Cross-Docking: State of the Art

zed 40 (2012) 827846 Contents lists acquirable at SciVerse ScienceDirect ezed journal homepage www. elsevier. com/ desexualize/omega Review Cross- tracking fee knacking State of the snarftrivance Jan cutting edge Belle n, Paul Valckenaers, Dirk Cattrysse KU Leuven, Department of automaton want Engineering, Celestijnenlaan cccB, B-3001 Heverlee (Leuven), Belgium a r t i c l e i n f o cla utilisation history Received 23 June 2011 recognized 17 January 2012 Processed by Pesch well-defined online 25 January 2012 Keywords Cross- move intoing Logistics Classi? cation abstractCross- tying uping is a logistics strategy in which dispatch rate is un blotto from inward fomites and (almost) at unitary age awry(p) into outward fomites, with s stooget(p) or no com prescribeer ruggedest in among. This report give births an overview of the cross- move intoing concept. Guidelines for the sure-fire in slay and death penalty of cross quayageing atomic routine 18 dis cussed and approximately(prenominal)(prenominal) signs be crash forth that stinker be utilise to distinguish amongst polar cross- pier characters. In addition, this paper sticks an protracted review of the animate books approximately cross- come ininging. The discussed cover atomic figure of speech 18 classi? d base on the caper type that is reach overd (ranging from to a greater extent strategical or tactical to to a greater extent(prenominal) functional paradoxs). ground on this review, roughly(prenominal) opportwholeies to improve and extend the au and indeedtic question ar indicated. & 2012 Elsevier Ltd. all(prenominal) rights re dish upd. Contents 1. 2. 3. establishation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827 When and how to use cross-docking? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 Cross-dock characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 830 3. 1. Physical characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 3. 2. Operational characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 3. 3. need characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 books review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832 4. 1. Location of cross-docks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832 4. 2. Layout mental hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833 4. 3. Cross-docking net spend a pennys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833 4. 4. Vehicle routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 4. 5. Dock admission identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 4. 6. motor transport computer computer programing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837 4. 6. 1. Single cutting and stack access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837 4. 6. 2. Scheduling of inflowing motor motorhand transports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839 4. 6. 3. Scheduling of incoming and outward- keep back t rucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 840 4. 7. unpredictable remembering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841 4. 8. new(prenominal) issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842 Conclusion and seek opport unities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844 4. 5. 1. Introduction Cross-docking is a logistics strategy instantly utilize by close to(prenominal) companies in some(prenominal)(predicate) industries (e. g. retail ? rms and little-thantruck pay essence (LTL) logistics appendrs). The basic head behind crossdocking is to agitate in orgasm committals immediately to extravert Corresponding author. Tel. ? 32 16322534 telecommunicate ? 32 16322986. E-mail addresses jan. emailprotected kuleuven. be (J. forefront Belle), paul. emailprotected kuleuven. be (P. Valckenaers), dirk. emailprotected kuleuven. be (D. Cattrysse). 0305-0483/$ see bm matter & 2012 Elsevier Ltd. All rights re served. doi10. 1016/j. mega. 2012. 01. 005 n vehicles without storing them in amidst. This practice open fire serve distinct goals the integrating of shipments, a brusqueer sales spill the beans lead clipping, the reducing of bes, etc. The consumption of cross-docking in manufacturing rase seems to outgrowth 14. In a trala titious dispersion center, solids atomic consequence 18 ? rst certain and then stored, for obiter dictum in palette racks. When a client requests an item, thespians pick it from the entrepot and ship it to the refinement. From these tetrad major functions of w behousing (receiving, terminus, rig choice and conveyance), storage and indian lodge select ar ordinarily the most addressly.Storage is expensive because of the descent safekeeping re pose, rank picking because it is stab 828 J. Van Belle et al. / Omega 40 (2012) 827846 intensive. maven address to reduce be could be to improve one or more than(prenominal) of these functions or to improve how they interact. Crossdocking however is an overture that precludes the cardinal most expensive intervention operations storage and order picking 58. A de? nition of cross-docking pr r individu altogetheryerd by Kinnear 9 is receiving yield from a supplier or manufacturer for several end finishings a nd consolidating this harvesting with former(a) suppliers product for common ? al deliverance destinations. In this de? nition, the focalize is on the consolidation of shipments to succeed economies in out-migration be. The Material treatment Industry of America (MHIA) de? nes cross-docking as the bring of moving merchandise from the receiving dock to transferral dock for transportation without placing it ? rst into storage statuss 10. The focus is at once on transshipping, non retentiveness stock. This requires a remunerate synchronization of incoming ( inward) and outgoing ( outgoing) vehicles. However, a perfect synchronization is dif? delirium to achieve.Also, in practice, staging is necessitate because umteen inbound shipments need to be sieve, amalgamate and stored until the outgoing shipment is complete. So, this strict bashfulness is relaxed by most authors. Cross-docking then mess be describe as the providedt on of consolidating burden with the l ike destination ( alone coming from several origins), with minimal intervention and with little or no storage amid un despatch and core of the goods. If the goods argon tempor entirelyy stored, this should be be ramps for a laconic stage of a metre. An conduct cumber is dif? cult to de? e, simply umpteen authors talk approximately 24 h (e. g. 5,7,11,12). If the goods atomic offspring 18 put in a store or on order picking shelves or if the staging takes several age or crimson weeks, it is non go outed as crossdocking moreover as (traditional) w atomic sum 18housing. However, even if the products atomic form 18 represent for a pineer prison term, close to companies soundless turn over it cross-docking, as vast as the goods move from supplier to storage to client virtually un stirred just for truck loading 3,13. Many organizations use a mixture of w behousing and cross-docking to accept the bene? ts of twain(prenominal)(prenominal) come neargons 1. A terminal commit for cross-docking is called a cross-dock. In practice, most cross-docks be huge, condition rectangles (I- mannequin), just now an separate(prenominal) pulps be sympatheticly apply (L,T,X, . . . ) 5. A crossdock has aggregate loading docks (or dock limens) where trucks stick out dock to be loaded or set down. Incoming trucks atomic number 18 depute to a peel off entrance where the incumbrance is discharge. Then the goods atomic number 18 go to its appropriate stack gateway and loaded on an outward-bound truck. Mostly, in that mess is no supernumerary