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IRP
M. Sevaux
Definition
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Inventory routingand on-line inventory routing
Prof Marc [email protected]
Helmut Schmidt UniversityLogistic Management Dept.
Hamburg, Germany
University of South-BrittanyLab-STICC, CNRSLorient, France
Research Seminar – Magdeburg, GermanyMarch 20, 2011
Joint work with M.J. Geiger
![Page 2: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/2.jpg)
IRP
M. Sevaux
Definition
Literature
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Problems
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The Inventory Routing Problem (IRP)
One depot
A set of customers
![Page 3: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/3.jpg)
IRP
M. Sevaux
Definition
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2/29
The Inventory Routing Problem (IRP)
One depot
A set of customers
A time horizon
![Page 4: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/4.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
2/29
The Inventory Routing Problem (IRP)
One depot
A set of customers
A time horizon
A known demand for eachcustomer and each period
![Page 5: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/5.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
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2/29
The Inventory Routing Problem (IRP)
One depot
A set of customers
A time horizon
A known demand for eachcustomer and each period
Minimize Inventory cost
![Page 6: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/6.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
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2/29
The Inventory Routing Problem (IRP)
One depot
A set of customers
A time horizon
A known demand for eachcustomer and each period
Minimize Inventory cost
Minimize Routing cost
![Page 7: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/7.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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The Inventory Routing Problem (IRP)
One depot
A set of customers
A time horizon
A known demand for eachcustomer and each period
Minimize Inventory cost
Minimize Routing cost
IRP is a real bi-objective optimization problem
![Page 8: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/8.jpg)
IRP
M. Sevaux
Definition
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Problems
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Improvements
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Important decisions
For solving the IRP, we must make the following decisions:
Decisions
![Page 9: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/9.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
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3/29
Important decisions
For solving the IRP, we must make the following decisions:
Decisions
1 When deliver customers?
![Page 10: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/10.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
3/29
Important decisions
For solving the IRP, we must make the following decisions:
Decisions
1 When deliver customers?
2 How much deliver?
![Page 11: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/11.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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Problems
Results
Improvements
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3/29
Important decisions
For solving the IRP, we must make the following decisions:
Decisions
1 When deliver customers?
2 How much deliver?
3 With which routes?
![Page 12: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/12.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
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Important decisions
For solving the IRP, we must make the following decisions:
Decisions
1 When deliver customers?
2 How much deliver?
3 With which routes?
All these decisions are linked together:
increase delivery quantities → change routes or frequency
change frequency → adapt delivery quantities
. . .
![Page 13: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/13.jpg)
IRP
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Important references
First papers
[Bell et al., 1983]Improving the distribution of industrial gases with and on-line computerizedrouting and scheduling optimizerInterfaces 13(6):4–23, 1983.
[Federgruen and Zipkin, 1984]A combined vehicle routing and inventory allocation problemOperations Research 32(5):1019–1037, 1984
Recent surveys
[Bertazzi et al., 2008]Inventory routingin The Vehicle Routing Problem: Latest Advances and New Challenges
49–72, 2008.
[Cordeau et al., 2011]Short-haul routingin Handbooks in Operations Research and Management Science:
Transportation. To appear.
![Page 14: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/14.jpg)
IRP
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IRP variants
There exists a large number of variants
planning horizon (finite/infinite)
inventory costs and capacities
production/demand rates (of single/multiple product)
specific restrictions/regulations
deterministic/stochastic demand/production
initial inventory
fleet (homogeneous/heterogeneous)
And different objectives
usually a combination of inventory level and routing cost
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IRP
M. Sevaux
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Practical IRP
What does mean Practical IRP?
Main goal: helping companies where IRP is important
Propose a simple output
![Page 16: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/16.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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Problems
Results
Improvements
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Practical IRP
What does mean Practical IRP?
Main goal: helping companies where IRP is important
Propose a simple output
Use simple rules (that can be understood)
Use simple implementation that can be reproduced
![Page 17: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/17.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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Problems
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Improvements
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Practical IRP
What does mean Practical IRP?
