the integrated warehouse- inventory-transportation problem: a … · 2013-07-15 · •...
TRANSCRIPT
The Integrated Warehouse-Inventory-Transportation Problem: A Stochastic Integer Quadratically-
Constrained Programming Approach
Christopher D. Hagmann , Nan Kong, Ph.D. Purdue University
Pratik J. Parikh, Ph.D. Data Analytics and Optimization Lab, Wright State University
CMMI #1235061 and #1235283
ICSP Bergamo XIII 12 July 2013
Introduction
Newest member of group (7 months)
First year PhD student
Studying Chemical Engineering at Purdue University
Newlywed
WAREHOUSE UTILIZATION
INVENTORY
TRANSPORTATIONM T W R F
OU
TB
OU
ND
INB
OU
ND
S1 S2 S3
W
V1 V2
S4
An illustration of the supply chain of an US-based apparel company
Weekly variation in the units picked at the warehouse of the US-based apparel supply chain
Warehouse Weekly Workload Variation • Period: Jan – Dec 2011
• 42-219% variation in warehouse workload
0
200
400
600
800
1,000
1,200
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
Un
its
Pic
ked
Per
Wee
k
(x 1
000)
Weeks
Daily Workload Variation
-
50,000
100,000
150,000
200,000
250,000
300,000
1 2 3 4 5 6 7
Un
its
Pic
ked
per
Da
y
Days
• A Fortune 500 Grocery Distributor
• Outbound activity at one of their warehouses in the US
• Period: Aug 29 – Sep 4, 2011
• Variation in workload: 76% - 153% of that week’s average
The Integration of W, I, T
Inventory Transportation
Warehouse
Forward Impact
Reverse Impact
Impact of Technology used Workforce level
on Shipment schedules and quantity Inventory at warehouse and stores
Impact of Shipment schedules Shipment quantity Inventory levels
on Warehouse workload Workforce planning
Research Objectives
• Proactive vs. reactive decision making (warehouse perspective)
• Warehouse-Inventory-Transportation Problem (WITP)
Objective of WITP
Explore complex and dynamic interdependencies between warehouse, inventory, and transportation decisions
Determine the optimal distribution strategy while minimizing total cost
• Warehousing decisions: – Technology Selection (aisle configuration, layout, picking method, IT, etc.) – Workforce (permanent and temporary) – Other (cross-docking and cross-training)
Incorporating Uncertainty
• Demand is an exogenous uncertainty.
• Full-time employees cannot be hired and fired with every time step.
• Technology is expensive and cannot be bought with every time step
• These motivate the need of a two-stage stochastic problem with full-time workforce level and technology usage decisions in the first-stage.
Scenario-Wise Decomposition and Non-Anticipativity Constraints
In addition to all previously stated constraints
Dual Decomposition in Stochastic Integer Programming Carøe & Schultz
Instance Generation
• Randomly generate the mean for each demand
• Generate demand scenarios by sampling from a uniform distribution between 75% and 125% of the mean demand
• All demand variations are completely correlated and linked to previous time step
Conclusion
• Warehouses are a crucial part of supply chain logistics and should be included in overall optimization problems
• It is important to optimize warehousing decisions under uncertainty
Future Research
• Finish augmented Lagrangian relaxation code
• Investigate alternative scenario-wise decompositions
• Progressive Hedging
• Investigate alternative methods for handling quadratic constraints
• Investigate better methods for scenario generation