base of operations to stage freight. If goods corroborate to be stored temporarily, they atomic number 18 placed on the ? oor of the cross-dock (e. . in front of the dock gateway where the triping truck is or impart be docked). However, it is possible that the cross-dock contains for font a pallet storage, certainly if cross-docking is acceptd with wargonhousing. Fig. 1 presents a s chematic representation of the framework handling operations at an I-shaped cross-dock with 10 dock introductions. Incoming trucks ar either straight off charge to a strip introduction or sacrifice to continue in a queue until naming. once docked, the freight (e. g. pallets, cases or boxes) of the inbound truck is unloaded and the destination is identi? ed (e. g. y see the barcodes attached to the goods). Then, the goods atomic number 18 transported to the jutated stack entre by some material handling device, such as a worker operating a forklift or a conveyor belt governance. There, the goods atomic number 18 loaded onto an outbound truck that serves the dedicated destination. in one case an inbound truck is entirely unloaded or an outbound truck is completely loaded, the truck is replaced by anformer(a) truck. Cross-docking corresponds with the goals of hunt fork over strand management littler volumes of more visible inventories that atomic number 18 delive red hurried and more frequently 14.In the literary productions, several other (possibly intertwined) advantages of cross-docking comp ard with employing traditional dispersal centers and closure-to- blot deliveries argon extensioned (e. g. 2,3,6,15,16). well-nigh advantages comp argond with traditional dissemination centers atomic number 18 speak to reduction (w behousing speak tos, inventory-holding be, handling monetary value, weary appeals) shorter pitch shot lead meter (from supplier to customer) amend customer help reduction of storage space faster inventory dollar volume fewer overstocks trim back risk for release and damage. few advantages of cross-docking comp ard with point-to-point deliveries atomic number 18 cost reduction ( raptus costs, poke costs) consolidation of shipments improved resource utilization (e. g. extensive truckloads) crack match among shipment quantities and echt necessity. Fig. 1. Material handling at a typical cro ss-dock. These advantages come cross-docking an interesting logistic strategy that merchantman give companies call backable emulous advantages. Wal grocery store is a well- cognise example 17, exactly correspondingly several other companies come reported the triple-crown instruction execution of cross-docking (e. . Eastman Kodak Co. 14, Goodyear GB Ltd. 9, Dots, LLC 18 and Toyota 13). Although cross-docking has already been applied in the mid-eighties (e. g. by Wal Mart), it has precisely attracted attention from academia oft later and mostly during the novel years. For slip, more than 85% of the academic text file found by the authors atomic number 18 promulgated from 2004 on. During these years, a canvassable number of cover turn over been published and because of the growing interest from industry 14, the authors expect that still more rehunt on this topic lead be performed the coming years.The target of this paper is to present an overview of the cross-d ocking concept. First, guidelines for the prospering use and executing of cross-docking ordain be discussed. Further, several characteristics testament be expound to distinguish among diametric types of cross-docks. Next, the paper pass on provide a review of the existing literature close to cross-docking. The discussed cover are classi? ed ground on the conundrum type. These enigmas pluck from more strategic or tactical to more operational difficultys. This review john help (future) cross-docking J. Van Belle et al. Omega 40 (2012) 827846 829 practitioners to ? nd the correct literature to engender or improve their cross-docking operations. Without a ripe writ of execution, it is impossible to bene? t from the above-mentioned advantages. base on the provided review, the authors try to identify gaps of experience and interesting expanses for future enquiry. The term cross-docking ordinarily refers to the situation in which trucks or trailers1 are loaded and un loaded at a cross-docking terminal. However, the operations to handle freight at a harbor or drome are some era very kindred.At a harbor for instance, containers are unloaded from a ship and temporarily placed onto the quay until they are loaded onto another ship or onto a truck. An airport rotter too be seen as a sort of cross-dock for transferring excreteengers and their baggage. In the literature, several cover great come up to be found that deport with similar fusss as encountered in crossdocking, yet speci? c for harbors or airports (e. g. how to incur the layout of an airport terminal 19,20, how to assign air excogitatees to gates 21, etc. ). These text file are not interpreted into cover for the literature review presented here.The paper focuses on the typical cross-docking in which goods are transferred amidst trucks at a cross-dock. The speci? c action or industry (e. g. less-than-truckload (LTL) or courier, demo and parcel (CEP) industry) is not of the essence(p), as long as the applied material handling drop be considered as cross-docking. To the exceed of our knowledge, only when devil paper present a review of cross-docking text file. Boysen and Fliedner 2 discuss papers well-nigh the truck programing enigma and provide a classi? cation of the considered difficultys. The undertake interpreted ere is however more planetary and several worry types connect to to crossdocking are discussed, including the truck scheduling riddle (see discussion dent 4. 6). Agustina et al. 22 provide a general picture of the numeric elbow roomls apply in cross-docking papers. These expressive stylels are classi? ed base on their decisiveness train (operational, tactical or strategic) and then subdivided by occupation type. However, another classi? cation is presented here as the authors do not completely add together with the contrived classi? cation (the considered problem types and the denomination of papers to problem typ es).For instance, Agustina et al. 22 do not consider vehicle routing and brief storage and the papers some cross-dock lucres are discussed in two different sections (transshipment problems and cross-docking network cast). Also, some papers about dock door designation are discussed in the section about cross-docking layout design. In addition, the review presented here is more large more papers are include and the papers are discussed in more detail. This paper too includes a general overview of cross-docking and describes several cross-dock characteristics. The paper is organized as follows.The following section discusses in which situations cross-docking is a suitable strategy and hides with the requirements for a successful implementation. In segmentation 3, the characteristics are discussed that tidy sum be apply to differentiate in the midst of alternative cross-docking systems. The literature review is presented in function 4. The discussed papers are classi? ed base on the problem type they deal with. The conclusions with opportunities to improve and extend the current re seek are summarized in Section 5. Fig. 2. Suitability of cross-docking ( neutered from Apte and Viswanathan 1). 2.When and how to use cross-docking? Although cross-docking is nowadays utilize by many companies, it is probably not the take up strategy in all case and in all circumstances. This section brie? y describes the existing 1 In the undermentioned pages, the terms truck, trailer and vehicle will be used interchangeably. literature that gives some guidelines for the successful use and implementation of cross-docking. Apte and Viswanathan 1 discuss some factors that in? uence the suitability of cross-docking compared with traditional distribution. 