Design and Modeling of A Crowdsource-Enabled System for Urban Parcel Relay and Delivery

Transcription

1 Design and Modeing of A Crowdsource-Enabed System for Urban Parce Reay and Deivery Nabin Kafe, Bo Zou 1, Jane Lin Department of Civi and Materias Engineering, University of Iinois at Chicago, Chicago, IL 60607, United States Abstract: This paper proposes a crowdsource-enabed system for urban parce reay and deivery. We consider cycists and pedestrians as crowdsources who are cose to customers and interested in reaying parces with a truck carrier and undertaking jobs for the ast-eg parce deivery and the first-eg parce pickup. The crowdsources express their interests in doing so by submitting bids to the truck carrier. The truck carrier then seects bids and coordinates crowdsources ast-eg deivery (first-eg pickup) with its truck operations. The truck carrier s probem is formuated as a mixed integer non-inear program which simutaneousy i) seects crowdsources to compete the ast-eg deivery (first-eg pickup) between customers and seected points for crowdsource-truck reay; and ii) determines the reay points and truck routes and schedue. To sove the truck carrier probem, we first decompose the probem into a winner determination probem and a simutaneous pickup and deivery probem with soft time windows, and propose a Tabu Search based agorithm to iterativey sove the two subprobems. Numerica resuts show that this soution approach is abe to yied cose-to-optimum soutions with much ess time than using offthe-shef sovers. By adopting this new system, truck vehice mies traveed (VMT) and tota cost can be reduced compared to pure-truck deivery. The advantage of the system over pure-truck deivery is sensitive to factors such as penaty for servicing outside customers desired time windows, truck unit operating cost, time vaue of crowdsources, and the crowdsource mode. Keywords: Crowdsource-enabed deivery, bidding, reay, truck routes and schedue, simutaneous pickup and deivery probem, Tabu Search 1 Introduction The need to rethink urban parce deivery is never more urgent. E-commerce in the US today has reached the size of $300 biion annua saes, five times ten years ago (Braunstein, 2015). Pushed by the e-commerce exposion, urban truck traffic has increased precipitousy. Looking at retai-reated truck trips in New York City, it is estimated that each estabishment generates an average of 1.89 truck trips per day (Hoguin-Veras et a., 2012). Considering that Manhattan has 105,998 estabishments (USCB, 2016), the tota number of retai-reated truck trips exceeds 200,000 per day. The rise of truck traffic has ed to many negative consequences on the urban environment, such as congestion, air poution, wear-and-tear of road infrastructure, and demand-suppy imbaance in truck parking space. Take air poution and parking space shortage as exampes. On average, freight vehices contribute 16-50% of tota vehice emissions in urban areas (Thompson, 2015). In New York City, truck carriers pay $ parking fines per truck-month (Hoguin-Veras et a., 2007; 2008). The payment is even higher in Manhattan, where a truck accumuates $750 weeky parking fines (Rodrigue and Dabanc, 2013). These negative consequences wi ony become more severe in the future, with e-commerce expected to more than doube its size by 2019 (Braunstein, 2015) and characterized by smaer parces and more frequent and expedited deiveries than today. 1 Corresponding author. Emai addresses: nkafe3@uic.edu (N. Kafe), bzou@uic.edu (B. Zou), janein@uic.edu (J. Lin). 1

2 In contrast to the push from e-commerce exposion, urban parce deivery is aso pued by the deveopment of ivabe urban communities that require significant reduction of truck traffic. Many of the pus are in the form of city ordinances such as restrictions on truck deivery time (Hoguin-Veras et a., 2014), routes (Hoguin-Veras et a., 2015), size and weight (Qureshi et a., 2012; Hoguin-Veras et a., 2013), and introduction of ow emission zones (Browne et a., 2005; Giuiano and Dabanc, 2013). In response, truck carriers have taken a variety of initiatives, incuding setting up urban consoidation centers (Quak and Tavasszy, 2011; Vie et a., 2013; Morana et a., 2014), depoying truck parking reservation systems (Taniguichi, 2012; PIARC, 2012), and impementing dynamic vehice routing techniques (Kritzinger, 2012; Wofe and Troup, 2013). The present paper contributes to reconciing the above push and pu by designing, modeing, and evauating a new system empowered by crowdsourcing parce reay and deivery for the ast-mie probem. The term ast mie is commony used in city ogistics and refers to trips between a depot ocated at the border of a metro area and customers in the city. The system design is from the perspective of a truck carrier, with focus on operationa panning (e.g., day-before). Conceptuay, the system functions in five steps: (1) the truck carrier posts onine pickup and deivery jobs to attract oca crowdsources in this paper cycists and pedestrians who are cose to customers to undertake the ast eg of the ast-mie deivery. 2 The ast eg is connected to the rest of the ast mie at points where parce reay between trucks and crowdsources occurs. In addition to jobs, a possibe reay points are posted onine; (2) on seeing the posted jobs, a crowdsource generates and submits bids for undertaking a subset of the jobs. Each bid specifies what customers to serve, the bid price, and the point for parce reay; (3) the truck carrier seects bids and determines truck routes and schedue for visiting the reay points in the seected bids as we as customers not covered by any seected bids; (4) the truck carrier informs crowdsources with winning bids about the time that a truck reays parces at each reay point; (5) crowdsources and trucks execute deivery based on the bid seection resuts and the panned routes and schedue (Figure 1). Urban area Departing depot Returning depot Seected reay points Unseected reay points Customers served by crowdsource Customers visited by truck Origins of seected crowdsources Origins of unseected crowdsources Figure 1: An iustration of crowdsource-enabed urban parce reay and deivery The core of the proposed system is the substitution of trucks by oca crowdsources for the ast eg of the ast-mie deivery, which is based on the foowing economic rationae. Traditiona truck deivery is not efficient in urban neighborhoods due to constraints imposed by city ordinances and geographic conditions such as imited truck access time and presence of one-way roads. However, the constraints generay do not appy to crowdsourcing cycists and pedestrians, who have high maneuverabiity in urban neighborhoods 2 Uness pickup is expicity mentioned, in the rest of the paper the term deivery refers to both pickup and deivery. The ast eg of the ast-mie deivery then aso covers the first eg of the first-mie pickup. 2

