1. Intermodal Supply Chain Optimization at a Large Retailer Part 1: Model Development
Scott J. Mason, Ph.D.
Fluor Endowed Chair in Supply Chain Optimization and Logistics
Professor of Industrial Engineering

2. k distribution centers
The Logistics Network
Mode: LTL
Modes: LTL or TL
Modes:
Intermodal and TL
i suppliers
j facilities
k distribution centers
Suppliers Consolidation Points Distribution Centers
Scott J. Mason,

3. Consolidation Point (CP) locations
Project Goals
Model and analyze the retailer’s distribution network to assess utilization levels resulting from the impact of various proposed strategic routing approaches.
Assess the operational feasibility of strategic recommendations using discrete event simulation
Consolidation Point (CP) locations
Scott J. Mason,

4. Two Phase Approach
In Phase 1, network optimization techniques used to study the CP network
Static, deterministic
Investigate strategic issues associated with long-term network configuration and growth
In Phase 2, discrete event simulation model developed to study any one CP
Dynamic, stochastic
Analyze operational feasibility of optimization model recommendations
Scott J. Mason,

5. Phase 1—Strategic Optimization Study
Develop an optimization-based approach to determine, over the next five years, which CP locations should
Be expanded
Be closed
Be opened/built
Objective is to minimize total cost of CP network transportation
Examine six month time buckets
Scott J. Mason,

6. Phase 1 Problem Formulation
Objective: Minimize Cost
Transportation costs
Truck
Intermodal (i.e., truck and rail)
Constraints:
Meet all demand
Transportation vehicle weight and volume capacity constraints
CP capacities in terms of pounds/cube per door and number of doors current/expandable to
Scott J. Mason,

7. Data Collection—CP Information
Name
Location
Number of dock doors
Capacity (lbs per dock door per week)
DC serviceability
Distances from suppliers
Costs to ship from suppliers by modes
Distance to DCs
Cost of shipping to DCs by modes
Scott J. Mason,

8. Data Collection—Demand Information
For each DC, what does it demand from every supplier in terms of
Weight (pounds)
Volume (cubic feet)
Scott J. Mason,

9. Optimization Model Assumptions
Unlimited supply
Demand in pounds and cube
Infinite number of trucks and rail cars
Modes for lane shipments are fixed
Fixed transportation cost from supplier to CP
Per mile cost for distances >= 150 miles
Fixed rate for distances < 150 miles
Scott J. Mason,

10. Analysis performed using CPLEX
Model Development
Model coded in AMPL
A mathematical programming language “front-end”
Model logic captured in a “model file”
“Data file” used to specify information for the problem of interest
Many data files can be run through the same model file
Analysis performed using CPLEX
Industrial-strength optimization solver
Scott J. Mason,

11. Example AMPL Model
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12. Constructed base optimization model of CP network for testing purposes
Base Model Validation
Constructed base optimization model of CP network for testing purposes
3 CPs, 6 DCs, 10 Suppliers
All suppliers capable of shipping through all CPs to all DCs
Validated and verified base model with simple data
Compared model results with hand calculations
Produced expected results when demand, costs, and other parameters were varied
Scott J. Mason,

13. Added constraints pertaining to
Expanding the Model
Added constraints pertaining to
Weight and volume limits on transportation
Either can restrict vehicle capacity
Calculating the number of trucks (LTL and TL) and rail cars used in the network
Expanded base optimization model to represent the retailer’s CP network
19 CPs
40 DCs
2000+ suppliers
Scott J. Mason,

14. Expanding the Model, Take 2
Even selecting the 100 highest-volume suppliers across all DCs, model solution performance was undesirable
Difference (“gap”) between optimal solution and best lower bound solution was approximately 40% after 24 hours on Pentium IV PC with 2 GB of RAM
Scott J. Mason,

15. Expanding the Model, Take 3
Per meeting with retailer, aggregated suppliers by rolling up to 3-digit ZIP codes
Model has 19 CPs, 40 DCs, and digit ZIP codes
Using the aggregated 3-digit ZIP approach, the number of suppliers is not a concern, as there exists some finite set of 3-digit ZIP codes
Model size should remain somewhat stable/consistent within any given time period
Scott J. Mason,

16. Improving Model Tractability
“Tightened” model formulation for improved solvability
354k  172k variables (8500 are integer or binary)
84k  35k constraints
Initial formulation required 24 hours to achieve 40% optimality gap
Current model reaches optimality gap of 0.5% in 30 minutes on 2.8 GHz Pentium IV PC with 2 GB of RAM
Scott J. Mason,

17. Promoting Model Usability
Worked with client to define a basic data file structure for time-based DC demand from various 3-digit ZIP codes
Constants file contains fixed information, such as set of CPs, set of DCs, and so on.
Input file 1 contains demand by 3-digit supplier ZIP code for each DC (dynamic)
Input file 2 contains distances from 3-digit supplier ZIP code to each DC (static)
Scott J. Mason,

18. Promoting Model Usability (2)
Created a C++ program to read in properly formatted data files, then automatically build the corresponding AMPL data file
Can save a considerable amount of time when performing multiple sensitivity analysis studies
Scott J. Mason,