Optimization of the Logistics of a Courier Business

Transcription

1 Applied Matheatical Sciences, Vol. 3, 2009, no. 36, Optiization of the Logistics of a Courier Business Khalid Moussaid Universit Hasan II_Ain Chock, Faculte des Sciences de Casa khoussaid@fsac.ac.a. Mohaed Azouazi Universit Hasan II_Mohaedia, Faculte des Sciences de Casa azouazii@hotail.co. Aina EL Ori Universit Hasan II_ Ain Chock, Faculte des Sciences de Casa a.elori@ fsac.ac.a. Abstract The logistics is a horizontal function with a strategic ipact at both the acro level of a country and the icro level of a copany. In fact, well run logistics systes have a direct ipact on the copetitiveness of the econoy of a country as a whole and increase the shareholder value of its constituent copanies. To increase their argins, provide cost effective solutions while increasing the quality of service offered to their prospects and custoers, transportation copanies are continuously looking to decrease their cost while offering the service level custoers expect. In this paper we consider the case of an actual international courier business willing to reduce its cost and enhance the quality of the service delivered, and we address the question of optiizing its Fleet Routing. It is a known proble for which we suggest a solution based on the Ant Colony Syste algorith. The different siulations we carried out allowed us to reach scenarios where we decreased both cost and shipping tie. In fact, we were able to slash delivery tie by 35.75% and tri down the total trip distance by 30.48%. Keywords: Logistics, Transport, Optiization, Siulation, Ant-Colony syste

2 1756 Kh. Moussaid, M. Azouazi and A. EL Ori 1 Introduction The courier business is essentially characterized by the pickup of the parcel and its delivery within a specified tiing selected by the custoer regarding the pickup, the delivery, or both. The rates the copanies operating in this industry offer is based on the distance between pickup and delivery locations, the weight of the parcel and its volue, and the type of service required by the custoer. To be copetitive and profitable, these copanies have to offer a good quality of service, ainly characterized by sticking to the tiing schedules of the pick and delivery, while at the sae tie they need to control the underlying cost. To achieve this cost control iperative, an ephasis is put on the optiization of the pick & delivery process. In this paper we selected an actual courier business and we looked at the optiization of the delivery process it ipleents. As presented by the copany itself, the proble is static. However, soe data ight change during the distribution of the courier (such as failure of a vehicle, street unreachable ); in such cases the proble can be qualified as a dynaic routing one and it will be addressed in a future article. The case to be optiized can be suarized as follows: For a given set of custoers of a delivery trip, the delivery driver has to total the iniu distance possible while satisfying the criteria below: 1. stop at each custoer once 2. pass by any street once 3. respect the tiing schedule constraints This optiization case looks like the Vehicle routing proble [1][2] which ais to: 1. respect the tiing schedule to enhance the custoer service 2. iniize the cost of the delivery trips 3. plan and deterine the sequence of the stops of the delivery trip 2 Matheatical forulation of the proble The proble is to iniize the criterion: under the constraints: i = 1 j = 1 x x = 1 = 1 j = i = 1,..., 1,..., (1) (2) i = 1 j = 1 d x

3 Optiization of the logistics of a courier business 1757 where: d : x : : distance between street i and street j binary variable which takes either value 1 if street i is visited iediately after street j or value 0 otherwise the nuber of the streets The constraints (1) and (2) enable us to visit each street once only. This is an Np-coplete proble [3], furtherore the solution we should recoend to the courier business before hand ust respect a coproise between the coputing tie and the cost effectiveness. Therefore, we abandon the exact ethods (such as Branch &Bound, Integer prograing ) [4] [5] and opt for an heuristic one based one the ACS (Ant Colony Syste) algorith. The basic idea of the ACS algorith is to odel the proble to solve as the search for a íniu cost path in a graph, and to use artificial ants to search for good paths. The behavior of these artificial ants is inspired fro real ants who are renowned to find out the quickest path between two points in tough terrains. In fact, real ants counicate with each other thanks to a volatile horone called Pheroone. On their way, ants lay pheroone leaving a trail behind. They select their path randoly according to the probability based on the quantity of pheroone left. This algorith proved to be efficient in solving the Travelling Salesan Proble [6]. It s ainly used because of its siplicity, the ease of its ipleentation and its efficiency. 3 Optiization by the ACS algorith The proble is represented as a graph where the nodes are the streets and the segents are the trips between these streets. The valuation of each segent is a function of the delivery tie at the node of destination. We associate to each segent (i,j) two values (τ, η ) defined as: * τ : the pheroone trail left by the ants in the segent (i,j) * η : the segent attractivity which, in our case, equals to the inverse of the delivery tie at street j. The previous delivery tie being the su of: 1. the tie of the trip fro street i to street j 2. the su of the tie required to service the custoers at street j