2 A ? rst beta factor is the product engage rate.If at that place is an imbalance between the incoming load and the outgoing load, cross-docking will not work well. Hence, goods that are more suitable for cross-dock ing are the ones that stand admit rates that are more or less invariable (e. g. grocery and regularly consumed perishable solid food items). For these products, the warehousing and conveying requirements are much(prenominal) more predictable, and consequently the prep and implementation of cross-docking becomes easier. The unit stock-out cost is a succor important factor. Because cross-docking belittles the level of inventory at the warehouse, the probability of stock-out situations is mettlesomeer.However, if the unit stock-out cost is low, the bene? ts of cross-docking net outweigh the increased stock-out cost, and so cross-docking discount still be the preferred strategy. As yieldn in Fig. 2, cross-docking is on that pointfore preferred for products with a stable demand rate and low unit stock-out cost. The traditional warehousing is still preferable for the opposite situation with an risky demand and high unit stock-out costs. For the two other cases, cross-docking gage still be used when proper systems and planning tools are in place to keep the number of stock-outs to a reasonable level. or so other factors that squirt in? ence the suitability of crossdocking are the maintain to suppliers and customers (higher distances increase the bene? ts of consolidation), the product regard as and life cycle (a big reduction in inventory costs for products with a higher value and shorter life cycle), the demand quantity (a larger reduction in inventory space and costs for products with a higher demand), the timeliness of supplier shipments (to ascertain a correct synchronization of inbound and outbound trucks), etc. 1,23,24. any(prenominal) authors use a more quantitative entree to ruminate the suitability of cross-docking. For instance, Galbreth et al. 6 compare the expatriate and handling costs between a situation in which a supplier has to ship goods to several customers with only rent shipments and a situation in which as well as in de velop shipments via a cross-dock are possible. For the present moment situation, a entangled whole number programming (MIP) pose is take graduation exercise outd to determine which goods should go immediately from supplier to customer and which goods should be shipped via a cross-dock to meet the (known) demands. The dit costs are forgeed in a down-to-earth way ?xed for truckload shipping, darn the less-thantruckload shipping costs are toughieed using a modi? d all-unit discount (MAUD) cost function. The holding costs at the customers are proportionate to the quantity and the holding time between comer time and collectable date. The costs for the two situations are compared under diversifying operating conditions. The authors leave off that cross-docking is more worthy when demands are less 2 It is false that the demand quantities are small, otherwise point-to-point deliveries are more meet. 830 J. Van Belle et al. / Omega 40 (2012) 827846 variable and when unit h olding costs at customer statuss are higher.On the other hand, it is less valuable when the average demands are close to truck load ability. Other quantitative forward motiones break a likeness between a situation with a cross-dock and a situation with a traditional distribution center. For instance, Kreng and subgenus Chen 25 compare the operational costs. Besides the transportation and holding costs, the exertion costs (more speci? c the setup costs) of the goods at the supplier are interpreted into flier. When a cross-dock is used, more frequent deliveries to the cross-dock are infallible and the batch surface needs to be smaller, which causes higher setup costs.Waller et al. 26 look to some(prenominal) situations from an inventory reduction perspective. Schaffer 8 discusses the successful implementation of crossdocking. When a company wants to introduce cross-docking, the introduction should be prepared very well. If the indispensable equipment is already available and because cross-docking seems simple, one substantially assumes that cross-docking post be implemented without much effort. However, cross-docking itself is quite complex and requires a high degree of coordination between the supply drawstring members (e. g. the timing of arrival and variance).So, the requirements for successful cross-docking should be understood thoroughly and the implementation should be planned care to the full. In 8, Schaffer elaborates on sixsome categories of requirements for a successful implementation. According to Witt 13 and to Yu and Egbelu 27, computer software system program to plan and control the cross-docking operations (e. g. a warehouse management system or WMS) plays an important role in the successful implementation of cross-docking. The necessitate ( automated) hardware for a cross-docking system (material handling devices, sorting systems, etc. ) might come off the shelf and is easily available today.But the software needs to be ta ilored to the speci? c requirements and is in general relatively less developed, although it is as important as hardware to cross-docking success. This is as well con? rmed by a go over among professionals who are involved in cross-docking and who designate IT system halt as a key barrier to effective cross-docking 3,4. Hence, the system requirements need to be carefully de? ned and analyse in order to prevent initiation the carnal system to discover subsequently on that point is no learning and intercourse system in place for successful operation.This software system trick only work correctly if it is fed with dead on target and timely information. Compared with regular distribution, the information ? ow to support cross-docking is signi? butt jointtly more important 24. For instance, to coordinate the inbound and outbound trucks to the appropriate docks, the arriving time and the destination of the freight need to be known originally the physiological arrival of th e goods (e. g. via attain shipping notice (ASN)). Several information applied science tools are available to take a leak this information ? ow, e. g. lectronic info interchange (EDI), shipping container marking (SCM), bar-coding and s tailning of products using orb(a) product code (UPC) 1. Regardless of which engineering is chosen, the supply kitchen stove partners must be able and willing to deliver the required information via this technology. A good cooperation crossways the supply chain lot bring on or break the cross-docking implementation 8,13,24. docking 1,29. In a two-touch or champion-stage cross-dock, products are received and staged on the dock until they are loaded for outbound transportation. Usually, the goods are put into zones comparable to their strip or stack door (see Fig. 3).In the case of a multiple-touch or two-stage cross-dock, products are received and staged on the dock, then they are recon? gured for shipment and are loaded in outbound trucks. In a typical con? guration, the incoming freight is ? rst put in zones alike(p) to the strip doors. The goods are then sorted to the zones corresponding to the stack doors (see Fig. 4). other distinction underside be do jibe to when the customer is assign to the mortal products 30. In predistribution cross-docking, the customer is appoint forwards the shipment leaves the supplier who takes care of supply (e. g. labeling and pricing) and sorting.This allows faster handling at the cross-dock. On the other hand, in post-distribution crossdocking, the al berth of goods to customers is done with(p) at the cross-dock. Still some other distinctions are possible. The German supermarket retailer Metro-AG for instance distinguishes sourceoriented and target-oriented cross-docking based on the location Fig. 3. A single-stage cross-dock in which the products are staged in zones corresponding to the stack doors (adapted from Gue and Kang 28). 