3 and ow cost in deivery. On the other hand, cycists and pedestrians can ony trave shorter distances, making parce reay necessary between crowdsources and trucks near customers. In fact, having a truck carry many parces from the depot to a common destination, e.g., a reay point, keeps deivery cost ow in this ine-hau part due to the economies of oad consoidation. Thus by everaging the advantages of crowdsourcing and truck modes in the ast-eg and the remaining part of the ast-mie deivery respectivey, the proposed system is expected to improve the overa deivery efficiency compared to the pure-truck deivery. We note a growing popuarity of crowdsourced deivery in the rea word over the past few years. A number of onine patforms (e.g., Postmates and Deiv in the US, Jing Dong in China, and PiggyBaggy in Europe) have been dedicated to faciitating or aows for crowdsourced deivery. Rouges and Montreui (2014) give a comprehensive documentation of recenty emerged business modes for crowdsourced deivery. Among them, the dominant mode is Business-to-Customer (B2C) deivery where a parce is picked up directy from a fixed point such as a retai store or a restaurant by a crowdsource and deivered to the customer s doorstep. Each deivery route is typicay associated with a singe parce. Our proposed system is different from the existing crowdsourced deivery practice in three aspects. First, rather than from fixed pickup points our mode considers greater coverage of the ogistics chain from the depot to customers, with trucks acting as intermediate moving pickup/deivery points. Second, whie the existing practices outsource deivery entirey, our mode is partia outsourcing because a truck carrier sti performs part of the deivery by itsef. Thus the truck carrier in our proposed system needs to simutaneousy seect crowdsources and determine its own truck routes and schedue with the objective of minimizing the overa cost. Third, we consider both facts that mutipe crowdsources may compete for one deivery job and a crowdsource may deiver mutipe parces in a singe tour, and consequenty introduce a combinatoria bidding process to seect crowdsources. Methodoogicay, this paper makes two major contributions. The first contribution is system design that invoves crowdsourcing and parce reay between crowdsources and trucks. We formuate the design probem as a mixed integer non-inear program (MINLP). Compared to traditiona vehice routing probems, the new formuation integrates crowdsource bids seection and reay points ocationing with truck routes design. The second contribution is on the soution approach for the MINLP. In addition to providing a inearized formuation of the MINLP which aows off-the-shef sovers to sove sma-size probems, an efficient agorithm is deveoped for arge-size instances. The basic idea of the agorithm is to decompose the overa design probem into a winner determination probem (WDP) and a simutaneous pickup and deivery probem with soft time windows (SPDPSTW), and iterativey sove the two subprobems based on the Tabu Search concept to improve the overa soution. The effectiveness of the agorithm is vaidated by comparing soutions with those using off-the-shef sovers for sma-size probems, and further demonstrated by soving probems of arger, reaistic sizes. In addition to the above contributions, we perform extensive numerica experiments to assess the cost savings using the new design compared to pure-truck deivery. Resuts indicate that at median 9.25% cost saving and 24% truck vehice mies traveed (VMT) reduction can be achieved. We further find that the advantage of the crowdsource-enabed system over pure-truck deivery is sensitive to factors such as penaty for servicing outside customers desired time windows, truck unit operating cost, time vaue of crowdsources, and the crowdsource mode. The paper continues with a review of the iterature in Section 2 on ast-mie deivery that bears reevance to the crowdsource-enabed system. Section 3 provides a conceptua description of the proposed system design, foowed by its mathematica formuations in Section 4. The soution approach is presented in Section 5. Section 6 offers numerica experiments and discussions of the resuts. Summary of major findings and directions for the future research are given in Section 7. 3

