Transcript Milk Collection in Western Norway Using Trucks and Trailers

ARILD HOFF
MOLDE UNIVERSITY COLLEGE
ARNE LØKKETANGEN
UROOJ PASHA
MILK COLLECTION IN
WESTERN NORWAY USING
TRUCKS AND TRAILERS
RESEARCH SEMINAR, MOLDE, JUNE 6th
A DAIRY COMPANY
TINE BA
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The leading dairy company in Norway,
owned by 18000 milk producers
Core business is producing dairy
products from raw milk
We look at a subproblem: Collecting milk
from 990 milk producers in the northern
part of Møre og Romsdal County in
Western Norway
3 different dairy plants in the same
district
DAIRY PLANTS
THE DAIRIES
• Circle – Elnesvågen
– 77.2% of total delivery
– Produces Jarlsberg, and other cheeses
• Star – Høgseth
– 17.4% of total delivery
– Produces milk for consumption
• Square – Tresfjord
– 5.4% of total delivery
– Produces cheeses Ridder and Port Salut
THE VEHICLES
• Each dairy has associated a certain
number of heterogeneous cars, with or
without trailers.
• The tanks have several compartments to
avoid mixing:
– Ecological milk from some producers.
– Contaminated milk (antibiotics) from farms
with possible diseases.
– Whey to be returned to the farms for animal
food (waste product when producing cheese).
MILK COLLECTION
PROBLEM
• Collect milk from producers and deliver at the plants
• Each plant has a certain daily demand
• Milk can be stored in cooler tanks at the producers
for at most three days
• Small farms which are inaccessible for a truck
carrying a trailer
• The plans generated are seasonal
– Fixed routes for the season (winter and summer)
– Some slack (spare capacity) is incorporated due to varying
daily production
CURRENT COLLECTION
STRUCTURE
• Milk can be stored for up to three days in
cooler tanks at farms
– Expensive to change
• Collection is according to prespecified
frequencies:
– 73 – Every third day, 7 days a week
– 72 – Every second day, 7 days a week
• Needs a smaller cooler tank at the farm
– 62 – Every second day, not sundays
• Needs same size tank as 73
SOLUTION STRUCTURE
• A trailer can be used as a mobile
depot
• The truck leaves the trailer at a
parking place and visits the farms to
collect milk
• When the truck returns to the parked
trailer, the milk can be transferred to
the trailer tank and the truck are
ready to collect milk from other farms
SOLUTION STRUCTURE
PARKING PLACES
SUPPLIERS
A REAL-WORLD PROBLEM
• Vehicle Routing.
• Multi Depot (3 plants in this district, totally 49 in
Norway).
• Pickup and Delivery (pickup milk, deliver whey).
• Fleet Size and Mix.
• Truck and Trailers / Satellite Depots
• Two-Echelon VRP
• Periodic VRP (frequency every 1, 2 or 3 days).
• Time Windows (to a small degree at suppliers, but
also for meeting ferry times etc.).
INITIAL SOLUTION
1. Compute the number of tours necessary
with reference to the available vehicle
fleet, the visiting frequency and the
needed supplies for each depot.
2. Select seed orders for each tour and
cluster around these.
3. Optimize each tour using a simple local
search.
4. Insert parking places for the tours that
are served with a truck and trailer.
HEURISTIC
• Neighborhood structure
– Move or swap orders between two
tours
– Reduce the neighborhood by only
considering tours containing other
close orders
– Partial neighborhood examination
HEURISTIC
• Reoptimization of subtours after
change
• Try to improve each tour by moving
orders to other subtours
• Recalculation to find optimal
parking places
HEURISTIC
• Tabu Search
– Variable Tabu Tenure
– Diversification strategy to avoid that the
same moves are performed too often
– Dynamic penalty for load-infeasible
solutions are added to the objective value
 ( )   ( ( Lr  Q)    ( Ltir  Qt )  )
r
r iRr
DIVERSIFICATION
• ξ(s) = ψ(s) + η τ(s)
• ψ(s) is the number of h-neighbors order s has
inside its own tour,
• τ(s) is the number of times order s is selected
from the current tour.
• The order s with lowest value ξ(s) is selected for
an eventual move from the tour as long as it is
not declared tabu.
• (h-neighborhood – the set s  S which consist of
the h suppliers closest to s. A tour with none of
the h closest suppliers is not considered for a
move.)