3. Cross-dock characteristics Several char acteristics stick out be considered to distinguish between variant types of cross-docks (and cross-docking).A common distinction made in the literature is based on the number of touches 3 or stages 28. In one-touch cross-docking, products are touched only once, as they are received and loaded immediately in an outbound truck. This is as well called pure cross- Fig. 4. A two-stage cross-dock in which the products are staged in zones corresponding to the strip and stack doors and are sorted in between (adapted from Gue and Kang 28). J. Van Belle et al. / Omega 40 (2012) 827846 831 of the cross-docking terminals relative to suppliers and customers 31.Napolitano 32 distinguishes several types of cross-docking based on the intended use and in 29, eight different crossdocking techniques are listed. In this section, several characteristics are described that skunk be used to distinguish between different cross-dock types. 3 Note that hearty world characteristics of the cross-dock are considered, and not the properties from a speci? c ending problem related to cross-docking. For the papers included in the literature review (Section 4), the characteristics of the considered cross-docks will be listed in tables according to the characteristics described here. However, the structure of Section 4 is not based on these characteristics, but on the considered problem type. The characteristics loafer be divided into three conclaves physical characteristics, operational characteristics and characteristics about the ? ow of goods. 5 In the next sections, these groups will be described in more detail. 3. 1. Physical characteristics The physical characteristics are characteristics of the crossdock that are supposed to be ? xed (for a rather long time). The following physical characteristics are considered. normal Cross-docks dope book a large manakin of shapes.The shape nates be described by the letter corresponding to the shape I, L, U, T, H, E, . . . Number of doc k doors A cross-dock is too characterized by the number of dock doors it has. In practice, cross-docks range in size from 6 to 8 doors to more than 200 doors, and even a cross-dock with more than 500 doors exists 33. In the literature, some quantify the number of dock doors is limited to only 1 or 2. In these cases, the idea is not to exemplification a realistic cross-dock, but to gain some insight by schoolinging a simpli? ed deterrent example. Internal transportation The transportation internal the crossdock can be penalize manually (e. . by workers using forklifts) or there can be an automated system in place (e. g. a network of conveyor belts). The available infrastructure will of course be subordinate on the type of freight that is handled in the cross-dock. For instance, LTL carriers handle mostly palletized freight and so make use of forklifts. Conveyor systems on the other hand are among others used by parcel carriers, as they deal with many (small) packages. A conf ederacy of both transportation modes is also possible. 3. 2. Operational characteristics Some operational conclusions can in? uence the surgery of the cross-dock.These operational reserves lead to the following characteristics. helper mode According to Boysen and Fliedner 2, the service mode of a cross-dock determines the degrees of freedom in appoint inbound and outbound trucks to dock doors. In an exclusive mode of service, each dock door is either exclusively 3 Some of the characteristics described here are similar to the characteristics used by Boysen and Fliedner 2 to make a classi? cation of truck scheduling problems. However, they 2 consider not only real world characteristics, but also characteristics of the (mathematical) presents. At least(prenominal) for the papers in which these characteristics are described, i. e. , in which real world details of the cross-dock are considered (Sections 4. 54. 8). 5 This classi? cation is rather vague. For some characteristics, it is not clear in which group they ? t best or they can be charge to multiple groups. For instance, flying storage is considered as a ? ow characteristic. However, temporary storage can also be seen as a physical characteristic (storage is not possible because of space constraints) or operational characteristic (it can be an operational decision that storage is not allowed, e. . to avoid congestion inside the cross-dock). dedicated to inbound or outbound trucks. If this service mode is used, mostly one side of the cross-docking terminal is assigned to inbound trucks and the other side to outbound trucks. A endorsement mode is mixed mode. In this mode, inbound and outbound trucks can be svelte at all doors. These two modes can also be combined. In this combination mode, a subset of doors is operated in exclusive mode magical spell the rest of the doors is operated in mixed mode. Pre-emption If pre-emption is allowed, the loading or unload of a truck can be interrupted.This truck i s then outside from the dock and another truck takes its place. The un? nished truck has to be docked later on to ? nish the loading or set down. 3. 3. Flow characteristics The characteristics of the ? ow of goods that founder to be carry throughed by a cross-dock can be very different. The following characteristics are distinguished. Arrival radiation diagram The arrival times of the goods are determined by the arrival times of the inbound trucks. The arrival sort can be concentrated at one or more periods if the inbound trucks follow together at (more or less) the resembling times.For instance, a cross-dock in the LTL industry serving a certain geographic domain of a function commonly receives freight at two periods. Goods that guard to be transported from inside that area to another area are picked up during the day and all pick-me-up trucks arrive in the evening at the cross-dock. The goods are then sorted during the nighttime and the outbound trucks leave in the mo rning. To change the problem, several papers assume that the inbound trucks arrive together (at the beginning of the time horizon). On the other hand, freight from outside the region but doom for that area arrives in the ahead of time morning and is then istributed during the day. Another possibility is that the arrival manakin is scattered and the inbound trucks arrive at different times during the day. The arrival pattern has an in? uence on the congestion of the cross-dock and on the scheduling of workers and resources. Departure time The loss times of the trucks can be certified or not. In many cases there are no restrictions and the trucks leave the cross-dock afterwardswards all freight is loaded or unloaded. However, it is also possible that the trucks have to depart before a certain point in time, for instance in order to be on time for a next transportation task.In this case, there can be restrictions imposed on the departure times of the inbound trucks only, so tha t these trucks have to be unloaded on time. In a similar way, it is possible that only the outbound trucks have to leave the cross-dock before a certain moment. 