4 2 Literature review Urban deivery system design has cose reevance to the genera topic of freight network design and faciity ocation (Bektas et a., 2015), which has seen a arge body of iterature (Daskin, 1995; Drezner, 1995; Drezner and Hamacher, 2002; to ist ony a few books on this topic). Yet the iterature dedicated to urban deivery is sparse. Two forms of urban deivery that are mosty studied are singe- and two-echeon systems. The singe-echeon system, suitabe for sma-size urban areas, considers that a city distribution centers (CDCs) are at the same eve (Crainic et a., 2009; Guyon et a., 2012; Gianessi et a., 2015). In twoecheon systems, sateite faciities are added between CDCs and customers, and the sateite faciities are where parce reay occurs. Two separate and dedicated feets of vehices move parces between CDCs and sateites, and between sateites and customers respectivey. The two-echeon systems bear some simiarity to our proposed system in terms of parce reay. Because of this, the rest of the iterature review focuses on routing probems in two-echeon systems. According to Cuda et a. (2015), research on two-echeon system routing can be cassified into three categories: (i) two-echeon ocation routing probem (2E-LRP); (ii) two-echeon vehice routing probem (2E-VRP); and (iii) truck and traier routing probem (TTRP). 2E-LRP presents the basic form of the three categories. 2E-VRP is a simper version of 2E-LRP, where the ocations of sateite faciities are given. TTRP is a specia case of 2E-VRP in that trucks in the second-echeon operation are attached to traiers in the first-echeon operation (in the first echeon, each vehice is a couped truck and traier). In our proposed system, truck-crowdsource reay points resembe sateites in 2E-LRP; truck routes are simiar to firstecheon routes; and crowdsource routes are anaogous to second-echeon routes. However, a distinctive feature of our proposed system is that it invoves a distributed bidding process. The truck carrier needs to simutaneousy seect crowdsource bids and design truck routes and schedue. 2E-LRP is we recognized as an NP-hard probem (Crainic et a., 2009; Nguyen et a., 2012a), which prevents the probem from being soved to optimaity using off-the-shef sovers. We are ony aware of two studies reporting optima soutions (Crainic et a., 2011; Contardo et a., 2012). The first one introduces three mixed integer inear program formuations for 2E-LRP using one-index, two-index and three-index variabes. The two-index and three-index formuations for up to 25 customers and 10 sateites are soved with a commerciay avaiabe sover. The second study proposes a branch-and-cut agorithm to sove a sma-size probem to optimaity. A other studies focus on deveoping heuristic approaches. Jacobsen and Madsen (1980) and Madsen (1983) are among the first researchers to heuristicay sove 2E-LRP. In their research, three heuristics based on the Minimum Spanning Tree method (Jacobsen and Madsen, 1978), the Aternate Location Aocation method in combination with Savings method (Rapp, 1962; Carke and Wright, 1964), and the Savings method in combination with Drop method (Cark and Wright, 1964; Fedman et a., 1966) are introduced. Boccia et a. (2010) deveop an iterative nested approach which is buit on the nested approach of Nagy and Sahi (1996) and the two-phase iterative approach of Tuzun and Burke (1999). The probem is decomposed into two components, one for each echeon. A bottom-up approach is deveoped to combine the two components, i.e., the first echeon soution is buit and optimized based upon the second echeon soution. An initia soution for each echeon is constructed using some fast and greedy heuristic and subsequenty improved with neighborhood searches incuding add, drop, and swap moves. Recenty, Nguyen et a. (2012a) present four constructive heuristics and a hybrid metaheuristics GRASP (greedy randomized adaptive search procedure), enforced by a earning process and path reinking to sove 2E-LRP. The constructive heuristics work in two phases: first constructing the second-eve routes from sateites to customers, and then the first-eve routes from the depot to sateites. The constructed routes are improved using reocation, swap, 2-opt, 3-opt and open/cose moves. The path reinking, originay proposed by Gover and Laguna (1993), adds a memory mechanism to improve the performance of the GRASP metaheuristic. The same authors aso deveop a muti-start iterated oca search couped with Tabu 4

5 search and path reinking (Nguyen et a., 2012b). For soving arge-size probems, an Adaptive Large Neighborhood Search (ALNS) heuristic is introduced and tested by Contardo et a. (2012). Review of the iterature shows that finding exact soutions for 2E-LRP has so far been successfu for ony sma-size probems. Heuristic approaches have received more attention to obtain quaity resuts for arge-size probems within a reasonabe amount of computation time. Given the simiar NP-hard nature of our probem, in this paper we aso seek to deveop a heuristic approach to sove the crowdsourcing-enabed parce reay and deivery system design. 3 Conceptua description of the system Before deving into the mathematica formuation and soution approach for the system design, it is usefu to have a conceptua picture of the system. Reca in Section 1 that the functioning of the system consists of five steps, in which decision-making occurs in steps 2 and 3, by crowdsources and the truck carrier respectivey (step 1 is simpy information post, step 4 communication of the decisions made, and step 5 execution of the panned deivery). In step 2, each crowdsource determines how to generate and submit bids, with the objective to maximize one s utiity. On receiving the bids, in step 3 the truck carrier simutaneousy seects bids and designs truck routes and schedue to minimize its tota cost. Beow we describe how decisions are made in steps 2 and 3. For crowdsource decision making, we consider that each bid incudes five pieces of information: (1) the customer(s) that the crowdsource pans to serve; (2) the reay point where parces are transferred between the crowdsource and a truck (we term the combination of the customer(s) and the reay point in a bid a bunde); (3) the crowdsource routing which starts and ends at the crowdsource s origin and visits a the customers and the reay point in the bunde; (4) the bid price for serving the customer(s); and (5) the crowdsource mode (cycing or waking). The ast piece is used to infer the crowdsource s trave speed. Each crowdsource can have a combinatoria number of possibe bundes. With the aid of persona computing devices (e.g., mobie Apps), we assume that each crowdsource can and wi enumerate a feasibe bundes. The feasibiity of a bunde is constrained by the maximum distance a crowdsource can trave, his/her carrying capacity, and the bidding rue. Subsection 4.1 wi provide further detai. Provided that bundes are feasibe, a crowdsource considers two aspects when submitting bids. First, the bid price shoud be competitive against bids from other crowdsources for a given bunde. This requires the route covering the chosen customers and the reay point to be the cost-minimum route for the crowdsource. Second, if feasibe bundes are a competitivey priced and each crowdsource is aowed to submit a imited number of bids, then the bids submitted by a crowdsource must be those with the highest bid prices, in order to maximize the possibe revenue (thus utiity) gained. We restrict the number of bids a crowdsource can submit, because otherwise an exponentia number of bids woud be received by the truck carrier due to the combinatoria nature of bidding (Song and Regan, 2005). This woud make the subsequent bid seection computationay difficut. For decision making by the truck carrier, seecting bids and designing truck routes and schedue are intertwined: seected bids determine not ony customers served by crowdsources, but aso reay points and customers not covered by the bids and to be visited by truck. The tota cost to be minimized is the sum of payment to seected bids, truck operating cost, and time penaty cost for servicing outside customers desired time windows. The first component depends on bid seection; the second component on truck routes; whereas the third component is coectivey determined by seected bids and truck schedue due to parce reay. We now proceed to the mathematica formuations of the decision-making probems facing each crowdsource and the truck carrier. 5

