# Inventory Management

If you run a company that needs to hold stock you know you face two major costs: (1) the cost of holding it, and (2) the cost of ordering. Both costs work in such a way that you need to balance them; there is a trade-off: stock too much and your holding costs will eat your profits, keep your ordering frequency at high levels and your ordering costs will increase.

For the sake of inventory management efficiency there are many models available. However, one of the most utilised systems is back from 1913, the ‘Economic Order Quantity’ (EOQ) model, developed by Production Engineer Ford Harris.

Harris, F.M. (1913). ‘How many parts to make at once’. Factory, The Magazine of Management, 10(2), pp.135-136,152.

This simple model allows to calculate the order size, and hereby the reorder point, that minimises the total cost of purchasing, ordering and holding stocks. The simplicity of the model resides in its ability to calculate such optimal quantity only considering three data:

**Demand**, in units/time; which is considered to be constant.**Ordering cost**, in currency/order; it includes the cost of paperwork, outsourcing, inspection, setting up the facilities, shipping, handling, etc.**Holding cost**, in currency/(unit x time);you must consider your cost of capital, the risk of obsolescence, warehousing, insurances, etc.

Actually, it is not as simple as it is, since considering your demand as stationary (constant, stable) might be difficult, and calculating your ordering and holding costs could imply some number crunching. However, a Qualified Management Accountant (i.e CIMA) could easily calculate them.

EOQ has many drawbacks and has been criticised because of the constant demand assumption, the stability of such demand or the costs, considering delivery lead-times are zero and/or not allowing for inventory shortages or capacity issues, or the inability to consider set-up quantities (integer quantities, fixed batches, and/or minimum orders), quantity discounts, or the existence of inflation. However, EOQ has proved either to be adaptable to incorporate such considerations either quite **robust** to changes in the average demand and/or costs ‘real’ values.

Although some modifications to the original model are not straightforward and make the calculation computationally difficult (although not impossible), the demand and costs critiques are easily assumable. For instance, it is recommended to compute several **‘demand & costs’ scenarios** in order to assess the suitability of the estimated economic order quantity (i.e. would our chosen optimal purchasing policy stand if demand was actually 20% lower? would the total cost rise too much? and if the holding cost was actually 15% higher? what would happen if the ordering costs fluctuated +/-7%?…).

Finally, if demand is considered non-stationary (stochastic), other models can be of interest to compute the optimum ordering quantity such as the ‘Newsvendor model’.