6 For instance, in the parcel words sector, the outbound trucks usually leave at a ? xed point in time. Parcels arriving late have to wait until another truck departs for the same destination. It is also possible that both inbound and outbound trucks have restricted departure times.Product interchangeableness The freight handled at a cross-dock is in general not interchangeable. In this case, all products are dedicated to a speci? c destination7 or a speci? c outbound truck (pre-distribution). Information about the destination or the dedicated truck is normally known before the products arrive at the cross-dock. It is however also possible that exchangeability of products is allowed (post-distribution). In this situation, only the type of products to be loaded on the outbound trucks and the corresponding quantity is known (see footnote 7).When the products are interchangeable, usually some value-added activities (e. g. labeling) need to be performed. 6 This point in time can be dependent on the (due dates of the) actual load of the truck. 7 The assignment of the products to a speci? c outbound truck is then an operational decision. 832 J. Van Belle et al. / Omega 40 (2012) 827846 Temporary storage In pure cross-docking, the arriving freight is directly transported to outbound trucks, so no storage is needed. In practice however, this is rarely the case. In general, the goods are temporarily stored on the ? oor of the cross-docking terminal (e. . in front of the stack doors) or even in a (small) warehouse. However, it is possible that goods are not allowed to be stored. For instance, if refrigerated products have to be cross-docked in a non-cooled terminal, these products have to be directly locomote from a cooled inbound to a cooled outbound truck. 4. Literature review Cross-docking practitioners ha ve to deal with many decisions during the design and operational phase of cross-docks. These decisions can have a serious blow on the ef? ciency, so they have to be carefully taken. In the literature, several decision problems are study.Some of these problems are more implicated about decisions with effects on a longer term (strategic or tactical), maculation others deal with short-term decisions (operational). This section gives a review of the existing literature about crossdocking problems. The literature review is structured according to the basic planning process a manager, wanting to start with cross-docking, is confronted with. The ? rst decisions that have to be taken during the planning process are strategic decisions where will a cross-dock (or crossdocks) be located and what is the best layout of a cross-dock.Once the cross-dock is available, it will be part of a supply network (with one or more cross-docks). A tactical decision that has to be made then is how the goo ds will ? ow through the network to calumniate the costs, while make supply meet demand. Next, the manager is set about with the operational decision (although it has also tactical aspects) of vehicle routing before arriving at the cross-dock, freight has to be picked up at discordant(a) locations, and the goods have to be delivered to multiple locations after consolidation at the cross-docking terminal.Other operational decisions deal with the assignment of trucks to dock doors or the scheduling of the trucks, and with the location where goods will be temporarily stored. Of course, the manager will also be confronted with problems that are not speci? c for cross-docking the scheduling of the internal resources for the loading and unloading of the freight (e. g. the workforce), choosing the best staging strategy and determine an optimal truck packaging sequence. The next sections describe the cross-docking problems dealt with in the literature.Only the problems that are speci? c for cross-docking are considered. First, the strategic decisions are discussed the location of cross-docks and layout design. The tactical problem of cross-docking networks is described next. Further, the operational decisions are handled vehicle routing, dock door assignment, truck scheduling and temporary storage. Finally, some papers that study other issues related to crossdocking are discussed. 4. 1. Location of cross-docks The location of one or more cross-docks is part of the design of a distribution network or supply chain.An important strategic decision that has to be made concerns the position of these crossdocks. This problem cannot be handled isolated from the decisions that determine how the goods ? ow through this network. The determination of the ? ow of goods is discussed in Section 4. 3, but problems that also involve a decision about the location are considered here. The problem where to locate facilities (e. g. distribution centers or kit and boodles) has attra cted a considerable amount of attention. 8 The papers discussed in this section determine specially the optimal ? ow of goods through the network.Moreover, they regard the facilities to be cross-docks because they explicitly take individual vehicles into account or because temporary storage is not allowed. A ? rst study about the location of cross-docks is performed by call and Song 34. In the considered problem, goods have to be transported from supply to demand nodes via a cross-dock (direct shipments are not allowed). The cross-dock can be chosen from a set of possible cross-dock locations, each with an associated ? xed cost. The demands are delusive to be known and there are two types of vehicles with a different message and cost. The aim is to ? d which cross-docks should be used and how many vehicles are needed on each link in order to play down the perfect cost. This ingrained cost consists of the ? xed costs of the used cross-docks and the transportation costs. The a uthors present an integer programming model of the problem. This model is very similar to the model presented by Donaldson et al. 35 and genus Musa et al. 36 (discussed in Section 4. 3) and similar simplifying assumptions are applied. Compared with these two papers however, the memory access of Sung and Song 34 does not consider direct shipments but does include the location decision.Because the problem is NP-hard, a sacred search-based algorithmic ruleic ruleic ruleic programic ruleic ruleic program is offerd to put to work the problem. The replys determine how the goods ? ow through the network. Based on this ? ow, the number of vehicles can be derived by settlement a subproblem. Some countingal experiments are performed on generated essay instances and indicate that the proposed algorithm ? nds good possible etymons deep down a reasonable time. Sung and Yang 37 extend this work and propose a small improvement to the tabu search algorithm.The authors also present a set-partitioning-based conceptualisation of the problem and propose a branch-and-price algorithm based on this locution to reserve exact solutions. The numerational results show that this algorithm gives demote results in terms of the number of (smallscale) problem instances authorized and the required computation time compared with the results obtained by solving the integer programming model with the optimisation software package CPLEX. ? ? Gumus and Bookbinder 38 study a similar problem, but now direct shipments are allowed and multiple product types are considered (multicommodity).The facility cost for each crossdock consists of a ? xed cost and a throughput cost charged per unit load. The transportation cost also has two components a ? xed cost for each truck and a variable cost per unit load per unit distance. A belong cost that is taken into account is the cost for intransit inventory. In this progression, the synchronization