6 4 Mathematica formuation 4.1 Crowdsource decision-making: bid generation and submission As mentioned in Section 3, on seeing the posted pickup and deivery jobs each crowdsource enumerates bundes which are subject to the foowing feasibiity constraints. First is the trave distance imit. We restrict a customers and the reay point in a crowdsource s bid to be within an R-mie radius from the crowdsource s origin. Second, a bid can ony incude a maximum number of customers, and there is a imit on the tota parce weight a crowdsource can carry in a bid. Third, as a bidding rue we consider that a bid is for pickup ony or deivery ony, but not a mix. The rationae for the ast constraint is that, at the time of bid generation when truck routes and schedue have not been determined, crowdsources woud be facing much more uncertainty and compexity in a bid whie coordinating pickup and deivery jobs than if deaing with ony pickups or ony deiveries. The three constraints add reaism to the bid generation process and hep reduce the computationa burden facing each crowdsource. Note that the generated bids do not invove the arriva time of the crowdsource at a customer, but ony the routes. Again, this is because at the bid generation step crowdsources have no information about the truck arriva time at the reay point in a bid. Consequenty, the cost-minimum routes are determined without considering whether pickup/deivery is within the desired time window (in fact, ony the truck carrier truy cares about this). If a bid is seected, the associated crowdsource shoud serve the customers according to the time determined by the truck carrier (in determining the time the truck carrier wi respect the trave speed of the crowdsource). In this sense, the system wi be mosty attractive to crowdsources who have fexibe schedue. For a bunde that meets the above feasibiity constraints, finding the cost-minimum route for the bunde is an Undirected Trave Saesman s Probem (U-TSP), which is we studied in the vehice routing iterature (Mier et a., 1960; Laporte, 1992). The cost to a crowdsource for servicing a route is cacuated as the sum of the time for traversing the route and the time for parce transfer at the reay point, mutipied by the time vaue of the crowdsource. For brevity, the expicit U-TSP formuation is not presented here. The ony added constraints in our probem is that the reay point must be connected to the origin of the crowdsource, because the crowdsource must first head to the reay point (for deivery), or returns from the reay point (for pickup). Due to the constraints on bunde construction, the sizes of the U-TSP probems wi be reativey sma. As a resut, optima soutions can be quicky found using standard integer programming sovers. Each time a U-TSP is soved, the consequent routing cost wi be the bid price for the bunde. Once the bid price for each feasibe bunde is obtained, foowing the discussions in Section 3 a crowdsource wi submit B highest priced bids to the truck carrier, where B is the maximum number of bids a crowdsource is aowed to submit. 4.2 Truck carrier decision-making: bid seection and truck routes and schedue design In seecting bids and designing truck routes and schedue, the objective of the truck carrier is minimizing its tota cost. The cost minimization probem is formuated as a mixed integer non-inear program, termed MINLP-(BS+TRS) (Mixed Integer Non-Linear Program for Bid Seection and Truck Routing and Scheduing). The formuation entais the foowing assumptions: Assumption 1: Each customer has a unique ocation 3 and corresponds to a singe pickup or deivery demand; Assumption 2: Each pickup or deivery demand must be met via a singe visit, either by a truck or by a crowdsource; 3 The terms ocation, node and point are used interchangeaby throughout the text. 6

7 Assumption 3: A reay point may not be visited, visited once, or more than once depending on the bids seected; Assumption 4: A truck is aowed to wait at a ocation before serving a customer, if the truck arrives earier than the start of the customer s desired time window. Assumption 5: Crowdsources are not expected to stop en route (from the panning perspective), which can be justified by the fact that in bid generation each crowdsource determines bunde bid price assuming no en-route stops. As utiity maximizers, crowdsources have no incentive to stop en route, as doing so woud increase one s time in undertaking the deivery job without generating additiona payment. Assumption 6: A truck route aways starts from the departing depot and ends at the returning depot. The departing and returning depots can be the same or different. Our mode formuation is adaptabe to both cases. The MINLP-(BS+TRS) is specified on an undirected, compete graph G = (V, E) where node set V is the combination of: (i) the customer set N = N p N d, where N p is the set of pickup customers and N d the set of deivery customers; (ii) truck s departing depot {d} and returning depot {r}; (iii) the set of reay points A. Set E corresponds to inks connecting the nodes in V. Assumptions 2 and 3 require the MINLP-(BS+TRS) formuation to distinguish between customers and reay points. A reay point wi not be visited by truck if not associated with a seected bid, must be visited once if associated with one seected bid, and may be visited more than once if associated with mutipe seected bids. To differentiate possiby mutipe visits to a reay point, copies of reay points are created. In this study, we set the number of copies of a reay point (incuding itsef) equa to the number of times the reay point is referred to in submitted bids. Each copy has a unique abe. These copies augment the origina set of reay points A to an expanded set A MINLP-(BS+TRS) formuation We now present the formuation of the MINLP-(BS+TRS). The sets, incidence reation, parameters, and decision variabes in MINLP-(BS+TRS) are first isted: Sets S L Incidence reation δ i bs Set of crowdsources Set of avaiabe trucks Incidence reation taking vaue 1 if customer i is incuded in bid b submitted by crowdsource s and 0 otherwise 4 Repication of reay points coud have negative effects, such as the symmetry generated. Symmetry occurs when the variabes of a probem can be permuted without changing the structure of the probem (Margot, 2010). This means different permutations of a soution can give the same objective vaue, and viewed as different soutions. For exampe, if there are two copies of a reay point (say 1 and 2) then for a given s and b, keeping everything ese constant, a s s s s soution with y b1 = 1 and y b2 = 0 is symmetric to a soution with y b1 = 0 and y b2 = 1 (see section for description of variabe y s bv ). The symmetry issue becomes more important with the number of repications made for each reay point. A arge number of such symmetries can ead to soving many unnecessary sub-probems in the branch-and-bound agorithm and even make reativey easy probems impossibe to sove with branch-and-bound (Ostrowski et a., 2010; Margot, 2010). Further detais about treating the symmetry issue in integer programming can be found in Ostrowski et a. (2010) and Margot (2010). We thank one of the reviewers for bringing up this issue. 7

