widows. Its complexity is also higher tha that of other airports ad depeds o the itersectio of log-haul ad short-haul routes. 2) Aircraft Types The aircraft type used for each flight represets the possible maximum amouts for ULD supply ad demad with a specific timig. Differet type scales are used for differet aircraft sizes as well as differet service categories. Larger wide-bodied aircraft ormally carry more ULDs tha medium ad stadard types. Passeger aircraft carry more cotaiers tha the same type of combi aircraft or freighter, but carry fewer pallets. III. METHODOLOGY The flight schedule for iteratioal airlie services always recurs weekly. This paper assumes that the schedule for each week durig the etire plaig period maitais the same flight patter. ULD movemet is limited to aroud the airport area without the possibility of movig outside the airport. Shippers or cosigees must deliver or pick up cargo to or from the airport. Moreover, the airlie ca acquire the distributio of the iboud ad outboud quatities of ULD types for each flight from the historical data. A time-sequeced etwork is applied to express the ULD flows withi the cyclic duratio. It ca be used to assess the safety stock level for each ULD type at each airport, icludig overseas airports ad the ULD repositioig ceters.. Time-sequeced Network A time-sequeced etwork is defied as a etwork i which odes are embedded with the elemet of the evet time of occurrece ad with arcs that are liked at two cosecutive odes by their time relatioships. Sice the movemet of ULDs accompaies flight departures or arrivals, the flight schedule at the airport is the basis for costructig a timesequeced etwork for ULD movemet. The loaded ULDs must be emptied before beig reused, whe the aircraft arrives at a airport. This breakdow period icludes the uloadig ad trasportatio processes o the ramp, as well as the emptyig ad serviceability ispectio i the warehouse. The ULD stadby time before beig loaded oto a aircraft requires takig ito accout the processes of cargo ad baggage buildup, ramp trasportatio ad loadig operatios beside the aircraft. Therefore, the time at which the ULDs are ready for reuse is later tha the aircraft arrival time, while the stad-by time of ULDs for use is earlier tha the aircraft departure time. This cocept is described by the time-sequeced etwork illustrated i the upper part of Fig.. The umber of p ULDs brought by the arrival flight ca be reused at the time of ode 3, while the required quatities of q ULDs for the departure flight must be prepared at the time of ode 2. These relatioships for ULD movemet ca the be directly simplified as depicted i the lower part of Fig.. The

4 434 Joural of Marie Sciece ad Techology, Vol. 2, No. 4 (22) Airport Airport Time Flight for departure or arrival ULD movemet p q Operatioal cocept m m-q m-q+p m-q+p ULD breakdow ad ispectio ULD buildup -q +p m 2 m-q 3 m-q+p Time-sequeced etwork cocept Fig.. Network cocept trasferred from flight schedule ito ULD operatio. Airport Time cyclic period 2 - u u = u u + u + cyclic arc Fig. 2. Expressio of a time-sequeced etwork for the movemet of available ULDs. + x ( i, j), u, u (3) ij move-i ad move-out of the ULDs are cosidered supply ad demad quatities of the odes ad are represeted as positive ad egative values, respectively. The arcs are the liked oe-by-oe for every two eighborig odes. The arc flows ca trace the ULD stock at the airport. The airports that play the role of ULD repositio ceters are required to cosider the possibility of ULD maiteace. I a time-sequeced etwork, these cases ca create aother ode accordig to the required time of completig ULD maiteace i additio to breakdow. The ULD supply quatities ca be shared from the ode represetig the breakdow of the same flight by the estimated maiteace ratio. Accordig to the trasferrig method, the flight schedule of a airport ca be costructed ito a time-sequeced etwork for ULD movemet. If the occurrig times of two odes are the same, the demad ode will be set earlier tha the supply ode. Moreover, the scheduled airlies