I'm working on an Inventory Optimization (Allocation) problem.
The decision variable is the amount of inventory budget to allocate for each product, from a set of products. My objective is to maximize my profit. My constraint is a total budget which limits how much inventory I can purchase (I can't satisfy demand for all products - otherwise my allocations would simply be my forecasts).
The inputs to the problem are the following:
- Future sales forecast for each product.
- Forecast intervals (analogous to standard deviation) for each product: For example, for product 1, the forecast is 190 Units +/- 50 units, while the forecast for product 2 is 200 +/- 20 units.
- A desired in-stock rate for each product.
- A profit margin for each product.
If I only use point forecasts (i.e. I discard the second input), then maximizing my total profit across all products becomes pretty straightforward. I would just allocate as much as possible to products that will get me the most profit based on the margin × forecast sales. Basically allocate to products in order of decreasing profitability.
But if I take into account the forecast intervals, then the problem becomes more complex, and a "risk" factor seems to come into play: Product 1 might be the most profitable if I consider the upper bound of the forecast interval, but product 2 might be the most profitable if I consider the median of the forecast interval.
The only way to optimally allocate my budget is if I define a risk factor (similar to portfolio optimization).
How do I go about deciding this risk factor? What the approaches for doing so? Does service level/in stock rate come into play?
To clarify based on LarrySnyder610♦ 's comments.
By risk I do not mean risk of running out of stock. I mean the risk that comes from the variance in the product forecasts. To take the example I mentioned above:
Say we have just two products, where all is equal: margins, cost, etc...and lets say that I am forced to choose between one or the other for space or logistics constraints.
Product 1 one has a mean forecast of 190 units and a forecast interval of 50 units, so my forecast can be thought of as most likely falling between 140 and 240.
Product 2 has a mean forecast of 200 units and a forecast interval of 20 units, so my forecast can be thought of as most likely falling between 180 and 220.
If I disregard my forecast intervals, then obviously should go with product 2, since that means I would sell 200 units instead of 190.
However, if I take into account the forecast intervals, then there is a possibility that I will make more money if I go with product 1 (I'm lucky and I sell 240 units, compared to 220 units for product 2). But there is also a chance that I sell only 140 units, hence making less the lower bound of 180 for product 2.
So there is this idea that there is a "risk" factor involved: If I am willing to take the risk, then my optimal solution is to allocate to product 1. If I want to play it safe, then my optimal solution is to go with product 2.
To reiterate the main question: How do I quantify the risk? And what are the approaches for deciding whether I should take a risk or not? And does this risk factor somehow tie into service levels/in-stock rates (I don't think it does, but I might be wrong) ?
Most of all how do I communicate this to business users and product managers who have no math or stats knowledge?