8 Parameters B t uv bs t vi ξ v q v q v D K C uv s P bu e u, u π(t u, e u, u ) Decision variabes T u T d T r Q u Q d Maximum number of bids a crowdsource is aowed to submit Truck trave time between nodes u and v Time required for crowdsource s to trave from reay point v to customer i incuded in the crowdsource s bid b Time for parce transfer at reay point v. Weight of parce(s) associated with node v; pickup demands are considered positive whie deivery demands are considered negative. Node v has a singe parce if it is a customer point and may have mutipe parces if it is a reay point Weight of deivery parce(s) associated with node v. q v D is positive for ocations with deivery demand(s). However, q v D wi be 0 for nodes with pickup demand(s), which is different from q v Loading capacity of a truck Trucking operating cost traveing from node u to node v Bid price of crowdsource s for serving customer(s) in bid b which aso incudes reay point u Desired eariest and atest service time for customer u Penaty for eary/ate service of customer u, which is a function of the truck (or crowdsource) arriva time T u, e u and u (for detais see Subsection 4.2.2) Service time at node u (by either a truck or a crowdsource) Departure time of truck from the departing depot d Arriva time of truck at the returning depot r Truck oad after serving node u Load of Truck when eaving the departing depot (node) d x uv Binary variabe taking vaue 1 if truck traves consecutivey from node u to v and 0 otherwise s y bv Binary variabe taking vaue 1 if the bid b submitted by crowdsource s with reay point v is seected and 0 otherwise With these notations, the MINLP-(BS+TRS) is written as the foowing program (1.1)-(1.23): min u N A {d} v N A {r} L C uv x uv + u A s S b=1 P + π(t bu u N u, e u, u ) (1.1) s.t. Truck routes constraints 8 B s s y bu u N A {d} L x uv 1 v N A {r} (1.2) v N A {r} L x uv 1 u N A {d} (1.3) v N A L x dv (1.4) u N A {d} x uv = w N A {r} x vw v N A, L (1.5)

9 Truck schedue constraints (T u + ξ u + t uv T v ) L x uv 0 u N A, v N A (1.6) (T d + t dv T v )x dv 0 v N A, L (1.7) (T u + ξ u + t ur T r )x ur 0 u N A, L (1.8) δ bs i (T v + ξ v + t bs vi s T i )y bv = 0 s S, b = (1 B), v A, i N D (1.9) δ bs i (T v t bs s vi T i )y bv = 0 s S, b = (1 B), v A, i N P (1.10) Truck oad and capacity constraints Q d = u N A v N A D {d} x uv q v L (1.11) Q d K L (1.12) x dv (Q d + q v Q v ) L 0 v N A (1.13) (Q u + q v Q v ) L x uv 0 u N A, v N A (1.14) Q u K u N A (1.15) Bid seection constraints B s v N A {r} L x iv + v A s S b=1 δ bs i y = 1 i N bv (1.16) B s b=1 sεs y bv u N A {d} L x uv v A (1.17) B s b=1 vεa y bv 1 s S (1.18) Non-negativity and binary constraints of decision variabes x uv {0,1} u N A {d}, v N A {r}, L (1.19) s {0,1} b = (1 B), s S, v A (1.20) y bv Q u, Q d, T u, T d, T r 0 u N A, L (1.21) The objective (1.1) minimizes the sum of truck operating cost (1 st term), payment to seected crowdsources (2 nd term), and time penaty cost for servicing outside customers desired time windows (3 rd term). We foow van Duin et a. (2007) and consider the time penaty cost to increase ineary with the deviation of the service time from a customer s desired time window. The specific functiona form of the time penaty cost is presented ater in Subsection The cost minimization is subject to five groups of constraints. The first group reates to truck routes: every ocation is visited by a truck at most once (constraints (1.2)-(1.3)). The number of vehices departing from the departing depot (d) shoud be no greater than the tota number of avaiabe trucks L (constraint (1.4)). Constraint (1.5) denotes truck fow conservation at each customer ocation or reay point. The second group of constraints reates to truck schedue. Constraint (1.6) cacuates the time change as a truck traves through a ink not invoving the departing and returning depots. It is a non-inear constraint and vaid ony when there exists a direct truck ink between u andv. The inequaity of this constraint suggests that truck waiting at a ocation is aowed. Constraint (1.7) cacuates the time change as a truck eaves the departing depot for the immediate downstream stop. Note that constraint (1.7) does not incude ξ u as no parce transfer time is required at the departing depot. Simiary, constraint (1.8) cacuates the time change as a truck eaves the immediate upstream stop for the returning depot. Constraints (1.7)-(1.8) are different from constraint (1.6) in that the departing and returning depots, unike customer ocations or reay points, invove mutipe trucks (thus the truck superscript is necessary for T d and T r ). Together, constraints (1.6)-(1.8) eiminate the formation of sub-tours (Ropke and Pisinger, 2006). Constraints (1.9)- (1.10) reate the pickup or deivery time of a customer by crowdsource to the truck service time at the 9