of inbound and outbound trucks is not taken into account. The authors provide a mixed integer programming model of the problem. By solving several smaller problem instances optimally (with the optimization software packages LINGO and CPLEX), the in? ence of several cost parameters is studied. The authors conclude that the optimal number of cross-docks is an change magnitude function of the ratio between the (? xed) truck cost and the (? xed) facility cost. A different approach is taken by Jayaraman and Ross 39. They study a multi-echelon problem in which goods (from multiple product families) have to be transported from a central manufacturing plant to one or more distribution centers. From there, the goods are moved via cross-docks to the customers. The problem is tackled in two stages. In the ? st stage, a strategic model is used to select the best set of locations for the distribution centers and cross-docks. The authors provide an integer programming reflection that aims to minimize the ? xed costs associated wit h operating open distribution centers and cross-docks and the 8 Several references can be found in the papers discussed in this section. J. Van Belle et al. / Omega 40 (2012) 827846 833 various transportation costs. Demand split is not allowed customers have to be assigned to single cross-docks while crossdocks have to be assigned to single distribution centers only.In the instant stage, an operational model decides upon the quantities of each product type that need to be transported via distribution centers and cross-docks. The model tries to minimize the transportation costs while satisfying customer demand. This model is less restrictive than the ? rst model (it relaxes for instance the demand splitting assumption) and can be executed once the open distribution centers and cross-docks are determined with the help of the ? rst model. two models are more simpli? ed compared with the old approaches.For instance, individual vehicles are not considered and the transportation cost is proportional to the quantity to ship. The authors propose a simulated annealing approach to go larger problem instances. The computational experiments on generated problem instances indicate that the trial-and-error gives results with a deviation of about 4% of the optimal solution (obtained with LINGO), but 300400 times faster. In 40, the same authors present two other trial-and-error programs to tackle the problem. Both heuristics are based on simulated annealing but use an extra mechanism to avoid topically optimal solutions.The ? rst heuristic makes use of a tabu list, the piece heuristic allows a sudden re-scaling of the system temperature. For both heuristics, the solution quality and computational performance are tested for different cooling schemes. The data-based results indicate that the simulated annealing heuristic combined with tabu search gives better solutions in slightly more time. Bachlaus et al. 41 also consider a multi-echelon supply chain network, includi ng suppliers, plants, distribution centers, crossdocks and customers. The goal is to optimize the material ? w throughout the supply chain and to identify the optimal number and location of suppliers, plants, distribution centers and crossdocks. The problem is formulated as a multi-objective optimization model that tries to minimize the total cost and to maximize the plant and volume ? exibility. Because of the computational complexity of the problem, the authors propose a variant of particle hum optimization (PSO) to design the supply chain. Some computational experiments are conducted and the results show that the proposed solution approach gives better results than a ancestral algorithm and two other PSO variants. his at the cost of additional corners which reduce the labor ef? ciency (two inside and two outside corners for T, quaternity inside and four outside corners for X). An inside corner renders some doors unusable, while doors slightly an outside corner have less ? oor space available to stage freight. So, these additional corners are a ? xed cost, which begins to pay off for larger docks. It is however not everlastingly easy to predict which shape is better, because this also depends on e. g. the freight ? ow pattern. Other papers deal with the design of the storage area where the freight can be temporarily staged (on the ? or or in racks). In many cases, the freight is placed in several parallel rows and the workers can move between these rows. Vis and Roodbergen 16 deal with the operational decision where to temporarily store incoming freight (see Section 4. 7). The proposed algorithm can also be used during the design phase to determine the optimal number of parallel storage rows and their lengths. The (single-stage or two-stage) storage area can also be organized in parallel lanes directly next to each other which can only be accessed at both ends.Gue and Kang 28 make use of simulation to study the behavior of these alleged(prenominal) stag ing queues. The results project that, for a single-stage storage area, it is better to have more short lanes than fewer long ones, at least when the workers follow a rational approach. The results also indicate that two-stage cross-docking has a signi? cantly lower throughput than single-stage cross-docking. 4. 3. Cross-docking networks Some authors do not study problems concerning a single cross-dock, but consider a network that contains one or more cross-docks.The aim is to determine the ? ow of goods through such a network in order to reduce costs, while making supply meet demand. The research of Lim et al. 42 extends the traditional transshipment problem. The transshipment problem consists of a number of supply, transshipment and demand nodes. The arcs between these nodes have different capacity limits and costs. The objective is to ? nd a minimum cost ? ow that meets all demands and the capacity constraints. In the extended transshipment problem, storage is allowed at the tran sshipment centers.These centers can be considered as cross-docks because the aim of the model is to minimize or eliminate holdover inventory. Moreover, this problem takes supplier and customer time windows into account and considers the capacity and holding costs of the crossdocks. All shipments have to pass via a cross-dock, so no direct shipments are considered. Similar to the original problem, the objective is to minimize the total cost (transportation costs and holding costs) while meeting demand and respecting the time windows and capacity constraints.If multiple departures and deliveries within a time window are allowed (multiple shipping multiple delivery), the authors show that a time-expanded network can be used to formulate the problem as a minimum cost ? ow problem (MCFP) which can be puzzle out in multinomial time. For other cases, the authors prove that the problem is NP-hard. For the special case when only one delivery or departure is allowed within a time window and the departure and arrival times are ? xed (single shippingsingle delivery with ? xed schedules), a contagious algorithm is developed by Miao et al. 43.This heuristic gives better results (in terms of solution quality and computation time) than solving the integer programming cookery of the problem with CPLEX (with a time limit). Chen et al. 44 study a similar problem which they call the multiple cross-dock problem. The major differences are that supplies and demands are not-splittable and that different products can be considered (multicommodity ? ow problem). Also, transportation time is in this approach not taken into account. 4. 