A retail store manager faces a complex challenge: balancing the fluctuating demand for products with the costs of holding excess inventory.
Complex numbers from mathematics can provide a solution to this problem.
The concept of complex numbers was always "complex" for me. I did not understand why someone would create "i" which is a square root of -1! Because till then, we were taught that we cannot have a square root of a negative number!
In our store manager's problem, the physical inventory can be thought of as the real part of a complex number - how many units of a product are actually on the shelves. Meanwhile, the potential sales beyond what's physically available in the store could be considered the imaginary part.
Real Part (Physical Inventory): The real part of the complex number represents the tangible assets in the store - the actual products available for sale. The store manager needs to keep track of how many units of each product are on the shelves to ensure there's enough stock to meet customer demand while avoiding excess inventory that ties up capital and incurs storage costs.
Imaginary Part (Virtual Inventory): The imaginary part of the complex number represents the potential sales that could be realized if the store had unlimited stock. This could include sales generated through backorders, pre-orders, or future shipments of products. While these sales aren't physically available in the store at the moment, they represent a significant aspect of the store's potential revenue.
In this analogy, the store manager's goal is to optimize both the real and imaginary parts of the inventory to maximize profits. By leveraging complex numbers, the manager can develop sophisticated inventory management strategies that balance the need to maintain adequate stock levels with the potential for future sales.
The manager could use mathematical models based on complex numbers to forecast demand, analyze sales patterns, and determine optimal reorder points and quantities.
One such equation may look like:
Inventory(t)= Real Inventory(t) + Imaginary Inventory(t)×i
Real Inventory(t)=Initial Inventory+Inflow−Outflow
Imaginary Inventory(t)=Projected Sales(t+Δt)−Backorders(t)
Where:
Inventory(t) - the total inventory at time t.
Real Inventory(t) - the actual physical inventory present in the store at time t.
Imaginary Inventory(t) - the potential sales or virtual inventory that could be realized if the store had unlimited stock at time t.
Initial Inventory - the initial stock level at the beginning of the time period
Inflow represents - the rate of new inventory coming into the store (e.g., through deliveries).
Outflow represents - the rate of inventory leaving the store due to sales.
Projected Sales(t+Δt) - projected sales in the future time period Δt.
Backorders(t) - orders that have been placed by customers but haven't been fulfilled yet.
Subodh
PS: At @Q10 Analytics we love to look at problems differently!
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