Maximizing Efficiency in Material / Resource Allocation: Leveraging the Maximum Matching Algorithm

In manufacturing setup, sometimes extra inventory is introduced in shopfloor due to number of operational, quality and commercial reasons. Allocating this extra inventory to existing orders are crucial to keep the free / excess WIP stock level in acceptable limits and improve the overall bottom line.

This article explores how Maximum Matching Algorithm can help optimize the allocation of materials to customer orders, ensuring maximum utilization of resources and enhanced customer satisfaction.

Basics of the Maximum Matching Algorithm

The Maximum Matching Algorithm is a combinatorial optimization algorithm used to find the best way to match elements from two distinct sets based on defined compatibility criteria. It is primarily used to solve problems related to pairing elements from two distinct sets based on certain compatibility criteria.

In graph theory, a matching in a graph is a set of edges such that no two edges share a common vertex. When applied to a bipartite graph, which consists of two distinct sets of vertices (U and V) and edges only between vertices in different sets, a maximum matching is a matching that contains the largest possible number of edges.

The Problem: Allocating Materials to Customer Orders

Consider a scenario where we have a set of customer orders and a set of materials, each with specific attributes such as type, quantity, and quality. Our task is to allocate these materials to fulfill the customer orders efficiently. Here's a practical example:

Example:

Customer Orders ( Requirement) :

- O1: Type A, Quantity 10, Quality High

- O2: Type B, Quantity 5, Quality Medium

- O3: Type A, Quantity 8, Quality Low

Materials Available on shop floor:

- M1: Type A, Quantity 10, Quality High

- M2: Type B, Quantity 5, Quality Medium

- M3: Type A, Quantity 8, Quality Medium

Using the Maximum Matching Algorithm, we aim to match orders to materials based on compatibility.

Implementing the Maximum Matching Algorithm

To solve this problem, we first need to define the compatibility criteria. In our example, an order is compatible with a material if the material’s type, quantity, and quality meet or exceed the order’s requirements.

Step-by-Step Implementation:

1. Define the Compatibility Criteria: Determine the criteria that make a material suitable for an order.

2. Build the Bipartite Graph: Create a graph where customer orders and materials are nodes, and edges represent compatibility.

3. Apply the Maximum Matching Algorithm: Use the algorithm to find the optimal allocation of materials to orders.

Here is an example of simple Python program that implements Maximum Matching Algorithm using Depth First Search (DFS)

class MaxMatching:
    def __init__(self, num_orders, num_materials):
        self.num_orders = num_orders
        self.num_materials = num_materials
        self.graph = [[] for _ in range(num_orders)]
        self.matching = [-1] * num_materials

    def add_edge(self, order, material):
        self.graph[order].append(material)

    def bpm(self, order, visited, match):
        for material in self.graph[order]:
            if not visited[material]:
                visited[material] = True
                if match[material] == -1 or self.bpm(match[material], visited, match):
                    match[material] = order
                    return True
        return False

    def max_matching(self):
        match = [-1] * self.num_materials
        result = 0
        for i in range(self.num_orders):
            visited = [False] * self.num_materials
            if self.bpm(i, visited, match):
                result += 1
        return result, match

# Define your orders and materials
# This is just a simple example - real world order attributes are very complex :) 
orders = [
    {'type': 'A', 'quantity': 10, 'quality': 'high'},
    {'type': 'B', 'quantity': 5, 'quality': 'medium'},
    {'type': 'A', 'quantity': 8, 'quality': 'low'},
]

materials = [
    {'type': 'A', 'quantity': 10, 'quality': 'high'},
    {'type': 'B', 'quantity': 5, 'quality': 'medium'},
    {'type': 'A', 'quantity': 8, 'quality': 'medium'},
]

# Create a MaxMatching object
num_orders = len(orders)
num_materials = len(materials)
max_matching = MaxMatching(num_orders, num_materials)

# Define compatibility criteria and add edges
for i, order in enumerate(orders):
    for j, material in enumerate(materials):
        if (order['type'] == material['type'] and
            order['quantity'] <= material['quantity'] and
            order['quality'] == material['quality']):
            max_matching.add_edge(i, j)

# Find the maximum matching
result, match = max_matching.max_matching()

# Display the results
print(f"Maximum number of orders fulfilled: {result}")
for material in range(num_materials):
    if match[material] != -1:
        print(f"Material {material} is allocated to Order {match[material]}")
        

Running the Maximum Matching Algorithm on our example yields the following optimal allocation:

- O1 is matched with M1

- O2 is matched with M2

This ensures that the maximum number of customer orders are fulfilled with the available materials, maximizing efficiency and customer satisfaction.

Benefits of Using the Maximum Matching Algorithm

1. Increased Efficiency: By ensuring the best possible matches, we minimize waste and maximize resource utilization.

2. Enhanced Customer Satisfaction: Meeting customer demands accurately and efficiently strengthens relationships and trust.

3. Strategic Decision-Making: Visual tools and algorithms like these empower us to make data-driven decisions, improving overall operational performance.

The Maximum Matching Algorithm is a powerful tool for optimizing resource allocation in manufacturing. By applying this algorithm, we can ensure that customer orders are fulfilled efficiently, maximizing both resource utilization and customer satisfaction. Embracing advanced algorithms and innovative approaches is key to staying ahead in the industry and driving operational excellence.

This is just an example on application of Maximum Matching Algorithm in it's most simplest form for illustration purpose. Real world material allocation problems are very complex but Maximum Matching Algorithm concepts can still be utilized for the same.

[The views expressed in this blog is author's own views and it does not necessarily reflect the views of his employer, JSW Steel ]