always operate a cyclically-fixed weekly timetable. The etwork ca employ a week as the cyclic period ad apped a cyclic arc to lik the last ode to the first ode to express this characteristic. Fig. 2 shows a time-sequeced etwork with odes for the movemet of available ULDs at the airport. This cyclic etwork is set with two extra slack arcs, flow-i arc for flow icremets ad flow-out arc for flow decreases (marked as u + ad u respectively), at the last ode i order to calculate the imbalace flows withi the cyclic period. A urestricted sig variable, u, is further defied as the differece of u ad u +, i.e. u = u u Properties of a Time-sequeced Network I the etwork flow model, the flow coservatio is held for every ode. Every ode i the time-sequeced etwork show i Fig. 2 has oly oe flow-out arc ad oe flow-i arc, with the exceptio of the last ode. The flow coservatio relatioships ca therefore be expressed as Eqs. () to (3), where x ij is the flow of arc (i, j), with u + ad u stadig for the flows of the slack arcs at the last ode ad b i represetig the supply or demad quatities of ode i (positive for supply ad egative for demad). x x = b, i the last ode () ij ji i + x + u u x = b, if i = the last ode (2) ij ji i Property : The least arc flow of x ij must be. Proof: The time-sequeced etwork is cyclic if slack arcs are eglected. No matter what the values of b i are, a certai umber of arc flows of x ij ca be deducted at the same time util the least arc flow equals. If the o-egative restrictio is temporarily violated for x ij, a certai umber ca also be added at the same time util the least arc flow equals, which the satisfies the o-egative restrictio. If there are odes i a time-sequeced etwork, variable u is equal to the sum of the supply ad demad quatities of all odes. + Property 2: u = u u = bi Proof: Accordig to Eqs. () ad (2), x x = b, 2, x x = b, x x = b, 2,,ad x + u u x = b. +,, Takig the summatio for the left ad right sides of the equal sig, all x ij will be deleted. It ca the be obtaied that + u u u b b... b b b. = = = 2 i Variable u represets the et supply ad demad of the cycle period. Whe u, the supply quatities are larger tha the demad quatities durig a cyclic period, ad the airlie ca move out u ULDs from the airport. Iversely, it meas that the demad quatities are larger tha the supply quatities whe u <, ad the airlie should move u ULDs to the airport. Supposig the plaer does ot take ay repositioig steps, the the ULD stock (T) at the phase betwee two cosecutive cycles are the sum of x, ad u, as show i Eq. (4).

5 H.-A. Lu ad C.-Y. Che: Safety Stock Estimatio of Uit Load Devices for Iteratioal Airlie Operatios 435 Network Flows Table. Example for u. Calculatio Steps Network Flows Table 2. Example for u <. Calculatio Steps A B C D u Step : Let x DA = A B C D u Step : Let x DA = A - B 5 C -3 D u = Step 2: Calculate the flows of x AB, x BC, x CD ad u A - B -8 C -3 D u = -5 Step 2: Calculate x AB, x BC, x CD ad u A B 5 C 7 D u = Step 3: δ = - = Step 4: Add to x AB, x BC, x CD, ad x DA A 8 B C 5 D 8 u = -5 Step 3: δ = -8 = 8 Step 4: Add 8 to x AB, x BC, x CD, ad x DA,, i T = x + u = x + b (4) Give b i, the arc flows i the time-sequeced etwork for the movemet of available ULDs ca be calculated by the followig steps. Step : Let x, =. Step 2: Calculate flows accordig to Eqs. () ad (2). Step 3: Check the arc flows. If ay arc flow is less tha, let δ equal the absolute value of the least flow ad go to step 4. Step 4: Add δ for all x i,j. A example for u is illustrated i Table. There are four flights for ULD movemet at a certai airport. Accordig to the flow calculatio steps, u =, x DA =. As a descriptio i Property, the critical arc with flow equalig is x AB. The value of u equals the sum of the supply or demad quatities of all odes, satisfyig Property 2. The ULD stock at the ed of the cyclic period is equal to the sum of u ad x DA, T = + = 2. The example for u < is illustrated i Table 2. It is same as the last example, with four flights for ULD movemet, but with a differet flight patter. Accordig to the same