The design of courier transportation networks with a nonlinear zero-one programming model

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1 The design of courier ransporaion newors wih a nonlinear zero-one programming model Boliang Lin School of Traffic and Transporaion, Being Jiaoong Universiy, Being , People s Republic of China (A preprin manuscrip submied o arxiv, May 2, 2018) Abrac: The courier indury is one of he mo essenial pars of he modern logiics. Meanwhile, he courier ransporaion newor is one of he mo imporan infrarucures of courier enerprises o ae paricipae ino operaion. This paper presens a combinaorial opimizaion model for he courier ransporaion newor design problem, and he aim of newor opimizaion is o deermine he ransporaion organizaion mode for each courier flow. A nonlinear zero-one ineger programming model is formulaed o describe he problem, he objecive funcion of he model is inended o minimize he oal co including he accumulaion co, he ransporaion co and he ransfer co. Also, we ae ransporaion modes and ypes of ranspor carriers ino accoun in he objecive funcion. The conrains of he combinaorial opimizaion model conain capaciies of ransfer and soring ceners and delivery daes predefined. Keywords: Courier ransporaion newor; Transfer ; Delivery dae; Nonlinear zero-one programming 1 Inroducion The rapid rise of e-commerce imulaed by he inerne, he increase of courier demand caused by he newor shopping and he developmen of various ransporaion modes have promoed he developmen of he courier indury. The courier indury has experienced fa developmen in China in he pa decade. Tae China as an example, in 2013, he growh rae of courier business reached he highe level in hiory which is 61.6%. According o he recen daa, he courier business volume reached billion pieces wih a growh rae of 51.4%, which was 6.5 imes he GDP growh rae of China in As he developmen growh of he economy ends o abilize, he developmen speed of he courier indury also ends o be able. In his siuaion, he opimizaion of he courier ransporaion newor can promoe he developmen of he courier indury furher, and improve he economic developmen in urn. Meanwhile, as he carriers of courier ransporaion, road ransporaion, railway ransporaion and air ransporaion have achieved grea progress and proposed brand new courier ransporaion ices o mee he courier ransporaion demand. Coninuous compeiion and cooperaion among hose hree ransporaion modes have promoed he improvemen of China s ransporaion syem and he address: bllin@bju.edu.cn (B.-L. Lin). 1

2 developmen of courier indury. Currenly, able Chinese courier enerprises include: S.F. Express, YTO Express, ZTO Express, STO Express, and Yunda Express, ec. The developmen scales of China s five large courier enerprises by he end of 2016 are shown in Table 1. Table 1. Five major courier enerprises developmen scales as of he end of S.F. 2 YTO 3 ZTO 4 STO 5 Yunda 6 Urban coverage above couny-level 91.6% 96.1% 96.6% 96.4% 95.0% Terminal oules Main ransporaion lines on Land Transshipmen ceners Self-operaed vehicles Self-operaed freighers Opimizaion of he newor has a deep influence on he imeliness and cos. This paper eablished a nonlinear zero-one ineger programming model o opimize he courier delivery newor so ha courier can be delivered o cuomers a a lower co wihin he specified delivery ime. The remainder of he paper is organized as follows. Secion 2 reviews relevan lieraure relaed o he courier ransporaion newor and is opimizaion. Secion 3 inroduces he problem we ry o solve in his paper. Secion 4 presens he noaions definiion and modeling assumpions of he opimizaion model, and also gives a mahemaical programming model for he problem. Secion 5 concludes he paper. 2 Lieraure review Before udying he design problem of he courier ransporaion newor, we should have a cerain degree underanding of he rucure and characeriics of he courier ransporaion newor. For he udy of he courier operaional newor, Ayin (1995) inroduced a framewor for he design of huband-spoe diribuion newor. Jeong e al. (2007) described he hub-and-spoe rail newors. Tan (2015) udied he opology rucure of he courier newor, he raffic spaial-emporal dynamics and he pacage delay diribuions based on he logiics daa. The courier ransporaion newor design and he opimizaion problem are our focuses in his paper. Barnhar e al. (2002) focused on a paricular ice newor design applicaion o deermine co minimizing roues and schedules wih ime windows. Schwind and unel (2010) presened he research aiming a a dynamic opimizaion of our planning process in courier, express and parcel delivery newors. Alibeyg e al. (2016) presened a class of hub newor design problems wih profioriened objecives inegraing several locaional and newor design decisions. Di e al. (2018) udied a new discree newor design problem for meropolian areas. In addiion, mulimodal ranspor is generally applied o courier operaional newor. The inermodal hub newor design problem began wih he pioneering wor of Slac (1990), who analyzed he changes ha were ransforming inermodal ransporaion in he Unied Saed and Canada. There re always ime conrains in he newor design problem. Iyer and Raliff (1990) organized a guaraneed ime diribuion syem. Kara (2011) focused on he minimizaion of he arrival ime of 1 Par of he daa is cied from he CICC repor (hp:// 2 The daa is cied from SF Holdings Co., Ld Annual Repor (hp://app.finance.china.com.cn/oc/daa/view_noice.php?symbol=002352&id= ) 3 The daa is cied from YTO Express Co., Ld Annual Repor (hp:// 4 The daa is cied from ZTO Express 2016 Q4h Repor (hp://ech.sina.com.cn/i/ /doc-ifyavvs shml) 5 The daa is cied from STO Express Co., Ld Annual Repor (hp:// 6 The daa is cied from Yunda Express Co., Ld Annual Repor (hp:// 2

