1. Facility Logistics Simulation at a Large Retailer
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
Simulating a single CP
Scott J. Mason,

3. What is being modeled?
A generic CP that includes the following aspects:
Inbound (IB) less-than-truckload (LTL) arrival process
Flexible assignment and dispatching of LTL shipments to dock doors
Processing at the purchase order (PO) level
Outbound (OB) truckload (TL) departure process
Flexible assignment of outbound trucks to dock doors
Flexible dispatching of cross-docked purchase orders to outbound trucks
Resource Requirements
Contention for dock doors, associates for loading/unloading, material handling equipment
Purchase Order (PO) Modeling
Origin and destination for each PO
Weight and cube
Scott J. Mason,

4. How can the simulation be used?
Tactical Analysis based on optimization
To evaluate the effect of the new supplier/CP/DC product flow decisions on CP performance
Can the CP handle the projected demand over the planning horizon? What should the size of the CP actually be?
# dock doors, # associates, material handling equipment
Operational Analysis
The simulation can be used to evaluate operational changes within a CP
New PO dispatching rules
Inbound trailer door assignments
Outbound trailer door assignments
Scott J. Mason,

5. Unloading/loading efficiency
What is being measured?
Utilization
Resource utilization (doors, associates, material handling equipment)
Space utilization (% of floor space utilized)
PO processing
# POs processed per week
PO cycle time (time to be processed through CP)
% of POs exceeding 48 cycle time threshold
Unloading/loading efficiency
Queuing times for POs
Queuing times for inbound trucks
% of outbound trucks leaving LTL
Scott J. Mason,

6. Overview of Model Process
LTL trailers arrive and wait for a free dock door
Dispatcher assigns LTL trailer to IB door
Each shipment has a number of POs
Each PO may be unloaded by either clamps, forklifts, slips, or carts
Each PO has an origin, destination, weight, and cube
Each PO is unloaded
Either sent directly to OB trailer designated for destination for loading, or
Waits within the CP’s bay until OB trailer is available for loading
OB trailers wait until they meet their weight requirement or until 48 hour threshold is passed
Scott J. Mason,

7. Demand: LTL Shipment Arrival Process
Assume 5 day operation (M-F)
LTL shipments that arrive during the weekend are processed on Monday
Weekend demand is added to Monday’s demand
LTL truck arrival data was collected and retailer personnel gave input
Number of trucks that arrive during each hour of the day is random and varies with the time of day
Mean arrival rate as function of time
Scott J. Mason,

8. CP 6901 LTL Arrival Model
Daily LTL arrival pattern varies with the time of day.
Weekend Model - summed 20 week aggregated weekend demand and divided by 20 to get 21.5 LTL arrivals per weekend, modeled with Poisson distribution
Scott J. Mason,

9. LTL Shipment Origin Modeling
Randomly determine the supplier zip that sent the shipment according to a discrete probability distribution
Where is the probability that the LTL came from origin zip and is the number of POs from origin zip processed through the CP
Scott J. Mason,

10. CP 6901 Shipment Origin Model
Let be the number of POs from origin zip i processed through CP The probability that the LTL came from origin zip i is:
Scott J. Mason,

11. LTL Shipment Purchase Order Model
Each LTL shipment contains a random number of POs to be processed.
We assume that the number of POs on a shipment does not depend on the shipment origin or destination.
We assume that the number of POs on a shipment is normally distributed with a mean and standard deviation and that there must be at least 1 PO per shipment.
CP 6901
Mean = 8.4
Standard deviation = 5.1
Scott J. Mason,

12. Purchase Order Weight and Cube Model
Each PO has its own weight and cube
May depend on supplier and destination (i.e., certain suppliers have heavier weights or larger cube products and certain destinations may tend to get heavier or larger products from certain suppliers)
Results in highly significant data requirements and statistical analysis
Simplifying Assumptions
We assume that weight and cube depends only upon supplier
We assume that the distribution of weight and cube is well modeled by a triangular distribution
We assume that the Pareto Principle applies
20% of suppliers account for 80% of POs passing through the CP, resulting in the need for only distributions for 20% of the suppliers
Combine other 80% of suppliers into group and use one distribution for the group
Scott J. Mason,