steps, u = -5, x DA = 8. The ULD stock at the ed of the cyclic period is equal to the sum of u ad x DA, T = 8 5 = Estimatio Approach After itroducig the etwork structure ad its characteristics, the stochastic case ca be discussed for coverig the variaces resultig from the ode supply ad demad quatities. Assume that the demad or supply quatities of the ULDs for odes are radom variables, referred to B i. Although they may have the same flight umber, they are idepedet to each other, because they occur at differet times durig a cycle. For a log-term observatio, they should have their ow distributios without ay ifluece o each other. The radom variable of the slack variable is defied as U. Accordig to the liear combiatio of radom variables ad Eq. (4), the expectatio value of U, E(U) or µ, is the sum of the expectatio values of B i as show i Eq. (5). The variace of U, Var(U), is the sum of the variaces of B i as show i Eq. (6). Hece, ULD stock at the fial stage ca be expressed as Eq. (7). E( U) = E( B) (5) i Var( U ) = Var( B ) (6) T = x + E( U) = x + E( B) (7),, i This paper suggests that the plaer ca take a coservative strategy whe estimatig the safety stock of ULDs (ST), meaig more ULDs should be kept at the airport to be ready for ay situatio. The stadard deviatio of U, σ U, ca be applied. Accordig to Chebyshev s Iequality, the probability of a radom variable fallig ito the rage betwee plus ad mius k times the stadard deviatio is ot less tha /k 2 for ay distributio. This is show i Eq. (8). At k = 2, the probability icreases to 75%, while the probability icreases to 88.9% at k = 3. Whe the radom variable follows the ormal distributio, the probability is 68% at k =, 95.5% at k = 2 ad 99.7% at k = 3. Regardig a sigle-tail value, the probability will ot be less tha /2k 2 to cover the variace of this radom variable. Pr(µ kσ x µ + kσ) /k 2 (8) Hece, the repositio-out quatities ca be set as the expectatio value of U mius k times of σ U, whe E(U). The repositio-i quatities ca be set as the absolute value of the expectatio value of U plus k times of σ U at E(U) <. Com- i

6 436 Joural of Marie Sciece ad Techology, Vol. 2, No. 4 (22) Move i ULDs (μ < ) MQ μ kσ μ μ + kσ μ kσ MQ μ Move out ULDs (μ ) μ + kσ Fig. 3. Move quatities of ULDs set at differet E(U). biig these two cocepts, the movemet quatities of ULDs (MQ) ca be expressed i Eq. (9). The settig priciple is displayed i Fig. 3. The safety stock equals the ULD stock mius MQ, as show i Eq. (). Because the stadard deviatio of U could be real, the maximal iteger value larger tha ST, i.e. ST, ca represet the itegral umber of ULD safety stock. MQ = E( U ) kσu (9) ST = T MQ = x + E( U ) (E( U ) kσ ) = x + kσ (), U, U From the ULD flow aalysis, the plaer ca cosider a stadard deviatio rage to calculate the safety stock level usig Eq. (). This level ca esure a certai probability to cover the ULD requiremets, o matter what distributio the supply or demad variables follow. Accordig to Property, there must be a critical arc with the least positive flow, which is called x ij i the time-sequeced etwork. The plaer ca use Eq. () as the safety stock level for short-term applicatio (STc). The maximal iteger larger or equal to it, i.e. STc, ca be set as the miimal quatity of ULD stock at the airport. STc = x + kσ () ij IV. CASE ANALYSIS This sectio applies the submitted method to estimate the safety stock level for the studied compay (a iteratioal airlie i Taiwa). This compay ows three mai types of ULDs (AKE, PMC ad PAG), i additio to others for loadig special freight. AKE is a stadard cotaier for loadig baggage ad small cosigmets. PMC ad PAG are pallets maily used for loadig freight. The followig aalysis is based o the witer schedule for 28 ad oly focuses o these three types of ULDs. Estimated results will be compared with the cotrolled stock at the ed of March 29.. Backgroud of the Test Cases Before executig the umerical estimatio, the flight schedule ad data relative to the ULD hadlig, the aircraft, ad the demad assumptios were collected courtesy of the compay. U Table 