3 he la arrived iem in cargo delivery syems. The conribuion of his paper is he consideraion of accumulaion process of courier flows, he limied capaciy of faciliies and he conrain of delivery ime based on real life condiions. The accumulaion ime calculaed in his paper is he accumulaion parameer muliplied by he andard courier uni. The delivery ime of courier flows consis of ransporaion ime, ransfer operaion ime and accumulaion ime. 3 Problem descripion Here, we use Fig. 1 as an example o illurae he courier delivery process. Courier a each pic-up aion is sen o he erminal delivery poins, hen delivered o local diribuion ceners, courier a local diribuion ceners can be sen o he airpors, railway aions or ransfer and soring ceners, or can be sen direcly o a cerain local diribuion cener of erminal ciy. Afer courier arrives a he local diribuion cener in he ciy, i ll be delivered o he nearby erminal diribuion s by small van-body rucs, hen, sen o he communiy oules by small ranspor carriers. S2 T2 S1 H1 A1 R1 A2 R2 H2 S3 T3 The Local diribuion cener The airpor The railwap aion The ransfer and soring cener The erminal delivery poin Air ranspor Railway ranspor Road ranspor Fig. 1. The courier ransporaion newor Here, we ae he courier flow N S1, from S1 o as an example o illurae he design idea of he courier ransporaion newor opimizaion. There are several possible ransporaion opions from S1 o : (1) S1 (2) S1 H1 (3) S1 H2 (4) S1 H1 H2 (5) S1 A1 A2 (6) S1 H1 A1 A2 (7) S1 A1 A2 H2 (8) S1 H1 A1 A2 H2 (9) S1 R1 R2 (10)S1 H1 R1 R2 (11) S1 R1 R2 H2 (12)S1 H1 R1 R2 H2 We need o consider he maer of which poin pairs provide direc ransporaion ices and wha ype of ransfer opion is used for each courier flow. The aim of opimizaion is o minimize he oal 3

4 co of he whole courier ransporaion newor wih real-world conrains lie delivery ime, capabiliy of ransfer s ec., which coniues he combinaorial opimizaion problem of courier ransporaion newor design solved by his paper. 4. Mahemaical formulaion This secion will derive a mahemaical model for he courier ransporaion newor opimizaion problem according he above descripion. In order o faciliae readers underanding of he model, here we fir li all he noaions involved in he modeling process (including ses, parameers and decision variables) as follows: 4.1 noaions Ses S The se of all s in he courier ransporaion newor. N. The ransfer s of courier flows which consi of origins, deinaions and S,,,. shp S The se of original courier flows S P ( i, j) ransfer s passed across by he courier flow, The se of poenial ransfer s (no including i and j, he j in his paper refers specifically o local diribuion ceners of he erminal ciy and i can be any ype of s) ha may be passed hrough by he courier flow f. Parameers λ The ime value used o unify he dimension of each facor in he objecive funcion. acum i rans The volume of he andard courier uni loaded by a ranspor carrier (such as a ruc of a cerain onnage capaciy) if he direc ransporaion is available beween i and j. The accumulaion parameer of i covering all he facors affecing he accumulaion ime excep for he ranspor uni. The ransporaion cos of a single ranspor uni from i o j. sor R The daily soring quaniy of he soring cener. opr The operaion cos of soring operaion uni volume of soring cener. The daily original courier flows (in andard courier unis) which origin a local N f diribuion cener i and are deined o erminal local diribuion cener j The daily average courier flows from i o j, including he original demand N a i and oher flows sored and ransferred a i arriving a local diribuion cener j. F The ice flows from i o j. The daily needed frequency of ranspor carriers on he direc ice arc i j. xfer The ransfer capaciy a. rans The ravel ime of he direc ransporaion from s o. opr The ransfer operaion ime a. 1 2 n 4

