Carl Bro a|s

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Carl Bro as

• International consulting engineering company

2100 employees worldwide 80 offices Specializes
in multi-disciplinary solutions
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(No Transcript)
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Center of ExpertiseLogistics Planning

• Tenna Kellberg Larsen, M.Sc.
• Anette Vainer, M.Sc.
• Graduates from the
• Dept. of Operational Research
• University of Copenhagen

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

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Theory vs. Practice

• The issue in designing algorithms for real life
  routing problems
• Usability
• Flexibility
• Consistency to (certain) changes in problem
• Generalizing

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Theory vs. Practice

• 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

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Theory vs. Practice Relaxing the demand

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

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Theory vs. Practice Relaxing the demand

• 2. Ordering after geographical areas
• Solving iterative problems
• Make 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.

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Theory vs. PracticeOrdering after geographical
areas
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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

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CasePresentation
Plants Depot Customer
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CasePresentation

• 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

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CasePresentation

• 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

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Casealgorithm

• Four step algorithm
• 1. Assign orders to depots
• Make plan for each depot in the have to visit
  area
• Swap orders between depots
• 4. 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

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Casealgorithm

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

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Casealgorithm
Solving the problem for each depot using a
parallel nearest customer algorithm

• 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 trip
• Step 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

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Casealgorithm

• 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

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Case algorithmThe 2-opt heuristic

• Improving the trip
• Swapping 2 arcs

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Casealgorithm

• 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.

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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