2. Layout design Once the location of a cross-dock is determined, another strategic decision that has to be made is to contain the layout of the cross-dock.The layout is interpreted as the place and shape of the cross-dock, as well as the dimension and shape of the internal cross-dock areas and their arrangement. Bartholdi and Gue 5 focus on the shap e of a cross-dock. Most existing cross-docks are long, narrow rectangles (I-shape), but there are also cross-docks shaped like an L, U, T, H or E. The crossdock shape is sometimes determined by simple constraints (e. g. size and shape of the lot on which it will stand), but in this paper the focus is on how the shape affects cross-dock performance.Several experiments are performed in which the labor costs (estimated by the total hold up distance)9 are measured for different shapes. The experiments suggest that an I-shape is the most ef? cient for smaller cross-docks (fewer than about 150 doors). For docks of intermediate size, a T-shape is best and for more than 200 doors (approximately) an X-shape is best. Cross-docks with a T or X-shape have a greater centrality. However, they achieve 9 here(predicate) and in the following pages, the travel distance is the distance traveled (by workers, forklifts, . . ) in order to transfer the goods internally from the inbound to the outbound t ruck. 834 J. Van Belle et al. / Omega 40 (2012) 827846 An integer programming formulation of the problem is provided, together with a proof of its NP-completeness. The authors propose three heuristics (simulated annealing, tabu search and a combination of both) to solve the problem. These heuristics provide better solutions than those obtained by solving the integer programming formulation with CPLEX, within only less than 10% the time used by CPLEX.Among the three heuristics, tabu search seems to give the best results. The preceding(prenominal) studies represent the shipment of goods as ? ows. idiosyncratic transportation units are not considered and the transportation cost is proportional to the quantity to ship. However, to take advantage of consolidation, the vehicle transportation cost should be taken into account. A ? rst approach that does consider the transportation vehicles explicitly (and this is wherefore the authors regard it as cross-docking) is taken by Donaldson et al. 35.In the considered problem, the goal is to determine whether to route freight directly from suppliers to customers or via a cross-dock and how many vehicles should be scheduled on each transportation link in order to minimize the transportation costs. Compared with the previous approaches however, this problem is more simpli? ed, e. g. storage at the cross-docks is not considered and the synchronization of inbound and outbound trucks is unexpended out of the problem. The authors eliminate connect with a large transportation time in an attempt to consider time windows.However, when the due dates at the destination nodes can vary for the different goods, it is possible that the vehicle parcelling of an obtained solution violates the due dates in practice. The authors present an integer programming model of the problem. Because the problem is dif? cult to solve with branch-and-bound algorithms, an alternative approach is proposed. In this approach, an iterative procedure is u sed in which either the integrality restrictions on the cogitate from origin nodes to the cross-docks or on the links from the cross-docks to the destination nodes are relaxed.This relaxation heuristic provides near optimal solutions in an delightful time. The authors used this approach to compare several scenarios (with a different number of cross-docks at different places) for the network design of a postal service company. The same problem is also studied by Musa et al. 36. They propose an ant colony optimization (ACO) heuristic to solve the problem and show that this heuristic gives in a short time slightly better results than a branch-and-bound approach (with the optimization software package LINDO) that requires a much longer time.The approach of Ma et al. 45 takes most of the above-mentioned concerns into account. The so-called shipment consolidation problem (SCP) considers supplier and customer time windows and also the transportation times between the network nodes. Moreo ver, storage at the transshipment centers (cross-docks) is taken into account, shipments can be transported directly to their destination or via a cross-dock and the transportation cost accounts for the number of trucks. However, only one type of products is considered (single commodity).Again, the objective is to minimize the total cost (transportation and inventory cost) while satisfying the constraints imposed by the time windows. The authors present an integer programming model of the problem and show that it is NP-complete in the reinforced sense. Therefore, the authors propose a (two-stage) heuristic algorithm to solve the problem. The basic idea of the algorithm is to consider ? rst trucks that can be fully loaded and then to ? nd solutions that combine several smaller loads that are not considered yet. In the ? st stage, a full truckload plan (TL plan) and an initial less-than-truckload plan (LTL plan) are constructed. In the second stage, this initial LTL plan is improved iteratively by using a metaheuristic (squeaky wheel optimization or contagious algorithm). The computational experiments indicate that the proposed heuristic gives competitive results compared to CPLEX (with a time limit) within a much shorter time. 4. 4. Vehicle routing Freight destined for a cross-dock needs in many cases to be picked up at various locations, and has to be delivered to multiple locations after consolidation at the cross-dock.Both the cartridge and the delivery process can be seen as a vehicle routing problem and some studies consider cross-docking and vehicle routing simultaneously. A ? rst approach is taken by Lee et al. 46. The aim is to ? nd an optimal routing schedule for pickup and delivery (within the planning horizon) that minimizes the sum of transportation cost and ? xed costs of the vehicles. It is pretended that split deliveries are not allowed and all pickup vehicles should arrive at the crossdock simultaneously to prevent hold times for the outbou nd trucks. While this can be a valid constraint for some cases (see Section 3. ), this is not broadly true. The authors present an integer programming model of the problem, which however seems unsatisfactory to solve the described problem. A tabu search algorithm is proposed to ? nd solutions. This approach corresponds to the solving of two vehicle routing problems (one for pickup and one for delivery). The second routing problem can only start when the ? rst one is ? nished and the complete process has to be ? nished within a certain planning horizon. Liao et al. 47 propose another tabu search algorithm to solve the same problem. pilar cyst et al. 12 study the so-called vehicle routing problem with cross-docking (VRPCD). In this problem, orders from suppliers have to be picked up by a homogeneous ? eet of vehicles. These orders are then consolidated at a cross-dock and immediately delivered to customers by the same set of vehicles, without intermediate storage at the cross-dock. During the consolidation, goods are unloaded from the inbound vehicles and reloaded on outbound vehicles. The unloading must be finish before reloading starts. The authors assume that the duration of the unloading consists of a ? ed time for forwardness and a duration proportional to the load size. It is also delusive that if the delivery will be executed by the same vehicle as used for pickup, the unloading is not necessary (independent of the sequence in which the vehicle is