Main goal: helping companies where IRP is important
Propose a simple output
Use simple rules (that can be understood)
Use simple implementation that can be reproduced
Give different alternatives
![Page 18: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/18.jpg)
IRP
M. Sevaux
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A major assumption in our work
To follow a common strategy in companies dealing with IRPWe have separated the decisions
![Page 19: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/19.jpg)
IRP
M. Sevaux
Definition
Literature
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Problems
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Improvements
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7/29
A major assumption in our work
To follow a common strategy in companies dealing with IRPWe have separated the decisions
Determine quantities for each period
![Page 20: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/20.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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Problems
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Improvements
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7/29
A major assumption in our work
To follow a common strategy in companies dealing with IRPWe have separated the decisions
Determine quantities for each period
Compute best routing for each period
![Page 21: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/21.jpg)
IRP
M. Sevaux
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The choice of policies
Standard policies:
DD Day-to-day delivery policyIf not enough in stock, deliver the missing demand
![Page 22: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/22.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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Problems
Results
Improvements
Perspectives
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8/29
The choice of policies
Standard policies:
DD Day-to-day delivery policyIf not enough in stock, deliver the missing demand
OU Order-up-to level policyWhen you ship, ship the maximum (customer capacity)
![Page 23: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/23.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
8/29
The choice of policies
Standard policies:
DD Day-to-day delivery policyIf not enough in stock, deliver the missing demand
OU Order-up-to level policyWhen you ship, ship the maximum (customer capacity)
ML Maximum level policy (bad name!)Any quantity less than the maximum level(but which quantity?)
![Page 24: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/24.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
8/29
The choice of policies
Standard policies:
DD Day-to-day delivery policyIf not enough in stock, deliver the missing demand
OU Order-up-to level policyWhen you ship, ship the maximum (customer capacity)
ML Maximum level policy (bad name!)Any quantity less than the maximum level(but which quantity?)
Assumptions
Serve only if current inventory is not enough
If served, only full number of period demands
![Page 25: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/25.jpg)
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The frequency policy encoding
Solutions are modeled as a frequency f of the deliveriesfor each customer
f = 1 → DD policyf = 2 → serve for the next two consecutive periods· · · → . . .f = k → serve for the next k consecutive periods· · · → . . .f = +∞ → OU policy
The policies are simple to understand (even for companies)and easy to encode for us (vector of integer)
![Page 26: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/26.jpg)
IRP
M. Sevaux
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Evaluation of solutions
Each solution is measured with the two criteria
Inventory cost
Sum of all inventory levels at customers’ at the end of eachperiod. This can be computed in O(np)
Routing cost
Sum of all distances run by the trucks at every period. Solve aVRP for each period. This is a NP-hard problem!!!
![Page 27: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/27.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
10/29
Evaluation of solutions
Each solution is measured with the two criteria
Inventory cost
Sum of all inventory levels at customers’ at the end of eachperiod. This can be computed in O(np)
Routing cost
Sum of all distances run by the trucks at every period. Solve aVRP for each period. This is a NP-hard problem!!!
Routingengines
Clarke & Wright+ savings heuristic
Record-to-recordtravel algorithm
![Page 28: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/28.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
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11/29
Initial solutions
We have implemented several initial solutions
![Page 29: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/29.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
11/29
Initial solutions
We have implemented several initial solutions
Identical frequency:f is the same foreach customer
Rou
ting
Inventory
b
b
b
b
b
![Page 30: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/30.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
11/29
Initial solutions
We have implemented several initial solutions
Identical frequency:f is the same foreach customer
Totally random:f is chosen atrandom for eachcustomer
Rou
ting
Inventory
b
b
b
b
b
b
b
b
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IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
11/29
Initial solutions
We have implemented several initial solutions
Identical frequency:f is the same foreach customer
Totally random:f is chosen atrandom for eachcustomer
Controlled random:f is chosen atrandom betweentwo bounds
Rou
ting
Inventory
b
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![Page 32: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/32.jpg)
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Neighborhood
Encoding is a vector of integersMany moves are possibles but think of the neighborhood size
Initial solution
s . . .2 3 1 5 1 2
![Page 33: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/33.jpg)
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Neighborhood
Encoding is a vector of integersMany moves are possibles but think of the neighborhood size
Initial solution
s . . .2 3 1 5 1 2
Move 1: Change frequency by ±1 (here +1)
s1 . . .2 3 5 1 22
![Page 34: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/34.jpg)
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Neighborhood
Encoding is a vector of integersMany moves are possibles but think of the neighborhood size
Initial solution
s . . .2 3 1 5 1 2
Move 1: Change frequency by ±1 (here +1)
s1 . . .2 3 5 1 22
Move 2: Change frequency by ±k (here −3)
s2 . . .2 3 2 1 22
![Page 35: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/35.jpg)
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General algorithm
Algorithm 1: MOEA-IRP
Initialization: create an initial population→ Identical frequency + controlled random
Cleanup: remove dominated solutionsrepeat
Improve all solutions with a local search→ steepest descent algorithm with Move 1
Rebuild archive with non-dominated solutions onlyuntil no more improvements
Other possible options
NSGA-II or SPEA
Path Relinking with elite population
![Page 36: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/36.jpg)
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Problem: the gap effect
Visualizing the Pareto front, we noticed important gaps
how to avoid them?