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DIVERSIFICATION
• Our test results are not unambiguous
about the value of η.
• We have chosen to use the value η = 0.75
for our subsequent tests, as this value
gave a slightly better result than the
other alternatives.
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PENALTY FACTOR
 ( )   ( ( Lr  Q)    ( Ltir  Qt )  )
r
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r iRr
β(σ) is the penalty for solution σ which are added to the objective
function
(x)+ = max{0, x}.
r is all tours in the solution
Rr are all subtours in tour r.
Q is the capacity of the complete vehicle
Qt is the capacity of the truck,
Lr is the total load in tour r and
Ltir is the truckload on subtour i in tour r.
The penalty factor α is initially set to 1 and adjusted during the
search by multiplying or dividing it with a value κ when the
solution is respectively feasible or infeasible. Preliminary tests
show that the value κ = 1.1 gives best results in our search.
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OBJECTIVE FUNCTION
f ( )   ( )  ( )  ( )
γ(σ) : Driving distance
ε(σ) : Additional costs i.e. for using
ferrys or toll roads
β(σ): Penalty for infeasible solutions
COMPUTATIONAL
RESULTS
• Want to find out the effect of
– Truck/hanger size
– Collection strategy
– Effect of parking places
VEHICLE SIZES
ID
1
51
5
12
17
71
36
39
Qv
Qt
Qx
M
Qv
10000
14500
18500
21000
29000
33500
29500
33500
–
–
–
–
Qt
10000
14500
18500
10000
10000
14500
18500
18500
Qx
0
0
0
11000
19000
19000
11000
15000
Freq.
7x3
7x3
7x3
7x3
7x3
7x3
7x3
7x3
Total vehicle capacity
Capacity of the truck
Capacity of the hanger
Number of tours
M
95
68
53
47
36
32
35
33
Obj.value
6849.45
5312.21
4526.99
4856.26
4347.30
3875.62
3975.95
3480.90
COLLECTION STRATEGIES
Relative objective value
2.50
2.00
7x1
1.50
7x2
7x3
1.00
0.50
1
51
5
12
17
71
36
39
Vehicle type
- Clearly better to collect every third day
- Need bigger storage tanks at the farms
- In practice a mix of 72 and 73
ONE OR MORE PARKING
PLACES
ID
71
71p
39
39p
Qv
33500
33500
33500
33500
Qt
14500
14500
18500
18500
Qx
19000
19000
15000
15000
Freq.
7x3
7x3
7x3
7x3
P – only one parking per tour
M - number of tours
M
32
33
33
32
Obj.value
3875.62
4292.43
3480.90
3968.38
CONCLUSIONS
• The visiting frequency should be as
long as possible (3 days)
• A strategy where trailers are used
as mobile depot are superior to only
using single trucks
• Tours in the local neighborhood of
the plant can be served by a single
truck without a trailer
CONCLUSIONS
• When the total capacity is equal, a
large truck with a smaller trailer is
better than the opposite
• The possible use of more than one
parking place on a tour can improve
the solution quality significantly
• The advantage of extending the
visiting frequency increases with
the size of the vehicle
Objective Function
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Driving distance
Vehicle acquisition cost
Ferry / toll roads
Extension
– Cost of changing cooling tanks
– Pay for driver (overtime, Sunday, etc.)
What to determine?
• Build an initial solution
– How to determine optimal fleet mix?
– How to decide number of clusters?
– How to find seeding customers?
– When stop clustering?
– How to assign clusters to depots?
Cluster
• The process of grouping a set of
customers into classes of similar/dissimilar
customers.
• What criteria should be used for
clustering?
• How it can be done?
• Is it good to use clustering approach?
How to cluster suppliers?
Proposed Methodology 1/3
• Cluster according to municipalities.
• Calculate demand for each cluster.
• Calculate number and types of vehicles
needed for each cluster.
• Calculate distances between clusters
and from/to depots.
• Merge two clusters if possible.
Proposed Methodology 2/3
• Sort clusters according to each depot.
• Find the most closest depot.
• Allocate further away cluster to this
depot.
– Minimize usage of ferry/toll.
Proposed Methodology 3/3
• Main Methodology
– Tabu Search, Iterated Local Search,
Guided Local Search
• Try to find appropriate fleet mix using Shrinking
and Expanding Heuristic.
EXAMPLE OF A TOUR
A
B