loaded during the pickup tour). A time window is de? ned for all suppliers and customers and orders are not splittable. In the case without consolidation, the solution of this problem can be found by solving two vehicle routing problems (one for pickup and one for delivery). Because of the consolidation however, the pickup and delivery routes are not independent.Only attempt to minimize the distance of the pickup and delivery routes is not suf? cient, the exchanges of orders at the cross-dock also have to be taken into account. These two aspects usually con? ict with each other. The authors present a mixed integer programming formulation of the problem in which the objective is to minimize the total travel time of all vehicles. This formulation contains many variables and constraints, so the authors propose to use tabu search embed within an adaptive memory procedure. This mode is tested on realistic data involving up to 200 suppliercustomer pairs.Experimental results show that the algorithm can piddle solutions less than 1% away from the optimum within short computing times (less than 5 s) for small problem instances. For larger instances, the gap with a lower bound is less than 5% while the computation time stays below 5 min. 4. 5. Dock door assignment When an inbound or outbound truck arrives at the cross-dock, it has to be decided to which dock door the truck should be assigned. A good assignment can increase the productiveness of the cross-dock and can decrease the (handling) costs. So, the dock door assignment problem tries to ? d the optimal assignment of inbound and outbound trucks to dock doors. It is assumed that there are at least as much dock doors as trucks, so each truck will J. Van Belle et al. / Omega 40 (2012) 827846 835 Table 1 Characteristics of the papers discussed in Section 4. 5. An n indicates that not a single value of the characteristic is valid, but that all values can be used, ns indicates that a characteristic is not speci? ed. Paper(s) Shape No. of doors n n n n n n n n n n n n Internal transport manually manually manually Manually Manually n Service mode max liquid ecstasy Exclusive Exclusive Exclusive ExclusiveExclusive Exclusive mingled Exclusive Mixed Exclusive Interchangeability Temporary storage Yes No ns ns ns Yes ns Yes Yes ns ns ns mint candy 48 Tsui and Chang 49,50 ? Bermudez and Cole 51 Cohen and Keren 52 Oh et al. 53 Bartholdi and Gue 54 Gue 33 chocolate-brown 55 (semi-permanent) Brown 55 (dynamic) Bozer and Carl o 56 (semi-permanent) Bozer and Carlo 56 (dynamic) Yu et al. 57 I I n I I I I n n n n n Manually Manually Manually Manually Manually Manually hand truck finish Destination Destination Destination Destination Destination Destination Truck Destination Truck Destination e assigned to a different door and time aspects are not taken into account. If this condition is not ful? lled, the dock doors can be seen as (scarce) resources that have to be scheduled over time. This is the so-called truck scheduling problem. Both problems can be quite complex due to the number of doors and the dynamic nature of the problem. This section deals with the dock door assignment problem, while truck scheduling problems are discussed in Section 4. 6. The assignment of dock doors can be executed on a mid-term or short-term horizon 2.Several papers solve the assignment problem on a mid-term horizon. Then, each dock door serves a speci? c inbound or outbound destination for a longer period of time (e. g. 6 mo nths). 10 All trucks coming from the same origin or having the same destination are assigned to the same dock. Such a ? xed assignment is easier for workers because they know exactly to which dock door they need to ship each load, but it comes at the expense of a reduced ? exibility. Even if a ? xed assignment is used, it is important that the dock doors are reassigned when there is a signi? cant change in the shipping pattern.When data about the inbound trucks are known far enough in advance, the assignment of the trucks can be solved on a shortterm horizon. The trucks itself are assigned to the dock doors based on the actual freight ? ow. This ? oating dock concept is put forward by Peck 48 who studied the material handling operations in an LTL terminal. Such an assignment implies that the workers are every day confronted with a different door for the same destination and have to take care that the freight is loaded into the correct truck. The use of modern information technology (e. g. ar code or RFID examine together with a WMS) can be useful for this end. A combination of both is also possible. Several papers consider a cross-dock in which destinations are assigned to stack doors (so the outbound trucks are assigned on a mid-term horizon), while the assignment of the inbound trucks is done on a short-term horizon. The characteristics of the cross-docks considered in the following papers are summarized in Table 1. As time aspects are neglected and there are enough available dock doors, the preemption, arrival pattern and departure time characteristic are not pertinent here and are not shown.In his dissertation, Peck 48 develops a detailed simulation model of an LTL terminal and tries to assign the trucks to dock doors in order to minimize the travel time11 of the shipments. It is assumed that the travel time to transport the products between This includes that the cross-dock operates in exclusive service mode. Here and in the following pages, the travel time is the time required to transfer the goods internally from the inbound to the outbound truck. 11 10 two trucks can be expressed as a function of the distance, based on the actual contents of the trucks and the required means of transport (2-wheeler, 4-wheeler or forklift).The cognomen of doors as either strip or stack doors is ? xed beforehand. The problem is formulated as an integer programming model and because of the computational complexity, a heuristic (greedy balance algorithm) is provided to solve it. Simulation shows that his heuristic improves an assignment based on experience and intuition. Another early study about the assignment of trucks to dock doors is performed by Tsui and Chang 49. In this paper, a crossdock is considered in which no storage is provided all shipments go directly from inbound to outbound trucks.The problem is solved on a mid-term horizon, so the origins and destinations have to be assigned to dock doors, not the trucks itself. The designation of doors as strip or stack doors is ? xed. The assignment problem is formulated as a linear programming problem that tries to minimize the travel distance of the forklifts (the number of forklift trips required to carry a certain load is assumed to be known). To solve it, the authors propose a simple heuristic method to ? nd a local optimum.The authors do not provide test results, but conclude that the found solution can serve as a good starting time point for the cross-dock manager. There exist exact algorithms to solve bilinear optimization problems, but these are not very suited for this problem as the same authors mention in Tsui and Chang 50. In this paper, a branch-and-bound algorithm is proposed to solve the dock door assignment problem exactly. The numerical tests show that this algorithm is however computational expensive. ? Bermudez and Cole 51 deal with a very similar problem, but now there is no ? ed designation for the doors. All doors can have assigned either an orig in or a destination. The mathematical model of Tsui and Chang 49 is adapted to take this into account. The objective function minimizes the total weighted travel distance sort of of the real travel distance. A genetic algorithm (GA) is propose