3. Times required for hadlig ULDs. Uit: hour Service Arrival Departure Category Cotaier Pallet Cotaier Pallet Passeger Combi 6 6 Freighter Repair Table 4. Plaig capacities of loadig ULDs for each type of aircraft. Aircraft type Type of ULD AKE PMC PAG B747-4 Passeger B747-4 Combi B777-3ER Passeger A33-2 Passeger A32 Passeger 7 B747-4 Freighter MD- Freighter 2 2 Time parameters for the ULD hadlig of arrival flights vary with differet service categories ad aircraft types. This test oly cosidered the service categories because all arrival ULDs are always staged i the termial ad treated by batch. Accordig to the suggestio of the studied compay, the total required time for cotaiers ad pallets to be ready for reuse is set as six hours for arrivig passeger flights. The discharge of ULDs from combi aircraft requires hours to empty ad ispect ad requires 2 hours for cargo freighters. I the repositio ceter, the average required time for repairig damaged ULDs is 72 hours for cotaiers ad 24 hours for pallets. The average umber of damaged ULDs is less tha oe ULD per flight i practice. The test value was set as oe uit per flight for each ULD type. As for the departure flight, all freight starts to build up i the termial six hours prior to flight departure, regardless of the aircraft type or service category. Therefore, the required time for a ULD to be ready to build up is cosistet. All hadlig performace is listed i Table 3. The aircraft fleet of the studied compay cosists of the followig types: B747-4, B777-3ER, B767-3, MD-9, A33-2 ad A32 for passeger service, B747-4 combi, ad B767-3, B747-4 ad MD- freighters. The plaig capacities of loadig ULDs for each type of aircraft are displayed i Table 4, which excludes the B767-3 ad MD-9 types. Sice B767-3 passeger ad cargo airplaes are used o alliace services with All Nippo Airways, the studied compay did ot cout the utilizatio i these routes. I additio, The MD-9 is a arrow-bodied aircraft that does ot use ULDs to load cargo ad baggage. The studied compay operates from a total of 43 airports

7 H.-A. Lu ad C.-Y. Che: Safety Stock Estimatio of Uit Load Devices for Iteratioal Airlie Operatios 437 Table 5. Estimated average utilizatio ratios of ULDs for various routes. Route Asia Asia to Asia to Europe N.A. to roudtrip Europe N.A. to Asia Asia Passeger Cargo throughout Asia, Europe ad North America. The variace of ULD utilizatio is small i roud-trip passeger flights due to passegers geerally travelig two ways. I cotrast, ULD demad quatities are quite differet i roud-trip cargo flights, sice there is a imbalace of the trade traffic. I cosiderig the operatig properties of the studied compay ad the geeral cocept of world trade, the load factors of used ULDs i various routes were set as the list i Table 5 for passeger ad cargo flights. Flights departig from Asia have a higher utilizatio ratio tha those departig from Europe ad North America to Asia. The Mea of populatios for every ULD type of each flight ca be calculated from Tables 4 ad 5. For coductig the umerical test, values were radomly geerated for every ULD type of each flight so that all would follow the stadard ormal distributio with Z (,.33). Each case radomly selected 52 samples out of existig values to be the demad quatities i a year. This assumptio for the demad quatities to follow the ormal distributio esured that the estimatio could cover 84% of the variaces with the stadard deviatio ad % of the variaces with two times the stadard deviatio, respectively. 