5 freq The waiing ime a of he accumulaed ransferred courier in he direcion v from o v. T The delivery ime limis from s o. nex The nex ransfer afer i on he ransfer S. hdway The headway on he direc ransporaion arc i j, which is he deparure inervals of ranspor carriers. Decision Variables x 1 if he fir ransfer is when he courier flow is ranspored from x y i o j, and is equal o zero oherwise. y 1 if he courier flow can be ranspored from i o j direcly, and is zero oherwise. 4.2 Basic assumpions of he mahemaical model Assumpion 1: Properies of he courier are consien (Usually, he courier can be divided ino wo ypes according o he delivery daes offered: he ordinary courier and he express, which can be spli ino wo ypes of courier newors when processing, hus, we only consider one of hem here.). Assumpion 2: The relaively low weigh of he courier resuls in he volume, no he weigh, which ranspor carriers fir reric. Because of he differen s of courier, we use a cubic meer (or a palle allowable volume) as a andard courier uni (which probably is composed of dozens or hundreds of he original courier). Assumpion 3: A courier flow is no allowed o be spli among muliple pahs or ransporaion modes. Assumpion 4: The of a bach of ransporaion volume (for example, for a 50-on ruc, andard courier uni could be =60) is nown if direc ransporaion ice is provided beween i and j. 4.3 Descripion of conrains and inermediae decision variables According o he above variable definiion, he binary variable x =1 represens he courier flow f is ranspored o hrough cerain ransporaion ices from i (which could be he local diribuion cener, he airpor, he railway aion or he soring cener). The binary variable y =1 expresses ha he courier flow f is ranspored o he erminal diribuion cener j direcly. According o assumpion 3, i s clear ha here is a uniqueness condiion for he direc and ransfer ransporaion: y x 1 (4) P (, i j) Noice ha i means he direc ransporaion ice is available beween i o j when x =1 (where direc refers o no changes in he ransporaion mode and no soring operaions on he way, and i ll ill be he direc ransporaion beween i o j from a courier enerprise s perspecive if he courier enerprise consigns shipmen o he airpor, and hen he air ranspor deparmen delivers shipmen o hrough several ransfers in ransi). Thus, here is a variable correlaion conrain: x y i, js, P(, i j) (5) i 5

6 The variable f is an inermediae variable according o definiion, whose specific expression is a recursive formula wih he following form: i f N fsj x i, j S (6) sj ss If he direc ransporaion ice is available beween i and j, and he daily direc volume is F, i is clear ha: F X f fx i, j S (7) j i i S I s easy o find ou ha he direc volume here conains he ransferred courier from s before i and courier flows whose deinaions are j or oher s behind j. When he capaciy of a ranspor carrier which es on a direc ransporaion arc is, he daily needed frequency of ranspor carriers on his direc ransporaion arc will be: F / (8) The courier flow which arrives a he diribuion cener and he soring cener is random, which maes he average waiing ime of a courier uni ha is on he direc ransporaion arc from i o j is he half of he headway. freq 1 12 hdway = 2 (9) F For example, we analyze he waiing ime (excluding he operaion ime) for he accumulaion of courier flows a a soring cener. Assume ha here are four rucs operaed on he direc ransporaion arc i j, which is, maing he headway is 12-hour, ha is, he average =4 frequency delay (he waiing ime for he accumulaion) of he courier flow in his circumance is freq 1 hdway 6 hours. 2 Noice ha he daily volume on he direc ransporaion arc i j is, hus, if he direc ransporaion ice is offered on he arc i j, he oal frequency delay of courier flows which is on his arc would be: freq F 12 (10) Considering ha courier flows are no always arriving evenly, here could exis accumulaion inerrupions. Therefore, he oal frequency delay of courier flows should be expressed more ricly as follows: freq acum F (11) i acum Here, i is less han 12 in general. In a real ransporaion process, courier flows don arrive in a balanced manner usually, and is value is also affeced by he of a aion and oher facors, he specific value may generally be recommended o be 10 o If is a soring cener, according o he definiion of decision f, we can conclude he daily soring quaniy of his soring cener would be: R X fx sor is js F x and inermediae variable (12) The oal ime consumpion of all pars in ransi of he courier flow should be less han he delivery dae T of he courier flow N if T is offered. The oal ime consumpion is discussed in he following wo pars: (1) The oal ransporaion ime of he direc ransporaion 6