10 corresponding reay point. The association is made possibe by the mode and routing information provided in the submitted bids (reca that the mode information gives the trave speed of crowdsource). The equaity sign refects that crowdsources do not stop en route. Constraint (1.10) does not invove ξ v because parce transfer is made after a parce-pickup crowdsource arrives at the reay point. The third group of constraints reates to truck oad and capacity, which foows Desrochers et a. (1987). Constraint (1.11) cacuates the tota deivery demands oaded on truck at the departing depot. The tota weight carried on a truck at the departing depot is the sum of deiveries to be made at downstream nodes. Constraint (1.12) states that the oad of a truck at the departing depot shoud not exceed capacity. Constraint (1.13) cacuates truck oads at the immediate downstream to the departing depot. Constraint (1.14) gives truck oads at each node visited by a truck, except the departing and returning depots. Constraint (1.15) states that the truck oad shoud not exceed capacity at any customer or reay points. Note that a capacity constraint at the returning depot is unnecessary because trucks ony offoad parces at the returning depot. As ong as truck capacity is not exceeded at the immediate upstream node, the capacity constraint wi aso be met at the returning depot. The fourth group of constraints reates to bid seection. Constraint (1.16) specifies that every customer must be visited, either by truck or crowdsource. Constraint (1.17) denotes that if a bid is seected, then the associated reay point must be visited by truck. Constraint (1.18) restrains that a crowdsource wins at most one bid. This is to avoid the circumstance that when a crowdsource wins mutipe bids, it may require pickup/deivery jobs with overapping (thus conficting) times. The ast group of constraints specifies the binary conditions of x uv s and y s bv s and the non-negativity of a decision variabes. With this formuation, the foowing observation is made. Observation 1: By impementing the crowdsource-enabed system, the truck carrier wi be no worse off than pure-truck deivery. Observation 1 is easy to verify. The optima soution to the pure-truck deivery probem aways presents a feasibe soution to MINLP-(BS+TRS) when no bid is seected. This feasibe soution provides an upper bound for MINLP-(BS+TRS). Therefore, the minimum cost under MINLP-(BS+TRS) is no greater than the minimum cost with pure-truck deivery, i.e., the truck carrier wi not be worse off by impementing the crowdsource-enabed deivery system Linearization of the objective function and constraints The non-inear objective and constraints above make it non-trivia to sove MINLP-(BS+TRS) using off-the-shef sovers even for sma-size probems, which is desired to assess the effectiveness of the heuristic approach we ater deveop to sove arge-size probems. One way to overcome this is to inearize the formuation (1.1)-(1.21). For the objective (1.1), the non-inear term is u N π(t u, e u, u ). Each π(t u, e u, u ) increases ineary with the deviation of service time from the desired time window. Assuming a constant penaty rate P ($/unit time), π(t u, e u, u ) can be expressed by the foowing piece-wise inear function ( u N): P(T u u ) if T u > u π(t u, e u, u ) = { 0 if e u < T u < u P(e u T u ) if T u < e u 10 (1.22) We inearize (1.22) by introducing two additiona decision variabes, ε u and τ u, repacing π(t u, e u, u ) in (1.1) by (1.23), and adding three new constraints (1.24)-(1.26): P(ε u + τ u ) u N (1.23) ε u e u T u u N (1.24)

11 τ u T u u u N (1.25) ε u, τ u 0 u N (1.26) where ε u is the amount of time customer u is served before e u, and τ u is the amount of time customer u is served after u. Proof of the equivaence between π(t u, e u, u ) and (1.23)-(1.26) is provided in Appendix A. Non-inear constraints (1.6)-(1.8) and (1.13)-(1.14), which have inequaity signs, can be inearized using big-m foowing Desrochers et a. (1987). Non-inear constraints (1.9)-(1.10), which have equaity signs, wi each require an additiona constraint to be inearized: (T v + ξ v + t bs vi T i ) (1 δ bs i y s bv )M s S, bεb D, v A, i N D (1.9a) (T v + ξ v + t bs vi (T v t bs vi (T v t bs vi T i ) (δ bs i y s bv 1)M s S, bεb D, v A, i N D (1.9b) T i ) (1 δ bs i y s bv )M s S, bεb P, v A, i N P (1.10a) T i ) (δ bs i y s bv 1)M s S, bεb P, v A, i N P (1.10b) The above transformations resut in a inearized version, MILP-(BS+TRS) (Mixed Integer Linear Program for Bid Seection and Truck Routing and Scheduing), of the origina formuation. Since MILP-(BS+TRS) contains VRPTW as a specia case when no crowdsources are present, MILP- (BS+TRS) is an NP-compete probem ike VRPTW. Given the NP-competeness, no poynomia-time running agorithms exist for soving MILP-(BS+TRS) uness P = NP. Off-the-shef sovers such as CPLEX are abe to sove ony sma-size probems. In the next section, we propose a heuristic approach to sove probems of arger sizes. 5 Soution approach The basic idea for soving MILP-(BS+TRS) is to decompose it into two sub-probems: i) seecting bids from the submissions; ii) routing and scheduing of trucks. The first sub-probem pertains to soving a Winner Determination Probem (WDP); the second one a Simutaneous Pickup and Deivery Probem with Soft Time Windows (SPDPSTW). We iterativey sove the two subprobems using a Tabu Search based agorithm to improve the overa soution to MILP-(BS+TRS). Beow is the outine of the agorithm. 11