how to fill them?
b
b
![Page 37: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/37.jpg)
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Problem: the gap effect
Visualizing the Pareto front, we noticed important gaps
how to avoid them?
how to fill them?
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![Page 38: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/38.jpg)
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Problem: the gap effect
Visualizing the Pareto front, we noticed important gaps
how to avoid them?
how to fill them?
b
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Potential solutions:
the more controlled random strategy
the controlled local search strategy
![Page 39: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/39.jpg)
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Problem: the swing effect
In the IRP-solver we developed, we noticed repeating identicalpatterns
Customers are groups together because they run out ofgoods at the same time
No cleaver grouping strategy
Customers may be served together even if they are faraway from each others
Potential solutions:
the double frequency encoding
the binary encoding
![Page 40: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/40.jpg)
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Problem: the number of solutions
This approach generates too many solutions→ thousands of solutions, how to handle them?
Implemented solution: the reference set strategy
b
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b b b b
![Page 41: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/41.jpg)
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Problem: the number of solutions
This approach generates too many solutions→ thousands of solutions, how to handle them?
Implemented solution: the reference set strategy
b
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b b b b
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![Page 42: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/42.jpg)
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Problem: the number of solutions
This approach generates too many solutions→ thousands of solutions, how to handle them?
Implemented solution: the reference set strategy
b
bb b
bb
bb b b
b bb
b b b b
b
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![Page 43: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/43.jpg)
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Numerical experiments
A new set of instances has been generatedinspired from Christofides, Mingozzi and Toth VRP instances
Parameters Possible values
# customers, n {50, 75, 100, 120, 150, 200}Horizon, p {240}Truck capacity, K {140, 160, 200}Demand {Constant, Increasing, Sinus}
This form a new set of 42 instancesavailable at http://logistik.hsu-hh.de/IRP
![Page 44: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/44.jpg)
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Results (too many solutions)
Output for an instance with 50 customers (2485 alternatives)
60000
70000
80000
90000
100000
110000
120000
130000
140000
0 100000 200000 300000 400000 500000 600000 700000
Tot
al r
outin
g co
st
Total inventory cost
Inventory-Routing alternatives
Initial Pop.Final Pop.
![Page 45: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/45.jpg)
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Results (too many solutions)
![Page 46: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/46.jpg)
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Results (gaps)
Output for an instance with 50 customers
60000
70000
80000
90000
100000
110000
120000
130000
140000
0 100000 200000 300000 400000 500000 600000 700000 800000
Tot
al r
outin
g co
st
Total inventory cost
Inventory-Routing alternatives
Totally random frq.Controlled random frq.
Identical frq.
![Page 47: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/47.jpg)
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Results (gaps)
![Page 48: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/48.jpg)
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Results (improved routing)
Output for an instance with 50 customers
60000
70000
80000
90000
100000
110000
120000
130000
140000
0 100000 200000 300000 400000 500000 600000 700000 800000
Tot
al r
outin
g co
st
Total inventory cost
Inventory-Routing alternatives
Improved controlled frq.Improved identical frq.
