Transshipment or Cross Docking Model

Explanation of the Transshipment or Cross Docking Model

The transshipment model, also known as cross docking, is a logistics methodology where products move directly from the supplier to the end customer with minimal handling and storage. This model involves the use of distribution centers, also called intermediate nodes, where incoming products are quickly sorted and rerouted without the need for long-term storage.

The main advantage of cross docking is supply chain efficiency, reducing storage costs and speeding up shipping times to the end customer. In the typical scenario, products arrive at a transshipment center and are transferred directly to an outbound vehicle headed to the final destination, which requires precise coordination but provides an efficient and continuous flow of goods.

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The transshipment or cross-docking model starts with the assumption that passing through intermediate nodes represents savings for the system, while the general transportation model only assumes direct deliveries.

Example:

where product X factories P_1 and P_2 are associated with three agencies D_1, D_2, and D_3 through two distribution centers T_1 and T_2.

1. Generate the network model for this section by hand and in collaboration. using Graphviz

from IPython.display import Image
Image(filename='/content/drive/MyDrive/Academic books in colab/1. Logistics/Image 03-16-23 at 1:26 p.m..jpeg')

The supply of plants is as shown in the following table:

Demand at P_n
- P_1 = 1000 Un
- P_2 = 1200 Un

Demand at D_n
- D_1 = 800
- D_2 = 900
- D_3 = 500

Note that nodes \(t_n\ and \ D_n\) function as input and output. These are called Transshipment Nodes

• Pure supply nodes are the issuers of units

• Pure demand nodes are those that only receive units

• Transshipment nodes are those that fulfill both functions simultaneously. (original supply + Buffer)

• Pure demand and transshipment nodes have (original demand + Buffer)

The Buffer Quantity must be large enough to ensure that all of the original supply or demand passes through any of the Transshipment nodes, with \(B\) being the desired buffer quantity. then:

B = Supply (Total Demand) = 1000 + 1200 (or 800 + 900 + 500) = 2200 units

With this buffer, this model transforms into an original transportation model (…)

Below is the response to the model using the traditional transportation model.

| - | \(T_1\) | \(T_2\) | \(D_1\) | \(D_2\) | \(D_3\) | | | ---------- | ---------- | ---------- | ---------- | ---------- | ---- | | \(P_1\) | 3 | 4 | M | M | M | 1000 | | \(P_2\) | 2 | 5 | M | M | M | 1200 | | \(T_1\) | 0 | 7 | 8 | 6 | M | B | | \(T_2\) | M | 0 | M | 4 | 9 | B | | \(D_1\) | M | M | 0 | 5 | M | B | | \(D_2\) | M | M | M | 0 | 3 | B |

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Crossdocking Exercises:#

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1. Formulate the model corresponding to the following diagrams:

from IPython.display import Image
Image(filename='/content/drive/MyDrive/Academic Books in Collab/1. Logistics/network2.jpeg',width = 300, height = 200)

from IPython.display import Image
Image(filename='/content/drive/MyDrive/Academic Books in Collab/1. Logistics/network3.jpeg')

1. Build and optimize the following crossdocking exercise.

Cano. Ltda is a growing company with a classic crossdocking problem. You are hired as an operations engineer and are faced with this decision. The company has three production plants located At different points in the city, these supply two of the company's own warehouses (CEDIS). However, due to market changes, the product must be repackaged in warehouses to be transported to the CEDIS. In this case, we have three warehouses that will provide this service. These warehouses are also our own.

