VRPTW with Multiple Service Workers

Transcription

1 VRPTW with Multiple Service Workers Route construction heuristics Gerald Senarclens de Grancy Marc Reimann graz.at)

2 Outline 1. Problem Background and Motivation 2. Route Construction Mechanisms 3. Numerical Results 4. Summary and Outlook

3 Problem Background and Motivation Delivery of soft drinks to small and medium sized retailers in Sao Paulo: 1. Time windows for delivery 2. High density populated region 3. Congested streets and scarcity of parking lots variation of the VRPTW Driver parks vehicle close to some customer sites Goods are delivered to nearby customers by foot (using hand trolley) long service times at each parking site Time windows pose additional problems for clustering customers

4 Typical Route

5 New Problems Service time can be reduced by assigning larger crews to the vehicles Particularly interesting if workers are cheap in relation to trucks Several new problems have to be dealt with 1. VRPTW with the additional decision of assigning multiple of service workers to each vehicle VRPTWMS 2. Customer clustering and parking space allocation need to be included in the algorithm 3. Fexibility in the delivery dates for selected customers calls for a multi period model 4. Customer clustering and parking space allocation on the fly Lexicographic objective 1. Fleet size 2. Crew size 3. Total distance Model assumptions Predefined nodes in our model correspond to the parking sites Parking sites are pre assigned the actual customers to be visited appropriate parking sites and allocation of actual customers to parking sites are given as inputs Service time in the nodes is a function of the local demand and the number of service workers assigned to the vehicle Problem complexity calls for a rapid metaheuristic Prior work only by Pureza et al. (2011)

6 Goals The objective of our current research is to study the effect of different solution construction heuristics and their parameters on the overall solution quality in order to obtain better results after applying different meta heuristics. 1. Reimplement solution construction mechanisms from Pureza et al. (2011) to compare their quality independent from the used meta heuristic 2. Perform computational experiments to determine their individual advantages 3. Implement ACO and other metaheuristics in order to obtain better overall results

7 Route Construction Mechanisms We're testing against the classical instances from M. M. Solomon (1987) r101 r112 serve as benchmarks to compare the quality of different algorithms service time s i = min(2 d i ;T max( a i ; t0i) t i0) where d i T a i demand at node i depot closing time EST at node i t0i, t i0 travel times between the depot and node i Solomon's I1 (adjusted) Importance of seed: furthest unassigned node Additional nodes are added one by one and selected by minimal cost cost = α * cost_dist + (1 α) * cost_time return cost λ * c_m[depot, node] All vehicles are initialized with max. workers Target size (1 worker) Given the best target fleet size Run I1 with 1 worker until given fleetsize is reached Add workers if unassigned clients are left For the remaining unassigned clients add additional trucks starting with one worker and adding workers as required

8 Parallel Solution Construction Main issues are seed selection and remaining nodes Allows more freedom when adding nodes Requires repair function

9 Aggregated Numerical Results Instances r101 r112 Without local search heuristic # trucks Solomon I1 (earliest closing TW) 183 Targetsize 185 Solomon (furthest seed) 166 With local search Solomon I1 166 Targetsize 183 Comparison to Best Prior Results Pureza et al. (2011): ACO 150 Pureza et al. (2011): TS 148 New ACO w/out local search 150

10 Summary and Outlook Adapted version of Solomon's I1 heuristic works currently best Remains to be done Implement same local search as Pureza et al. (2011) for systematic comparison Implement other metaheuristics Determine best tradeoff between more powerful local search operators and faster runtime when applying meta heuristics Improve performance with result hashing Determine parking location and customer clustering Extend system to allow multiple periods

11 Selected Bibliography OLLI BRÄYSY AND MICHEL GENDREAU Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms Transportation Science vol. 39, iss. 1, pp , INFORMS (2005) OLLI BRÄYSY AND MICHEL GENDREAU Vehicle Routing Problem with Time Windows, Part II: Metaheuristics Transportation Science vol. 39, iss. 1, pp , INFORMS (2005) ASVIN GOEL AND VOLKER GRUHN Solving a dynamic real life vehicle routing problem Operations Research Proceedings 2005, pp , Springer (2006) DAVID PISINGER AND STEFAN ROPKE Large neighborhood search Handbook of Metaheuristics, pp , Springer (2010) VITORIA PUREZA, REINALDO MORABITO AND MARC REIMANN Vehicle Routing with Multiple Deliverymen: Modeling and Heuristic Approaches European Journal of Operational Research (2011) M. M. SOLOMON Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints Operations Research, Vol. 35, No. 2, pp (1987)