7 The oal ransporaion ime of he direc ransporaion would be rans when y 1, ha is, courier flow N is ranspored direcly from original local diribuion cener s o erminal local diribuion cener. (2) The oal ransporaion ime of he ransfer ransporaion The ransporaion ime required is composed of he ravel ime on each ransporaion arc and he ransfer ime a each ransfer if he courier flow N is ransferred several imes before reaching he erminal local diribuion cener. The ransfer for courier flow N denoed as S 1, 2,, n, where 1 is he origin s of he courier flow and n is he deinaion, 2 would be he fir ransfer which he courier flow nex ransfer of courier flow N as, S N passes hrough. Recording he nex S can be defined as follows: s,,, nex nex 1 2 1, n n1, The recursive formula of ransfer s can be expressed as: nex jy x (13) P (, i j) According o he expression of he ransfer, he oal ravel ime of arcs should be: rans uv uvs, uv In he above formula, uv S means u v is one of he ransporaion arcs of he ransfer S, he ime delay on he s of he ransfer S is he sum of ransfer ime a each. For he soring cener, he ransfer ime consis of operaion ime and accumulaion ime: opr freq vs, s, 4.4 The nonlinear zero-one ineger programming model According o he above discussion, he opimizaion model of he courier ransporaion newor design can be presened as: s.. v acum rans sor opr opr min Z λi X y R X λ is js S x y y sor P (, i j) i x R X 1 (14) i, j S (15) i, js, P(, i j) (16) xfer y T rans rans opr freq uv v uvs, uv vs, s, y, x 1, 0 S (17),, (, ) shp N S (18) i js P i j (19) In he objecive funcion (14), he fir erm accouns for he accumulaion cos and ransporaion cos in he direc ransporaion, he second erm calculaes he ransfer operaion cos and ransfer ime cos of ransfer ransporaion. Conrain (15) ensures ha each courier can reach is deinaion and limis he ransporaion organizaion mode for courier ha can only be seleced for he direc ransporaion or he ransfer ransporaion. Conrain (16) limis he connecion beween s: 7

8 y = 0, x = 0 means ha he direc ransporaion is unavailable beween i and, and y i i 1, x 0 or 1 means ha could be he fir ransfer on he pah from i o j when direc ransporaion is available beween i and, ha is, he courier flow from i o j can choose he direc ransporaion or he ransfer ransporaion. Conrain (17) is he capaciy conrain a he ransfer. Conrain (18) is he delivery ime limiaion, he delivery ime includes ransporaion ime, ransfer operaion ime and accumulaion ime. Conrain (19) is he binary conrains on he decision variables. 5. Conclusion In his paper, we developed a nonlinear zero-one programming model o opimize he courier newor. We considered hree ransporaion modes: road ranspor, air ranspor and railway ranspor, and differen ypes of ranspor carriers. In his model, oal courier delivery ime includes ransporaion ime, ransfer ime and accumulaion ime. This model deermines ha direc ransporaion ice is offered beween which pairs and ransfer ransporaion ice should be provided a which s, aiming o minimize he oal ransporaion co conaining he direc ransporaion co of which are composed of he accumulaion co and he ransporaion co and he ransfer ransporaion co of which consi he ransfer operaion co and he ransfer operaion ime co. For fuure research, we can discuss how o choose he ype of ranspor carriers ed on a courier ransporaion ice arc since ypes of ranspor carriers are already nown in his paper. Also, he number of ranspor carriers on he road should be rericed o avoid a congeion, which could be considered in he model. Reference Ayin T, Neworing policies for hub-and-spoe syems wih applicaion o he air ransporaion syem. Transporaion Science, 29(3): Jeong S J, Lee C G, Boobinder J H, The European freigh railway syem as a hub-and-spoe newor. Transporaion Research Par A, 41(6): Tan, X., Analyzing and modeling express shipping ice newor based on logiics daa. Zhejiang Universiy. Barnhar C, Krishnan N, Kim D, e al., Newor Design for Express Shipmen Delivery. Compuaional Opimizaion & Applicaions, 21(3): Schwind M, Kunel M. Collaboraive Opimizaion of La Mile Newors for Courier, Express and Parcel Delivery Services. 2010, Alibeyg A, Conreras I, Fernández E., Hub newor design problems wih profis. Transporaion Research Par E Logiics & Transporaion Review, 96: Di Z, Yang L.X., Qi J.G., Gao Z.Y, Transporaion newor design for maximizing flow-based accessibiliy, Transporaion Research Par B. 110: Slac B, Inermodal ransporaion in Norh America and he developmen of inland load ceners. Professional Geographer, 42(1): Iyer A V, Raliff H D, Accumulaion poin locaion on ree newors for guaraneed ime diribuion. Managemen Science, 36(8): Kara B Y, The lae arrival hub locaion problem. Informs. 47(10):