12 Agorithm 1: Soving MILP-(BS+TRS) Step 0: Set up an empty Tabu ist of reay points. Step 1: Sove WDP to seect crowdsources to serve customers. The soution indicates the reay points to be used by the seected crowdsources. Based on the soution, cacuate the payment to each seected crowdsource. Step 2: Sove SPDPSTW in which trucks visit the seected reay points as we as customers not covered by the seected crowdsources. Add the resuting truck operating cost and time penaty cost to the payment to crowdsources in Step 1. Labe it as the current best tota cost. Step 3: Among the seected reay points that are not Tabu, seect the one with the minimum associated cost and temporariy remove it. Re-sove WDP and SPDPSTW. Two cases may occur: 3.1: If the tota cost is higher than the current best cost, abe the temporariy removed reay point as Tabu and add it back to the set of seected reay points. Go back to the beginning of Step 3; 3.2: If the tota cost is ower than the current best cost, permanenty remove the reay point; update the current best cost and the set of seected reay points. Go back to the beginning of Step 3; Stop when a seected reay points are abeed as Tabu, or when the current best soution does not invove reay points (i.e., a customers directy served by truck). Store the Tabu ist. Go back to Step 0 to start the next iteration. Step 4: Terminate when the stored Tabu ists in two consecutive iterations are identica. Whie most parts of the agorithm are sef-expanatory, two points are worth highighting. First, after we temporariy remove the reay point with the minimum associated cost in step 3, the tota cost resuting from WDP wi increase or remain the same because the number of avaiabe bids is now fewer (the bids associated with the removed reay point wi become infeasibe). However, conditiona on the bids and reay points seected the remova may reduce the SPDPSTW cost. Thus it is sti possibe that the tota cost is reduced. Second, each time we start a new iteration in step 0, fewer reay points wi remain as some are permanenty removed in the previous iteration in step 3.2 (If the number of reay points does not change over two iterations, then the agorithm wi terminate (step 4)). Beow we describe in detai how the two sub-probems, WDP and SPDPSTW, are soved. 5.1 Soving WDP We formuate WDP as a binary integer program and sove it to optimaity using the branch-and-bound agorithm. The probem is sighty modified compared to the cassic formuation (for exampe, Bumrosen and Nisan (2007)), to aow trucks to serve customers not covered by seected bids. The modified WDP is formuated as beow: s s y bu min u A s S bεb P bu + M i N z i (2.1) z i + δ bs s v A s S b B i y bv = 1 i N (2.2) s v A bεb y bv 1 s S (2.3) 12

13 s y bv {0,1} bεb, s S, v A (2.4) z i {0,1} i N (2.5) In the objective (2.1), the first summation is payment to seected crowdsources. In addition, a big-m term is added to penaize not having crowdsources serve customers. The underying assumption is that the truck carrier wants crowdsources to cover as many customers as possibe, because crowdsourcing is expected to be cheaper than using trucks. z i is a binary variabe taking vaue 1 if customer i is not served by seected crowdsources and 0 otherwise. Constraint (2.2) states that a customers must be served exacty once, either by crowdsource or by truck (in the atter case, z i = 1). This constraint impicity assumes that the bidding crowdsources are interested ony in obtaining an entire bunde, not any subset of it. Constraint (2.3) stipuates that each crowdsource wins at most one bid. Constraints (2.4)-(2.5) state that the decision variabes are binary. Note that consistent with our discussions in Subsection 4.1, the WDP does not consider time windows. Soution to the WDP yieds seected bids and reay points. In addition, the truck carrier wi know the sequence of customer visits in each winning bid. Then the truck carrier needs to sove SPDPSTW to determine truck routes and schedue, so that a reay points in the seected bids as we as customers uncovered by the seected bids are visited by truck. 5.2 Soving SPDPSTW SPDPSTW is a variant of vehice routing probems with time windows (VRPTW), with the difference that customers can have both pickup and deivery requests. In addition, in SPDPSTW a deiveries originate from the departing depot and a pickups are destined to the returning depot. Thus SPDPSTW is different from traditiona Pickup and Deivery Probems (PDP) where the origin of pickups and destination of deiveries can be customers. Soft time windows stipuate that pickups/deiveries are acceptabe outside customers desired time windows, abeit with penaty. We consider that if a truck arrives at a customer eary, it shoud wait ti the beginning of the customer s desired time window to serve the customer. Simiar treatment is made when a truck visits a reay point. Since a reay point itsef does not have a desired time window, we construct the desired time window of a reay point based on the desired time window of the first or ast customer visited in the associated bid, depending on whether it is a deivery or pickup bid. If the associated bid is for deivery, e u for the reay point is set to e u t u,u, where u is the first customer to visit in the bid and t u,u is the crowdsource trave time from u to u. u is e u pus a pre-specified time window ength. If the associated bid is for pickup, u for the reay point is set to u + t u,u, where u is the ast customer to visit in the bid and t u,u is the crowdsource trave time from u to u. e u is u minus a prespecified time window ength. Our SPDPSTW bears some simiarity with the simutaneous pickup and deivery probems with hard time windows, which has been investigated by severa researchers. Angeei and Mansini (2003) consider different branch-and-price strategies to sove a probem of this type to optimaity. As this type of probems is aso NP-hard, severa heuristics have been deveoped, incuding an Improved Differentia Evoution (IDE) agorithm (Mingyong and Erbao, 2010), a muti-ant coonies agorithm (Boubahri et a., 2011), a coevoution genetic agorithm (Wang and Chen, 2013), and a parae Simuated Anneaing method (Wang et a., 2015). However, we are not aware of previous efforts considering soft time windows for simutaneous pickup and deivery, athough VRP with soft time windows has been studied in Baakrishnan (1993), Qureshi et a. (2009), and Figiozzi (2010). Compared to deivery with hard time windows, SPDPSTW has the advantage of reducing truck feet size and improving vehice capacity utiization, both of which reduce truck carrier cost. Our agorithm for soving SPDPSTW uses the Simuated Anneaing principe to improve or fine tune routes through various node moves. Simuated Anneaing beongs to the cass of probabiistic hi cimbing agorithm to approximate the goba optima for compex combinatoria optimization probems (Daganzo, 2005). It mimics the cooing of materia in a heat bath. The theoretica background to Simuated 13