13. CP 6901 PO Weight/Cube Models
Scott J. Mason,

14. CP 6901 PO Weight/Cube Models
Scott J. Mason,

15. CP Resource and Process Modeling
Model the processing within the CP at the PO level
When a LTL shipment arrives the number of POs on the shipment is generated. Each PO is given a weight, cube, destination DC, and load type. After the LTL is assigned an unloading dock, the POs are unloaded when resources are available.
Each PO is unloaded (individually) using an associate and the material handling equipment for its type of load (pallet, slip, or floor).
Material handling equipment (forklifts, clamps, carts, and slips) are modeled as transporters that can move at a given velocity over a given distance.
Scott J. Mason,

16. Resource and Process Modeling Data Requirements
Quantity
Number Dock Doors 20
Number of Associates 6
Number of Fork Lifts 4
Number of Clamps
Number of Carts 10
Length of CP (ft)
400
Width of CP (ft)
200
Load Type
Discrete Distribution
Pallet
0.4
Slip
Floor
0.2
Transporter Type
Cube (ft3)
Lbs
Forklift 70
3,000
Clamp
Cart
192
500
Slip
Transporter
Minimum
Mode
Maximum
Clamp 5 7 9
Cart 1 3
Fork Lift
Scott J. Mason,

17. Unloading/Loading Process
The unloading and loading Process times were obtained through onsite time studies
10 observations per load and unload process per transporter type were averaged
Type
Minimum
Mode
Maximum
Floor 52
208
375
Pallet 6 11 15
Slip 7 20 36
Type
Minimum
Mode
Maximum
Floor 40
192
310
Pallet 5 9 13
Slip 6 16 32
Scott J. Mason,

18. CP Physical Modeling
Distances were calculated using rectilinear calculations from dock to dock door and the dock door to bay
Scott J. Mason,

19. Example Distance Matrix
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20. IB and OB Shipment Dispatching
Whenever a dock door is freed, we randomly determine whether it should be designated for IB or OB according to the distribution, 25% OB, 75% IB
We know that the CP consolidation ratio is roughly 3:1 (3 LTLs for 1 TL); therefore, dock door usage is 25% for loading OB, 75% for unloading IB.
IB shipments are assigned to a door based on a first come first served basis.
OB trailers are assigned to a door based on discrete distribution
PMF from destination distribution such that an assignment will be made to a door if one is not already been assigned
IB/OB trailer to dock assignment
This is an area of active research. Many companies are beginning to use optimal assignment strategies to improve cross-docking efficiency.
Develop heuristic assignment rules based on optimization and expert dispatchers.
Scott J. Mason,

21. PO Dispatching and Load Building
Logic used for load Building
If IB arrives with OB destination truck ready, then IB will be unloaded and loaded onto OB truck
If POs on Bay have an OB destination truck ready, then POs will be loaded onto OB truck
If OB truck exceeds 48 hour threshold, then check POs in Bay, if none then immediately ship OB truck to destination else load then ship
If OB truck is at capacity (cube/pound) then dispatch OB truck to destination
Scott J. Mason,

22. Verification and Validation
Collected data from real system and compared real system to simulation output
Optimization model showed an 84.03% CP dock door utilization
Simulation showed an 82.90% dock door utilization!
Retailer Actual
Simulation Output
Expected Number of POs
2057
2029
CP Consolidation Ratio (LTL to TL)
3 to 1
2.75 to 1
Maximum Time PO Spends at CP
48 + grace*
51.7
% of Late POs 5%
5.20%
* grace time to load remaining POs in Bay
Scott J. Mason,

23. Validation Example for a Single CP
Increased demand by 10% – 12% over ten years
Door and Bay utilization increases as demand increases
Scott J. Mason,

24. Validation Example for a Single CP (2)
As demand increases, PO time in Bay increases
As demand increases, average OB trailer waiting time decreases
Scott J. Mason,

25. Your Takeaway?
The iterative use of optimization and simulation in practice can provide powerful insights into smarter, more effective decision making.
However, there is a non-trivial amount of time and resources required to pull this off!
This project was funded by the retailer over a 12 month period for $75,000 through the CELDi research center
As a consultant myself, I can honestly say that no consultant could have done this any cheaper!
Scott J. Mason,