Rule-based Price Discovery Methods in Transportation Procurement Auctions
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Transcript of Rule-based Price Discovery Methods in Transportation Procurement Auctions
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Rule-based Price Discovery Methods in Transportation
Procurement Auctions
Jiongjiong SongAmelia Regan
Institute of Transportation StudiesUniversity of California, Irvine
INFORMS Revenue Management Conference 2004
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Outline
• Introduction to Procurement Auctions• The Business Rule based Bid Analysis
Problem– Shippers’ business considerations – An integer programming model
• Our solution methodologies– Construction heuristics and Lagrangian heuristics– Experimental results
• Conclusion and extensions
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Procurement Auctions
• Combinatorial auction– An allocation mechanism for multiple items– Multiple items put out for bid simultaneously– Bidders can submit complicated bids for any
combinations of items
• Unit auction– Packages are pre-defined and are mutually exclusive
• Applications in freight transportation– Freight transportation exhibits economies of scope– Shippers gain more benefits to bundle lanes– Carriers dislike this combinatorial auction idea
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Procurement Auctions
• Combinatorial auction– Complicated optimization problems for both
shippers and carriers– Shippers lose control over bundles, carriers have
more freedom
• Unit auction– Shippers gain control– Carriers have much simpler pricing problem to
solve
• Shippers still have a difficult optimization problem to solve
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Business Considerations
• If price is the sole reason for assigning bids – the unit auction problem is simple to solve
• However, shippers have additional considerations
• Caplice and Sheffi (2003) identify the primary considerations for the trucking industry case
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Business Considerations
• Minimum/maximum number of winning carriers (core carriers)
• Favor of Incumbents
• Backup concerns
• Minimum/maximum coverage
• Threshold volumes
• Complete regional coverage
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Business Considerations
• Performance factors – these are necessary to ensure that high priced carriers don’t “Lose the auction but win the freight”
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Our Model
• We include the following: – maximum / minimum number of winning
carriers– maximum / minimum coverage– incumbent preference– performance factors (penalty cost)
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Our Model
• We assume that:– backup considerations– regional coverage
• Can be taken care of in pre-processing and pre-screening steps
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The General Model
,
min
. . 1 (1)
(2)
(0,1) (3)
Where:
is a bid package in set
is a bidding carrier in set
kj kjj J k K
kjk K
kj
kj
c x
s t x j J
x
j J
k K
c
is the cost for carrier to serve package
1 if carrier k wins package j =
0 otherwise
are any business or logical constraints
kj
k j
x
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Our Model
min max
min max
min
. .
1, (4)
, (5)
, (6)
, (0,1)
kj kj k kk j k
kjk
kk
k kk kj k
j
k kj
c x p y
s t
x j J
K y K
T y x T y k K
y x
(7)
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Our Model
min max
mi
Where:
is the penalty cost for carrier to be included in the winning bids
1 if carrier k wins one or more package
0 otherwise
, are the minimum and maximum number of winning carriers
k
k
p k
y
K K
T
n max , are the minimum and maximum number of packages that can be
assigned to carrier
k kT
k
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Our Model
• Our objective function problem minimizes total procurement costs including the bid prices and the penalty costs to manage multiple carrier accounts
# of Carriers
Cost
Relationship between procurement costs and number of winners
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Our Model
• The penalty cost can also be used to capture the shipper’s favoring of specific carriers at the system level– incumbents have a zero penalty cost and non-
incumbents have a positive penalty cost
• This could be extended to specific packages• Though we model the maximum and minimum
volume constraints at the system level, these could be applied at the regional or facility level
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Our Model
• Even with the simplification of some business constraints to the network level this problem can easily be shown to be NP-Complete
• Solving problems of reasonable size (thousands of lanes, hundreds of carriers) using exact methods is not feasible– CPLEX failed to solve such as a case in two
days with a moderately fast computer
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Our Solution Approach
• Simple construction techniques based on the relationship between our problem and the capacitated facility location problem– MDROP and MADD for Modified DROP and
ADD
• Lagrangian Relaxation– Constraint (4) is relaxed (a lane is only
assigned to a single carrier)– Network flow based algorithms to solve the
relaxed problem
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Test Data
• Input data for each problem includes:– Each carrier’s bid prices for each lane– penalty cost for each carrier– minimum and maximum number of lanes if this carriers
is a winner– minimum and maximum number of winners– a carrier’s bid price is randomly distributed between 10
and 100– the penalty cost is randomly distributed between 0 and
3% of total bid prices
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Results
• Small Problems
Case Index 1 2 3 4
# of carriers 20 20 20 30
# of lanes 200 300 400 300
Lower / Upper 99.8% 99.9% 99.3% 99.6%
Upper / CPLEX 1.0 1.0 1.0 1.0
MADD / CPLEX 1.01 1.0 1.001 1.007
MDROP / CPLEX 1.0 1.0 1.001 1.0
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Results
• Small Problems
Case Index 5 6 7 8 9
# of carriers 30 40 40 40 50
# of lanes 400 300 400 500 400
Lower / Upper 96.9% 97.4% 97.9% 97.5% 97.9%
Upper / CPLEX 1.0 1.001 1.001 1.0 1.0
MADD / CPLEX 1.003 1.009 1.004 1.002 1.003
MDROP / CPLEX 1.0 1.003 1.001 1.001 1.001
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Solution Times (minutes)
• Small Problems
Case Index 5 6 7 8 9
CPLEX 66.3 66.2 137.5 231.0 192.5
Lagrangian 0.7 0.6 0.8 0.7 0.7
MADD 0.04 0.05 0.06 0.06 0.07
MDROP 0.03 0.03 0.04 0.04 0.05
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Results
• Larger Problems
Case Index 11 12 13 14
# of carriers 100 100 200 200
# of lanes 2000 4000 4000 6000
Lower/Upper 99.2% 96.9% 97.9% 99.0%
MADD/Upper 1.057 1.051 1.063 1.063
MDROP/Upper 1.056 1.050 1.058 1.062
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Results
• Larger Problems
Case Index 15 16 17 18 19
# of carriers 300 300 400 400 500
# of lanes 6000 8000 8000 10000 10000
Lower/Upper 99.6% 99.3% 99.0% 99.1% 99.0%
MADD/Upper 1.070 1.067 1.068 1.090 1.080
MDROP/Upper 1.065 1.066 1.067 1.076 1.071
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Solution Times (minutes)
• Larger Problems
Case Index 11 12 13 14
Lagrangian 6 14 31 48
MADD 0.4 0.4 0.6 1
MDROP 0.5 1.1 3.9 6.6
Case Index 15 16 17 18 19
Lagrangian 76 101 136 181 225
MADD 1.1 1.4 2.1 4 7.6
MDROP 13.9 20 34 46 69
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Conclusion
• We show that unit auctions with side constraints can be solved in reasonable time and with a high degree of confidence
• The Lagrangian Relaxation solution method could be used to make final decisions while the heuristics (or improved versions of these) could be used to conduct sensitivity analysis
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Extensions
• Shippers may have additional or more complicated business rules
• As optimization tools improve, requirements will increase
• Eventually, pure combinatorial auctions (for large shippers and large carriers) may be feasible and preferable – we are working to solve bidding and winner determination problems for those auctions
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Thank You