A Vehicle Routing Problem with Periodic Replanning †

In this work we focus on the problem of truck fleet management of the company GESUGA. This company is responsible of the collection and proper treatment of animals not intended for human consumption. On a daily basis, with the uncollected requests, the company designs the routes for the next day. However, these routes have to be replanned during their execution as new requests appear from customers that the company would be interested in attending. The problem treated belongs to the family MDCVRPTW with the particularity of the route redesign. For its resolution we have adapted linear programming models, simulation techniques and metaheuristic algorithms.


Introduction
After the spread of Bovine Spongiform Encephalopathy, typically known as mad cow disease, the European Union took a number of measures (e.g., Regulation (EC) No 999/2001) to prevent its spread and transmission.This regulation forbids the burial of carcasses of dead animals at livestock farms.In Galicia, one of the main companies responsible for this task is GESUGA.This company focuses its business area on the integrated management of meat by-products not intended for human consumption.Its main activity consists of the collection and transport of the different meat by-products, generally animal carcasses, from livestock farms to treatment plants, for their appropriate treatment.
To serve customers, the fleet of the company is composed by 32 trucks (12 in Cerceda, 10 in Outeiro de Rei and 10 in Vilamarín) which, from Monday to Friday, visit the different farms and transport the products to the intermediate plants.Taking into account the characteristics of this problem, it could be classified as a MDCVRPTW.A general review of VRP can be found in [1].

Description of the Problem
As mentioned in the introduction, the company has to visit its customers all over Galicia on a daily basis.Some of the restrictions that define this problem are the following:

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The trucks leave and return from the plant to which they are assigned only once a day.

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Truck drivers have a maximum working day of 8 h which includes a rest and disinfection of the vehicle at the end of the day.

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Trucks have a maximum loading capacity.

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Orders must be picked up within 48 h from receipt.
Currently, route planning is manually made by the logistics department and the organization is as follows:

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At 19:00 there are some pre-routes with the notices not collected until that moment.

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At 20:00 these pre-routes are reviewed with the logistics manager adding new requests and making the necessary changes.

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At 21:00 drivers receive the set of places that they must visit, but they are free to organize it.

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During the day, incoming requests are assigned manually by the logistics department to drivers in order to free up work for the next day.
Note that the route design is manually made by the logistics department.Therefore, the company is interested in a tool to calculate the routes automatically, satisfy the needs of customers and achieve the following objectives:

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Minimize the total distance traveled by trucks.

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Minimize the number of trucks used.

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Maximize the number of collected requests.

Implementation of the Algorithm
The implementation of the algorithm was made in JAVA language using the libraries lpsolve and jsprit.The second library includes the Ruin and Recreate principle (see [2] and strategies inspired by [3].The problems mentioned above are solved automatically according to the following scheme: 1. Requests that are not collected during a day are assigned to a plant by solving the GAP problem with lpsolve library.2. For each plant, the corresponding VRPs are resolved with jsprit library.3. The requests that arrive online are assigned to each truck automatically taking into account the position and the load of each truck.
Currently, we are considering two strategies to address this problem: • Lazy: No orders are collected during the online phase, i.e., the routes computed the day before collecting are not modified.

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Minimum-k: A truck leaves the plant when, at least, k orders are assigned to it.
Note that the Lazy strategy can only be used from Monday to Thursday since on Fridays no orders can be left uncollected.Thus, Lazy strategy must be combined with Minimum-k.

Results
Many scenarios have been considered for the different strategies varying different parameters: cost of taking out a truck, minimum number of orders needed to take out a truck and time at which the optimization online is performed.
The appendix shows the best results obtained for each of the strategies as well as the real case.We see that the real case (Table A1) collects 6040 requests using 309 trucks.The Lazy strategy (Table A2) can collect 5782 requests using 275 trucks and the Minimum-k (Table A3) collects 6224 using 304 trucks.Therefore, we can conclude that the Lazy strategy always picks up fewer requests and uses fewer trucks than the real case.On the other hand, the Minimum-k strategy collects more requests and uses more trucks than the real case but the proportion between trucks and collected requests improves with respect to the real case.

Table A2 .
Results obtained with Lazy strategy.

Table A3 .
Results obtained with Minimum-k strategy.