MATHEMATICAL MODELING LOGISTICS NETWORKS BY ANALOGY TO CONVENTIONAL PHYSICAL SYSTEMS

LOGISTICS ARE THE BALL AND CHAIN OF ARMORED WAREFARE ‘’ HEINZ GUDERIAN ‘’

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.

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

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"

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.

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:

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.

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).

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.

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''''

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)

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.

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.

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)

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

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.