Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Carl Bro a|s

International consulting engineering company

2100 employees worldwide80 officesSpecializes in multi-disciplinary solutions

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Center of ExpertiseLogistics & Planning

Tenna Kellberg Larsen, M.Sc.Anette Vainer, M.Sc.

Graduates from the Dept. of Operational ResearchUniversity of Copenhagen

Working fields:

•vehicle routing•localization•work flow analysis•demand specification•project planning

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Theory vs. PracticeThe issue in designing algorithms for real life

routing problems:• Usability• Flexibility• Consistency to (certain) changes in problem• Generalizing

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

• Exact algorithms often focuses on the structure

• Heuristics often give a framework to a variety of problems

– For example when the demand can not be met

Theory vs. Practice

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

1. Ordering the customers/orders after importanceSolving iterative problemsMake a solution meeting the demand of all costumers with importance 1. If there is more capacity add costumers with importance 2 and so on

Theory vs. PracticeRelaxing the demand

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

2. Ordering after geographical areasSolving iterative problemsMake a solution meeting the demand of all costumers in geographic area 1. If there is more capacity add costumers in geographic area 2 ...In this way you have a flexible algorithm. Both according to the nature of the problem and the problem size / computing time.

Theory vs. PracticeRelaxing the demand

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Theory vs. PracticeOrdering after geographical areas

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

CasePresentation

The client is a major Danish company delivering goods of own production as well as other goods. The demand for one day can often not be met. The client have a variety of staff policies.The client is divided into sections, that have different distribution pattern.Their customers are evenly distributed over the country

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

CasePresentation

Plants

Depot

Customer

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

• There are two types of orders: high priority and low priority

• There are three types of areas: have to be visited, can be visited and areas, that are not taken into consideration.

• Some orders must be placed in the beginning of the trip

• There can be several trips in one route. • The vehicles are previously assigned to depots.

Orders are assigned to plants in the ERP-system

CasePresentation

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

The solution must be feasible according to:

• Time windows• Working hour restrictions• Driving and resting rules• Capacity• Vehicle characteristics• Availability of the vehicle• Opening hours at the depots

CasePresentation

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Casealgorithm

Four step algorithm1. Assign orders to depots2. Make plan for each depot in the ”have to

visit” area3. Swap orders between depots4. After having completed planning for the ”have

to visit” area, the algorithm tries to add orders from the ”can visit” area with an insertion algorithm

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Assigning orders to depots:

The orders are assigned to the one of the three nearest depots, that generates the lowest transportation costs

Casealgorithm

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Use a heuristic to create as many routes as there is vehicles assigned to the depot. The routes may contain of more than one trip.High-priority orders first

Step 1.Select a vehicle. Randomly select an order to the trip. Repeat step 1 until all vehicles have a tripStep 2.Search all the trips. Add the order, that renders the lowest cost and that does not violate the constraints. The cost is defined as the minimum distance from any order on the trip (or the depot itself) to any order not on the trip

CasealgorithmSolving the problem for each depot using a parallel nearest customer algorithm:

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

• Create N different initial solutions.

• Use a r-opt based heuristic to improve the initial solutions. The arcs, that joins the orders within the trip is being swapped

Casealgorithm

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Improving the trip:Swapping 2 arcs

Case algorithmThe 2-opt heuristic

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

• A r,p-opt based Tabu Search heuristic is used to improve the N1 N best solutions by swapping r orders from one trip with p orders from another trip. Both trips from the same depot.

• A r,p-opt based Tabu Search heuristic is used to improve the N2 N1 best solutions by swapping orders between the depots to minimize the load costs.

Casealgorithm

Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

Conclusions

The academic research in exact algorithms for the VRP is hard to take advantage of in the kind of consulting areas, where problem changes constantly

The growing amount of research done within the heuristic algorithms gives a good framework for creating tools suitable to solve many different kinds of planning problems