Rule-based Price Discovery
Methods in Transportation
Procurement Auctions
Jiongjiong Song
Amelia Regan
Institute of Transportation Studies
University of California, Irvine
INFORMS Revenue Management Conference
2004
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
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
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
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
Business Considerations
• Minimum/maximum number of winning
carriers (core carriers)
• Favor of Incumbents
• Backup concerns
• Minimum/maximum coverage
• Threshold volumes
• Complete regional coverage
Business Considerations
• Performance factors – these are
necessary to ensure that high priced
carriers don’t “Lose the auction but win
the freight”
Our Model
• We include the following:
– maximum / minimum number of winning
carriers
– maximum / minimum coverage
– incumbent preference
– performance factors (penalty cost)
Our Model
• We assume that:
– backup considerations
– regional coverage
• Can be taken care of in pre-processing
and pre-screening steps
The General Model

min
jJ , kK
s.t.
x
kK
kj
ckj xkj
 1 j  J
(1)

(2)
xkj  (0,1)
(3)
Where:
j is a bid package in set J
k is a bidding carrier in set K
ckj is the cost for carrier k to serve package j
1 if carrier k wins package j
xkj = 
0 otherwise

are any business or logical constraints
Our Model
 c
min
x   pk yk
kj kj
k
j
k
s.t.
x
kj
 1,
j  J
(4)
k
K min   yk  K max ,
(5)
k
k
k
Tmin
yk   xkj  Tmax
yk ,
k  K
(6)
j
yk , xkj  (0,1)
(7)
Our Model
Where:
pk is the penalty cost for carrier k to be included in the winning bids
1 if carrier k wins one or more package
yk  
0 otherwise
K min , K max are the minimum and maximum number of winning carriers
k
Tmik n , Tmax
are the minimum and maximum number of packages that can be
assigned to carrier k
Our Model
• Our objective function problem minimizes
total procurement costs including the bid
prices and the penalty costs to manage
multiple carrier accounts
Cost
# of Carriers
Relationship between procurement costs and number of winners
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 nonincumbents 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
Our Model
• Even with the simplification of some
business constraints to the network level
this problem can easily be shown to be NPComplete
• 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
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
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
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
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
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
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
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
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
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
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
Thank You