2. Estimated Results ad Comparisos ) Asia Airports Taipei (Taoyua airport) is the home airport of the studied compay ad also its uique ULD repositioig ceter. All routes cosist of flights radially spreadig from this airport ad the back. The Taipei stock is ot limited i the cotrolled rules of this compay because all extra ULDs from overseas airports will be set back to this locatio. I the estimatio by this paper, Taipei must prepare the largest quatities of ULDs for 625 flights per week. The stock at Kaohsiug, Macau, Phom Peh, Haoi, Nagoya, Miyazaki ad Komatsu would be zero, as their flights were served by arrow-bodied aircraft (MD-9) without usig ULDs i the selected schedule. Hog Kog had larger stores of ULDs, to meet the possible requiremets of progress betwee mailad Chia ad Taiwa i the sprig of 29. At k =, stock levels of other Southeast Asia ad Australia airports were all revealed to be less tha the levels of the studied compay. Some airports safety stock for various types of ULDs were estimated higher tha the levels of the studied compay, at k = 2, such as PAG pallets ad AKE cotaiers at Sigapore, i additio to PAG pallets at Bagkok, Jakarta ad Brisbae. Amog Northeast Asia airports, the estimatio was higher tha the compay s level, other tha those for PMC pallet stock at Osaka, Narita ad Seoul, AKE cotaiers ad PMC pallet stock at Fukuoka, ad all types at Nagoya. Estimated AKE cotaier stock levels at Seoul were also less tha the practical quatities, at k =. The detailed estimatio ad compariso with the studied compay for Asia ad Australia airports is listed i Table 6. 2) Europea ad America Routes Flights betwee Asia ad Europe or betwee Asia ad North America require a trasit statio for the deployed aircraft. The studied compay selects airports i the Middle East as the trasshipmet statios for Asia/Europe routes, while Achorage is the ladig airport for refuelig for Asia/North America routes. Table 7 lists a detailed estimatio ad compariso with the studied compay for airports served by these two routes. Brussels is the cargo ceter of the studied compay i Europe. PMC pallet stock levels at this airport are obviously higher tha at other Europea airports. However, the gap betwee practice ad the estimatio i this study, which oly takes the umber of flights per week ito accout, is quite large. Amog other Europea airports, most ULD stock levels were estimated to be lower, except for the AKE quatities at Viea ad Amsterdam. PAG pallet stock levels at Viea were closer tha the practice. At Middle Easter airports, the estimatio for all ULD types was higher tha the practice o matter if k = or 2, except for PMC pallet stock levels of k = at Delhi. Amog North America airports, the estimatio was almost always less tha that for the studied compay. Exceptios oly occurred at Seattle, Newark ad Dallas for AKE cotaier stock levels. A portio of the practical quatities slightly fell ito the estimatio for k = ad 2, such as AKE cotaier stock levels at Sa Fracisco, Vacouver ad Atlata, ad pallet stock levels at Seattle. Achorage had ull stocks because of its techical role for ladig. 3) Stocks at the ULD Positioig Ceter This sectio takes the stock status of the ULD positioig ceter, i.e., Taipei airport, at k = as the example to explai the preparatio of safety stock. Fig. 4 displays the case of AKE cotaier levels whe the airlie complemets ULDs at the ed of a week for the utilizatio of the ext week. The airlie eeds to retai a total of 546 AKE cotaiers at the ed of a week. With 255 cotaiers left from the previous week, the extra umber to be prepared is 29. This meas that the airlie must hold a additioal 29 cotaiers, o matter whether repositioig from other statios or purchasig ew oes, i order to cover the possible variaces of demad ad operatioal requiremets. If so, the smallest stock level is 99 cotaiers for a week, which is also the stadard deviatio of the supply ad demad variace for AKE cotaiers. The greatest stock level is 693 cotaiers for a week.

8 438 Joural of Marie Sciece ad Techology, Vol. 2, No. 4 (22) Area Southeast Asia & Australia Northeast Asia Airport/City a Pax. meas passeger flight. Table 6. Safety stock levels for Asia ad Australia airports. Flights/week AKE PMC PAG Pax. a Cargo Taipei 58 7 N.A N.A N.A Kaohsiug 34 Hog Kog Sigapore Bagkok Jakarta Macau Maila Phom Peh 4 2 Ho Chi Mih Surabaya Haoi Kuala Lumpur Depasar Peag Brisbae Osaka Tokyo (Narita) Fukuoka Sedai Nagoya Sapporo Miyazaki 4 Komatsu 4 Seoul Area Europe & Middle East North America Table 7. Safety stock levels for airports i Europea ad North America routes. Airport/City a Pax. meas passeger flight. Flights/week AKE PMC PAG Pax. a Cargo Lodo Viea Amsterdam Paris Brussels Frakfurt Dubai Delhi Los Ageles Seattle Achorage 6 78 Sa Fracisco Vacouver Newark Chicago Atlata Dallas New York