• Build the network and node diagram based on the following information: the graph should be viewed from left to right. In the first part, we find three nodes corresponding to the company's three manufacturing plants. These nodes are P_1, P_2, and P_3. These are connected by road to the warehouses that handle the packaging change, called B_1. B_2 and B_3 are located in the center of the graph, the existing routes force us to have the following distribution: P_1 can only send material to B_1 with a distance of 20km between them, P_2 can send materials to B_1, B_2 and B_3 with distances of 10 km, 50 km and 20 km respectively, finally P_3 can send material to B_3 with a distance of 15 km; These three warehouses can send already processed material to the CEDIS in the following way B_1 can send to CEDI_1 which is at a distance of 10 km, B_2 can send to CEDI_1 and CEDI_2 which are at a distance of 50km and 20 km respectively and B_3 can send to CEDI_2 which is at a distance of 30 km; In some cases, it may happen that the processing capacity of one of the warehouses is exceeded and they can help each other with other warehouses, for this there are communication routes between them, such as B_1 is connected to B_2 at a distance of 10 km and B_3 with B_2 at a distance of 15 km.

import networkx as nx
import matplotlib.pyplot as plt

# Create a directed graph (since paths have a direction)
G = nx.DiGraph()

# Add nodes
nodes = ['P_1', 'P_2', 'P_3', 'B_1', 'B_2', 'B_3', 'CEDI_1', 'CEDI_2']
G.add_nodes_from(nodes)

# Add edges with distances (weights)
edges = [
('P_1', 'B_1', 20),
('P_2', 'B_1', 10),
('P_2', 'B_2', 50),
('P_2', 'B_3', 20),
('P_3', 'B_3', 15), 
('B_1', 'CEDI_1', 10), 
('B_2', 'CEDI_1', 50), 
('B_2', 'CEDI_2', 20), 
('B_3', 'CEDI_2', 30), 
('B_1', 'B_2', 10), 
('B_3', 'B_2', 15)
]
G.add_weighted_edges_from(edges)

# Draw the graph
pos = nx.shell_layout(G) # Node positioning
nx.draw(G, pos, with_labels=True, font_weight='bold')
labels = nx.get_edge_attributes(G,'weight')
nx.draw_networkx_edge_labels(G,pos,edge_labels=labels)
plt.show()

Cost Matrix:

Nodes	1	2	3	4	5	6	7	8
1	-	-	-	20	-	-	-
2	-	-	-	10	20	50	-	-
3	-	-	-	-	15	-	-	-
4	-	-	-	-	20	10	10	-
5	-	-	-	-	-	30		30
6	-	-	-	-	-	-	50	20
7	-	-	-	-	-	-	-	-
8	-	-	-	-	-	-	-	-

• Production costs:

	Production costs
1	400	unit
2	450	unit
3	470	unit

1. Based on the cost matrix, the shipping matrix must be created, that is, with costs only.

The model considers that:

1. It must be leveled.

2. All supply must pass through the mixed nodes (transshipment).

3. Build the transshipment matrix.

Cano.ltda is a growing company and has just signed alliances with different companies to market its flagship product. The company owns two factories (P1) and (P2), which have a supply of 1,000 units and 1,200 units, respectively. The group now has two distribution centers, which we call T1 and T2. At the end of the chain, there are three distributors (D1), D2, and D3), which have a demand of 800, 900, and 500 units, respectively.

The corresponding distances between each of the actors are given in the following distance table:

	P_1	P_2	T_1	T_2	D_1	D_2	D_3
P_1	0	-	3	4	-	-	-
P_2	-	0	2	5	-	-	-
T_1	-	-	0	7	8	6	-
T_2	-	-	-	0	-	4	9
D_1	-	-	-	-	0	5	-
D_2	-	-	-	-	-	0	3
D_3	-	-	-	-	-	-	0

Supply	qty
P_1	1000 Units
P_2	1200 Units

Demand	qty
D_1	800 Units
D_2	900 Units
D_3	500 Units

1. We define the transshipment nodes T_1 and T_2

2. We define the system's "Buffer" B_n must be large enough to supply the process

$$B\_n = Supply - Demand$$

1. We proceed to create the transshipment matrix

	T_1	T_2	D_1	D_2	D_3	Demand
P_1	3	4	M	M	M	1000
P_2	2	5	M	M	M	1200
T_1	0	7	8	6	M	B
T_2	M	0	M	4	9	B
D_1	M	M	0	5	M	B
D_2	M	M	M	0	3	B
Offer	B	B	800+B	900+B	500	-