Former Pareto frontNew Pareto front
![Page 49: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/49.jpg)
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Results (improved routing)
110000
120000
130000
140000
Tot
al r
outin
g co
st
![Page 50: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/50.jpg)
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Results (improved routing)
![Page 51: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/51.jpg)
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The Inventory Routing Solver
![Page 52: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/52.jpg)
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The Inventory Routing Solver (alternatives)
![Page 53: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/53.jpg)
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The Inventory Routing Solver (Cost details)
![Page 54: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/54.jpg)
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The Inventory Routing Solver (Inventory)
![Page 55: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/55.jpg)
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The Inventory Routing Solver (Periods)
![Page 56: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/56.jpg)
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The Inventory Routing Solver
![Page 57: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/57.jpg)
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Vizualization
![Page 58: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/58.jpg)
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Vizualization
![Page 59: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/59.jpg)
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Vizualization
![Page 60: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/60.jpg)
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Vizualization
![Page 61: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/61.jpg)
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Vizualization
![Page 62: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/62.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
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23/29
Forthcoming improvements
Already in the box
The double frequency or binary encodingsolves the swing effect
Path Relinkingsolves the gap problemCome and see us at MIC 2011 ;-)
![Page 63: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/63.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
23/29
Forthcoming improvements
Already in the box
The double frequency or binary encodingsolves the swing effect
Path Relinkingsolves the gap problemCome and see us at MIC 2011 ;-)
Other improvements should be considered
improve the routing software
find new operators (dedicated or combined)but be careful with the time for exploration
![Page 64: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/64.jpg)
IRP
M. Sevaux
Definition
Literature
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Problems
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24/29
Forthcoming improvements (cont’d)
In addition, we want to benefit from what we compute
![Page 65: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/65.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
24/29
Forthcoming improvements (cont’d)
In addition, we want to benefit from what we compute
Determine quantities for each period
![Page 66: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/66.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
24/29
Forthcoming improvements (cont’d)
In addition, we want to benefit from what we compute
Determine quantities for each period
Compute best routing for each period
![Page 67: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/67.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
Perspectives
Visit us
24/29
Forthcoming improvements (cont’d)
In addition, we want to benefit from what we compute
Determine quantities for each period
Compute best routing for each period
![Page 68: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/68.jpg)
IRP
M. Sevaux
Definition
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Strategy
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25/29
The on-line Inventory Routing Problem
Question:– Can you ask a company what will be its demand next year?Answer:
![Page 69: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/69.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
Problems
Results
Improvements
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Visit us
25/29
The on-line Inventory Routing Problem
Question:– Can you ask a company what will be its demand next year?Answer:
– Yes you can, but the answer will be: We don’t know
![Page 70: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/70.jpg)
IRP
M. Sevaux
Definition
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Strategy
Methodology
Problems
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25/29
The on-line Inventory Routing Problem
Question:– Can you ask a company what will be its demand next year?Answer:
– Yes you can, but the answer will be: We don’t know
Statistical vs Predictive data
Company have forecasts (predictive demands)
At period k , estimation of demand for next 5, 20, 60 days
We can exploit this information
![Page 71: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/71.jpg)
IRP
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26/29
A first methodology
Data
For each period, we know
the demand of the current day
a rough idea for the next 5, 20, 60 days
![Page 72: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/72.jpg)
IRP
M. Sevaux
Definition
Literature
Strategy
Methodology
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26/29
A first methodology
Data
For each period, we know
the demand of the current day
a rough idea for the next 5, 20, 60 days
A possible methodology would be
decide of your short term planning horizon
compute the average demand for it
solve the problem every period with average values
cross your fingers that demand will not be too highotherwise send an extra vehicle (at any cost)
![Page 73: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/73.jpg)
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But predictions are helpful
Cumulative data for 5, 20, 60 days gives you a tendency
You can use this tendency
Increasing values→ store more at customer’s place (increase stock)
Decreasing values→ deliver less frequently (for example)
You can also set up a safety stock level
And many more. . .
![Page 74: IRP Inventory routing - OVGU · The Inventory Routing Problem (IRP) One depot A set of customers A time horizon A known demand for each customer and each period Minimize Inventory](https://reader030.vdocuments.site/reader030/viewer/2022041012/5ebf6a9e97d61558d513aa80/html5/thumbnails/74.jpg)
IRP
M. Sevaux
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28/29
Instances for the on-line IRP
A new set of instances has been generatedinspired from Christofides, Mingozzi and Toth VRP instances
Parameters Possible values
# customers, n {50, 75, 100, 120, 150, 200}Horizon, p {240}Truck capacity, K {140, 160, 200}Demand {Constant, Increasing, Sinus}Predictions for each period, cumulative value of
the next 5, 20 and 60 periods
This form another new set of 42 instancesavailable soon at http://logistik.hsu-hh.de/IRP
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IRP
M. Sevaux
Definition
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Strategy
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Problems
Results
Improvements
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Visit our web site. . .
OR-Group@Lab-STICChttp://www-labsticc.univ-ubs.fr/or/
or the project pagehttp://logistik.hsu-hh.de/IRP
Contact: [email protected]