4 1758 Kh. Moussaid, M. Azouazi and A. EL Ori Fig 1: representation of the proble as a graph 4. The algorith to solve the proble For each segent, set τ to τ 0 Randoly allocate an ant to each street For t=1 to t ax For k fro 1 to For each non-visited street Select a destination street, within the reaining streets J i k, according to the forula: j argaxu J J = k i β {[ τ ( t)][ η ] } iu iu else if q q Where j is chosen according to the probability P k ( t) = ( τ ( t)) k l J i τ ( t ) (1 ρ ) τ ( t ) + ρτ End for ( τ ( t il 0 ( η ) α β α β )) ( ηil ) Calculate the length L k for each trip cycle of the ant k If ant k totals the shortest length then store it in T + For each segent (i,j) T +, calculate τ t ) (1 End-For Return T + and its length L + End-For ( ρ ) τ ( t ) + ρ / L 0 +

5 Optiization of the logistics of a courier business Illustration with an exaple Current Situation The graph below suarizes a real case of a delivery itinerary used by our courier business. Fig 2: existing delivery itinerary Where R 0 is the warehouse ; R 2,, R 9 designate the streets; and the values 1 to 18 designate the order of the trips between those streets. The itinerary is: R 0 -> 1 R 3 -> 2 R 1 -> 3 R 9 -> 4 R 2 -> 5 R 3 -> 6 R 7 -> 7 R 4 -> 8 R 5 -> 9 R 6 -> 10 R 3 -> 11 R 5 -> 12 R 7 -> 13 R 4 -> 14 R 2 -> 17 R 1 -> 18 R 9 We notice that the driver goes through a street for ore than once (exaple: R 2 is visited three ties). This redundancy generates an additional cost, a waste of tie and lack of productivity, and probable late deliveries which ight entail a custoer non satisfaction.

6 1760 Kh. Moussaid, M. Azouazi and A. EL Ori Solution suggested by our algorith We took the previous case and applied to it our algorith to develop an optiized solution that we represent in fig 3. As paraeters, we took = 10, α=1.0, β = 2.0, ρ=0.5 and t ax =10 A; R9 R0 R8 R1 R2 R6 R5 R4 R3 R7 Fig3: delivery itinerary suggested by our algorith Our solution suggests the following itinerary: R 0 -> R 7 -> R 4 -> R 6 -> R 1 -> R 8 -> R 2 - >R 3 -> R 5 -> R 9. The current solution does respect the criteria previously outlined and ost notably gives a better itinerary to use for the delivery trip. In fact, 1. the total tie is reduced by 35.75% fro 2h45 to 1h46 2. the total distance is reduced by 30.48% fro 16.4 k to 11.4k 6 Conclusion Our solution enables the copany to reduce its cost, to be ore productive, and yet, to better serve its custoers ainly by respecting the delivery tiings. These enhanceents and gains ade at the level of the distribution will have a direct and iediate positive ipact (in ters of cost reduction, productivity and custoer satisfaction) at the acro level of the supply chain as the distribution is one link of the entire value chain.

7 Optiization of the logistics of a courier business 1761 References [1] G. Laporte,G. et I.H. Osan, Routing probles : A Bibliography, Annals of Operations Research, 1995 [2] G.Laporte, M. Potvin, J.Y et F. Seet, Classical and odern heuristics for the vehicle routing proble, International Transactions in Operational Research, 2000 [3] J.K. Lenstra and A.H.G Rinnoy Kan : Coplexity of vehicle routing and scheduling probles. Networks, 11 : , 1981 [4] G. Laporte, Y. Nobert : An exact algoriths for the vehicle routing proble. Networks, 14, n 1, pp , 1984 [5] P. Blaise : Tournées de véhicules d une société coopérative: algorithes séquentiels et parallèles: [6] M.Dorigo, L.Maria Gabardella. Ant colony syste : A cooperative Learning. Approch to the travelling Salesan Proble. IEEE Transactions on Evolutionary Coputation, Vol.1, No.1, 1997 Received: Noveber, 2008