What is inventory modeling? Inventory theory (or, more formally, the mathematical theory of inventory and production) is the sub‐specialty within operations research that is concerned with the design of production and inventory systems to minimize costs. It studies the decisions faced by firms in connection with manufacturing, warehousing, spare part allocation and so on. It also provides the mathematical foundation for logistics1.
The discussion that follows is based on a simple production system consisting of a limited number of raw materials (A, B, and C); a manufacturing system; a single end product (P); and a simple end‐product distribution system, all of which are depicted in the figure below. The two gray boxes represent the major inventory considerations that mathematically translate to temporary storage‐space requirements and associated overhead costs. The illustrations above the two inventory boxes attempt to capture the notion that inventory quantities change over time as raw materials arrive and end products are completed and shipped. (Note: The use of a simple production system allows us to capture the key components within the production system, identify related processes and variables, and conduct mathematical analysis. From there, advanced systems can be developed and analyzed in a similar fashion.)
One of the biggest challenges that they will face, especially when in a start‐up or restructuring mode, is identifying their inventory needs and implementing an effective supply chain management process. In the beginning, it seems like a simple process. The stories that we have heard in the past go something like this:
Production Goal ‐ Near Zero Inventory:
Production Goal - Minimize Distribution Costs:
It does not take long to realize that the optimal solution to a company’s inventory management lies somewhere between these two extremes. Additional OR techniques are available to provide the decision makers mathematical solutions to their inventory concerns. The most common approach is to determine the Economic Order Quantity (EOQ), which is the order quantity that minimizes total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models.
EOQ applies only when:
The graphic below is one visual representation of the EOQ over time. The light blue vertical lines represent the arrival of a new order whereas the light blue diagonal lines represent the constant demand. This particular representation introduces one additional planning factor (modification to EOQ) known as safety stock, which is determined by the management.
The variables required to determine a company’s EOQ are:
However, rarely do things remain constant, but there is still hope for management. Dynamic Lot Size Models exist that are designed to address varying demand, varying costs, multiple customers, etc.
In closing, company management should always be prepared for the “rainy day” scenarios whether it be from production line failures, transportation problems, surge orders, etc. OR Techniques are designed to provide “Scientific Solutions” to company problems, however it is by great leadership and management where companies obtain the competitive advantage. Open Source Integrators can help you maximize both.
1 Wikipedia: The Free Encyclopedia, https://en.wikipedia.org/wiki/Inventory_models, accessed 4 June, 2012.
2 Wikipedia: The Free Encyclopedia, https://en.wikipedia.org/wiki/Economic_order_quantity, accessed 6 June, 2012
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