14 Anneaing is derived from the concepts in statistica mechanism and Markov Chains (Dowsand and Thompson, 2012). With sound generate, accept, and update functions, Simuated Anneaing is shown to converge the soution in probabiity to a minimum cost configuration (Mitra et a., 1986; Laarhoven and Aarts, 1987; Daganzo, 2005). It is simpe, fexibe, we suited for soving VRPs, and cose to being an idea genera purpose too for fine tuning (Robuste et a., 1990). It has aso been reported that Simuated Anneaing produces reasonaby good soutions for arge routing probems faster than other heuristics such as Genetic Agorithm (Tan et a., 2001; Adewoe et a., 2012; Antosiewicz et a., 2013). Beow we present first the components (i.e., initia soution generation, route improvement, and acceptance criteria) and then the overa fow of the agorithm Initia soution construction To generate the initia truck routes, we consider scheduing trucks to first fufi deivery demands and then pickup demands. Trucks need to visit a reay points in the seected bids and customers uncovered by the seected bids. A truck route is progressivey constructed using the nearest neighbor heuristic, i.e., from the current end node of the route to an unvisited node that has the owest generaized ink cost. The generaized cost on a truck ink (v, u), GC vu, is the sum of truck operating cost C vu and time penaty cost for visiting the node π(t u, e u, u ): GC vu = C vu + π(t u, e u, u ) (3.1) Reca that our previous definition of π(t u, e u, u ) is for customer nodes (equation (1.22)). If u is a reay point in A, we further define π(t u, e u, u ) as the sum of time penaty cost for a customers in the associated bid. The nearest neighbor heuristic proceeds as foows. We start from the first truck. Among the reay points in the seected bids and the customers uncovered by the seected bids, the point having the owest generaized cost from the departing depot is added to the truck s route. We then connect this added point to the next point among the remaining reay points in the seected bids and the customers uncovered by the seected bids, such that the generaized cost from the added point to the next point is the owest. We repeat this unti no more deivery oad can be added due to truck capacity constraint. Then we start constructing the second truck s route, again from the depot. This process ends when a deivery demands are assigned to truck routes. After competing deivery, the above trucks are reused for pickups. Pickup truck routes are formed in a simiar fashion as deivery truck routes. However, the pickup route of a truck starts from the ast deivery node. If additiona trucks are needed due to capacity restrictions, these additiona trucks wi start from the depot Route improvement An iterative process is adopted to improve the initia truck routes. In each iteration, three neighborhood search based node moves are performed: 2-opt move, node interchange and node reocation (Figure 2). The first move is an intra-route improvement, whereas the second and third are inter-route improvements. In a 2-opt move, two non-adjacent inks within a truck route are reshuffed (Figure 2(a)). A reshuffe changes the node visiting orders, and consequenty the truck capacity constraint may be vioated. If the move is feasibe, i.e., truck capacity is not exceeded, and the tota cost for the truck is reduced, then the move is definitey accepted. If the move is feasibe but the tota cost for the truck is increased, then additiona acceptance criteria (Subsection 5.2.3) are appied to determine whether to accept the move. The 2-opt move is performed for every truck route and every possibe non-adjacent ink pair in a truck route. In a node interchange/reocation move, two nodes which beong to two truck routes are exchanged/moved from one route to another (Figure 2 (b)/(c)). If the move is the feasibe, i.e., truck capacity is not exceeded on both truck routes, and the tota cost for both trucks is reduced, then the move is definitey 14

15 accepted. If the move is feasibe but the tota cost for both trucks is increased, then the same additiona acceptance criteria mentioned above are appied to determine whether to accept the move. The node interchange/reocation move is performed for a possibe truck route pairs, and given a route pair, a possibe node pairs. The iterative process stops when no reduction in tota cost can be found for n consecutive steps. We aso empoy an upper bound N as the maximum number iterations to be performed. (a) (b) (c) Figure 2: Route improvement moves: (a) 2-opt move: two inks connecting the back nodes are reshuffed; (b) Node interchange: back nodes are interchanged between two routes; (c) Node reocation: back node is reocated from one route to another Acceptance criteria The acceptance criteria for a move when truck cost increases refects the Simuated Anneaing principe that accepting some non-improving soutions makes the search more extensive to avoid being trapped in oca minimum. Specificay, the acceptance criteria are based on a probabiistic approach. When a move eads to higher truck cost, the move woud sti be accepted with a probabiity of e cost T, where cost = cost before the move cost after the move, which is negative (note that for a positive cost, the probabiity of acceptance e cost T wi be greater than 1, in which case the soution wi aways be accepted). T is the current temperature which is greater than 0. The temperature decreases at a given cooing rate c < 1 at every iteration. At the beginning of the iterative process, the temperature is high, meaning that the probabiity of accepting a non-improving soution is high for a given negative cost. As the iterative process proceeds, both temperature and the probabiity of accepting a cost-increasing move decrease. It has been found that the quaity of Simuated Anneaing soutions depends on the initia temperature and cooing rate c (Ropke and Pisinger, 2006). In this study, the initia temperature is set such that tota cost that is w% greater than the initia tota cost is accepted with 0.5 probabiity, where w is a pre-specified parameter (Ropke and Pisinger, 2006). For c, existing research does not suggest any definite vaues. Section 6 wi provide further detais on how we choose w and c Overa agorithm to soving SPDSPTW Based on the discussions in Subsections , Agorithm 2 beow gives the pseudo code to sove SPDSPTW. Four functions: initia_soution, 2-opt_move, node_interchange, and node_reocation are invoved. The variabes appearing in the parentheses after each function name specify outputs of the function. In Agorithm 2, ines 1-3 generate initia truck routes. The initia routes and costs are abeed as the best found at iteration 0. Line 4 sets up the initia temperature (such that the soution that is w% worse than the initia soution is accepted with 0.5 probabiity). Line 5 stipuates that the agorithm woud proceed up to N iterations (note that it can terminate earier, as specified in ine 36). At the start of each iteration, the temperature is updated (owered) as in ine 6. A 2-opt move is performed in ine 7. Line 8 cacuates the acceptance probabiity based on the cost at the current iteration and the best cost found so far. If the acceptance probabiity is greater than a randomy 15