9 H.-A. Lu ad C.-Y. Che: Safety Stock Estimatio of Uit Load Devices for Iteratioal Airlie Operatios 439 Table 8. Total safety stocks of ULDs for various areas. ULD (hold umber of the studied compay) Area AKE (32) PMC (4) PAG (96) Asia (Taipei excluded) Asia (Taipei icluded) N.A N.A N.A Europe & Middle East North America Total (Taipei excluded) Total (Taipei icluded) N.A N.A N.A Number of Stocks Hour AKE Fig. 4. Stock status of AKE cotaiers i the positioig ceter estimated by k =. Number of Stocks Hour PMC Fig. 5. Stock status of PMC pallets i the positioig ceter estimated by k =. Number of Stocks Hour PAG Fig. 6. Stock status of PAG pallets i the positioig ceter estimated by k =. The case of PMC pallets, as show i Fig. 5, is similar to that of AKE cotaiers o the fial flows at the ed of oe week. The airlie must prepare a total of 435 PMC pallets for the circulatio of the ext week. Amog these pallets, 9 are left from the last week ad 344 extra pallets must be prepared. Durig the whole week, the lowest stock level is 54 pallets, while the highest is 525 pallets. The case of PAG pallets, show i Fig. 6, is opposite to the last two cases due to a cotrary demad patter. At the ed of the week, the airlie eeds to prepare a total of 97 PAG pallets to use for the ext week. The airlie ca move out five pallets, as there are 2 pallets left from the previous week. Durig the whole week, the lowest stock level is 35 pallets, while the highest is 69 pallets. 2. Discussio From Tables 6 ad 7, the safety stock level is higher for more flights as well as for flight itesity. The summary of safety stock levels for differet areas is show i Table 8. The subtotals for the whole of Asia for the three types of ULDs are all less tha the levels of the studied compay, o matter if k = or 2, whe Taipei stocks are excluded. The estimated AKE cotaier stock levels i Europea ad North America airports are higher, with several higher tha the sum of the practice at k = 2. Other comparisos are similar to the Asia results. I all, the estimatio of this study is less tha the safety stock level of the studied compay (excludig the stock at Taipei). Although the hold umber of each ULD type might ot represet the safety stock level of the whole compay, it ca be a precise target to compare with the estimatio of this study. The compay ows these three types of ULDs at roughly two times, four times ad three ad a half times the safety stock estimatio for AKE cotaiers, PMC, ad PAG pallets, respectively. V. CONCLUSIONS AND FUTURE RESEARCH has discussed how to set the safety stock level of ULDs at a airport for a airlie that provides iteratioal services. From a log-term perspective, the ULD safety stock level is defied as the miimum amout that ca support utilizatio for the ext whole plaig period. Employig the cyclic characteristics of scheduled flights, this study has submitted a aalytic method based o the applicatio of a time-sequeced etwork for calculatig ULD safety stock levels. As see from the case study for the studied compay,

10 44 Joural of Marie Sciece ad Techology, Vol. 2, No. 4 (22) airlies ormally prepare more stock to avoid the risk of lackig available ULDs, as the cost to purchase ULDs is isigificat relative to the etire airlie s operatig costs. The key factor that iflueces the assessmet result is fidig the log-term distributio of ULD supply ad demad for each arrival ad departure flight. did ot evaluate the actual distributio for the studied compay due to the difficulty of data collectio. However, it is easy to follow usig the discussio of sectio 3.3 if airlies have prepared the available data. Airlies ca the decide how may times the stadard deviatio should be used i order to cover the risks. It should be oted that the safety stock level is dyamic. Airlies should survey trasport requiremets cotiuously whe assessig the stock level of each airport. The