In this slide, there is a method to design a system that uses modeling such as the supply chain management which is an important tool for the management of products or services from its raw state to its final state.

1. MATHEMATICAL MODELING LOGISTICS NETWORKS BY
ANALOGY TO CONVENTIONAL PHYSICAL SYSTEMS
LOGISTICS ARE THE BALL AND CHAIN OF ARMORED WAREFARE ‘’ HEINZ GUDERIAN ‘’

2. INTRODUCTION
Our system has a logistics flow that can transport the product from one country to another.
The stock and transport are the main elements that saw major problems incurred by the supply
chain.

3. GENERALIZATION
In general, logistics flow is
generalized by the following
illustration.
P: Provider
C: Capacity
M: manufacturing
D: Distribution
Distribution
Processing
Storage
Supplying P
C1
M1
D1
M2
D2
C2
M3
D3

4. GENERALIZATION
 The product is distributed in the
following manner to different
countries.
 Sometimes the product is
transported directly from the
mother plant to the consumer.
 Our logistics flow is generalized by
the following illustration.
Customer
Packaging
Storage 2
Storage 1
Manufacturing Manufactoring
Transit
Warehousing
Sous-traitance
Distribution
Warehousing'
-
Distribution'
Transit '
Warehousing''
-
Distribution"

5. DESCRIPTION
 We will create a mathematical model which corresponds to a mechanical
analogy by the fluid which calculates the flow of water in a porous media, this
is equivalent to the logistic flow that begins with the provider and ultimately
the customer after storing and transported the product.
 The next page shows the way forward.

6. APPROACH TO FOLLOW
non-optimized supply chain
Continuous mathematical model
Discrete solution of the mathematical
model
Optimized supply chain
Analogy
Digital
resolution
Analogy: Solution
of the supply
chain
We want a concept as follow:

7. ANALOGY
 If one attaches to existing models, we will not find a model that succeeded in combining the
design and implementation perspective tools since the accumulated complexity prevents a
clear solution.
 To do so, we tried in this project to combine simple tools to achieve a solution in a simple
manner while putting the problem through a simple analogy to unify the two systems for this
field.
 A correspondence between two different systems in the structure but common in their criteria
is sufficient for a simple model on which we will apply the calculation originated by the fluid
mechanics tools.
 The flow of water in a porous medium is a close system having logistics system that the flow
of water is similar to the product transport.

8. ANALOGY
 Moreover, the analogy between the two systems is a link between the two networks and it requires a
calculation through the selected system (water flow) to use the final outcome for the resolution of our
system (Supply Chain) .
 We work on equivalence of the supply chain to avoid falling into the problem of the plurality of variables
and it's hard to solve all seen that the calculation will be extended to meet the most complicated
problems.
 After attaching the equivalence, the analogy is applied again to be able to find the numerical solution.
We obtain a discrete solution with fewer variables and then an optimized supply chain (Slide page 6).

9. MODEL
 We now move to the flow model that describes the flow of water through a hierarchical
manner as the approach of the Huawei supply chain who is interested in the stock transport
and monitoring of its behavior.
 This leads to such a mapping logistics flow to show how the analogy is the common factor
between the two models. With that, the parameters of the supply chain have their matches in
the string of flow in porous media water.

10. GENERALIZATION
L: Underground Layers
S: Coefficient of stored water
T: water Transmissivity
S,T
S,T
S,T
S,T
S,T L1
L2
L3
L4
L5
L4'
L5'
L2'
L 3'
L4"
L5"
L4'''
L5'''
L3"
L4''''
L5''''

11. ANALOGY BOARD
Supply chain flow Flow of a flow in porous media
Product construction Injection or pumping water
Storage Water storage in layer 1
Storage Water storage in Layer 2
Transport (distance) Water movement (transmissivity)

12. UNDERGROUND FLOW IN POROUS MEDIA
According to hydrogeologists, a rock is characterized by the following parameters:
 The transmissivity: When changing from one layer to another, it depends on the space
 The storage coefficient: which measures the ability to store water for a rock.
 The pressure head: which is a variable that measures the water level relative to the level of the
sea.

13. UNDERGROUND FLOW IN POROUS MEDIA
 We will use these parameters for the model to find convenient resolution of our system.
 By combining these parameters, we found that This analogy is explained by a mathematical
model based on mass conservation law and then Darcy that explain the movement of
underground water. We finally deduce the general equation of flow in saturated porous
media.
 We finally deduce the general equation of flow in saturated porous media.

14. UNDERGROUND FLOW IN POROUS MEDIA
 S: storage coefficient (How the layer of water stores after a runoff)
 T: Transmissivity (The ability to filter the water from one layer to another)
 ᶲ: Height Piezometric (water level measurement to the surface of the sea)

15. UNDERGROUND FLOW IN POROUS MEDIA
 These elements require a definite calculation to finally have finished results.
 regarding the conservation law we will use and then Darcy's law would have the following
equation:
ܵ.߲ᶲ / ߲‫߲−ݐ‬ / ߲‫ݔ‬ (ܶ.߲ᶲ / ߲‫)ݔ‬ = ܳ
S: storage coefficient as a function of space: S (x)
T: transmissivity as a function of space: T (x)
ᶲ: Height water table over time and space: ᶲ (x, t)
Q: Source term

16. CONCLUSION
 These slides show how much underground in porous media is quite identical to the logistic
flow from which we can apply the analogy and then the model in a simple structure as an
equivalence of all the supply chain trying to minimize the quantity of variables and be able to
apply the digital resolution with less of complexity.
 This solution is able to improve the performance of the company and reduce the problems of
storage and transport of the products.