estimatios of this study ca provide airlies with bottom lies for ULD stock levels at operatig airports. These results ca be used as fudametal requiremets for explorig the problems of ULD fleet sizig ad repositioig. I particular, airlies that operate hub-ad-spoke service etworks ormally set their repositioig ceters at the hub airport. How to best pla a ULD repositio amog airports to satisfy the safety stock level is aother valuable issue both i practice ad i theory. The proposed method i this study ca also be applied to lier carriers i estimatig the cotaier safety stock for operatig ports. It must be kept i mid that the characteristics of cotaier circulatio for ilad operatios are more complex tha for iteratioal airlie services. ACKNOWLEDGMENTS We would like to thak Mr. C. Y. Li, Juior Vice Presidet of EVA AIR, for sharig with the authors his valuable kowledge of ULD maagemet. REFERENCES. Cha, F. T. S., Bhagwat, R., Kumar, N., Tiwari, M. K., ad Lam, P., Developmet of a decisio support system for air-cargo pallets loadig problem: a case study, Expert Systems with Applicatios, Vol. 3, pp (26). 2. Cheug, R. K. ad Che, C. Y., A two-stage stochastic etwork model ad solutio methods for the dyamic empty cotaier allocatio problem, Trasportatio Sciece, Vol. 32, No. 2, pp (998). 3. Feg, C.-M. ad Chag, C.-H., Empty cotaier repositio plaig for itra-asia lier shippig, Maritime Policy ad Maagemet, Vol. 35, No. 5, pp (28). 4. Gao, Q., A operatioal approach for cotaier cotrol i lier shippig, Logistics ad Trasportatio Review, Vol. 3, No. 3, pp (994). 5. Heidelberg, K. R., Parell, G. S., ad Ames IV, J. E., Automated air load plaig, Naval Research Logistics, Vol. 45, pp (998). 6. Iteratioal Air Trasport Associatio, ULD Techical Maual, 8th Ed., IATA, Motreal (23). 7. Kasiligam, R. G., Air cargo reveue maagemet: characteristics ad complexities, Europea Joural of Operatioal Research, Vol. 96, pp (996). 8. Krupp, J. A. G., Safety stock maagemet, Productio ad Ivetory Maagemet Joural, Vol. 38, No. 3, pp. -8 (997). 9. Lai, K. K., Lam, K., ad Cha, W. K., Shippig cotaier logistics ad allocatio, Joural of Operatioal Research Society, Vol. 46, pp (995).. Lau, H. Y. K. ad Zhao, Y., Joit schedulig of material hadlig equipmet i automated air cargo termials, Computers i Idustry, Vol. 57, No. 5, pp (26).. Li, J. A., Liu, K., Leug, S. C., ad Lai, L. K., Empty cotaier maagemet i a port with log-ru average criterio, Mathematical ad Computer Modellig, Vol. 4, pp. 85- (24). 2. McAree, P., Bodi, L., ad Ball, M., Models for the desig ad aalysis of a large package sort facility, Networks, Vol. 39, No. 2, pp. 7-2 (22). 3. Mogeau, M. ad Bes, C., Optimizatio of aircraft cotaier loadig, IEEE Trasactio o Aerospace ad Electroic Systems, Vol. 39, No., pp. 4-5 (23). 4. Sog, D. P. ad Carter, J., Empty cotaier repositioig i lier shippig, Maritime Policy ad Maagemet, Vol. 36, No. 4, pp (29). 5. Ta, M. Y. ad Tag, X. W., The further study of safety stock uder ucertai eviromet, Fuzzy Optimizatio Decisio Makig, Vol. 5, No. 2, pp (26). 6. Verwijmere, M. A. A. P. ad Tilaus, C. B., Network plaig for schedulig operatio i air cargo hadlig: a tool i medium term goods flow cotrol, Europea Joural of Operatioal Research, Vol. 7, pp (992). 7. Wu, Y., Modelig cotaierisatio of air cargo forwardig problems, Productio Plaig ad Cotrol, Vol. 9, No., pp. 2- (28). 8. Ya, S., Lo, C. T., ad Shih, Y. L., Cargo cotaier loadig pla models ad solutio method for iteratioal air express carriers, Trasportatio Plaig ad Techology, Vol. 29, No. 6, pp (26). 9. Ya, S., Shih, Y., ad Shiao, F., Optimal cargo cotaier loadig plas uder stochastic demads for air express carriers, Trasportatio Research Part E: Logistics ad Trasportatio Review, Vol. 44, No. 3, pp (28). 2. Zi, W. ad Marmorstei, H., Comparig two alterative methods of determiig safety stock levels: the demad ad the forecast systems, Joural of Busiess Logistics, Vol., No., pp. 95- (99). 2. Zizka, M., The aalytic approach vs. the simulatio approach to determiig safety stock, Problems ad Perspectives i Maagemet, Vol. 3, pp (25).