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Using operations research for “look-ahead” inventory policies

How much inventory is held in the United States? If you count finished goods, partially finished goods and the raw materials needed to make those goods, there is over $4,000 of stock for every person in the country – or over a trillion dollars of ‘stuff’ sitting in distribution centers, factories and warehouses. Factor in the costs of carrying inventory (meaning storing and managing it) at about one quarter of the market value of that inventory, and it becomes clear why inventory management is such a big deal. It’s no accident that operations research methods for optimizing inventory management have their roots in some of the biggest inventory operations ever, namely military inventory handling during the last world wars.

How OR models operations like inventory management Image source: commons.wikimedia.org

The inventory theory behind your washing machine

The washing machine (or flat screen, or shoes, etc.) that makes it into a consumer’s home is typically the subject of well-developed inventory management. According to predictability of demand, operations research solutions for handling inventory can be divided into two categories: deterministic for stable demand; and stochastic for variable demand. In both cases, input factors may include cost of ordering, holding cost, shortage cost (the impact on an enterprise when it can’t supply an item), revenue, salvage value (what value can be retrieved from an item left unsold) and monetary discount rate (affects items with long inventory holding times). When demand is completely stable (dream on!), the inventory model may be very simple, as in the ‘economic order quantity’ model.

Simplest inventory/replenishment model Image source: people.brunel.ac.uk

Sorry, you’ll have to wait (unless you want to buy 100)

This mixture of inventory management techniques describes on the one hand a deliberate policy allowing for stock to run out (for instance, if inventory holding costs are relatively high), and on the other a pricing policy of discounting bulk orders. So far and assuming stable demand, operations research methods allow for these cases to be treated with equations and algorithms in a deterministic sense. Constraints on carrying inventory such as sellability, warehouse space, profitability and production capacity can be managed using minimax type decision techniques for instance.

Money, oil prices, ecology and more

Somebody considering buying a washing machine and therefore allowing a manufacturer to offload inventory may however have a number of considerations in mind. If the national economy is down and the job market looks dismal, such buying decisions may be put off – only to come back again if the manufacturer counters with a ‘special discount’ – which may involve a few days of waiting time, because rising oil prices  are forcing the manufacturer to ship complete truckloads of inventory, instead of partial loads – which might then tip the buyer’s decision in favor of a more expensive, but immediately available and ecologically friendlier machine, if this happens to attract more favorable credit terms. At this stage, deterministic methods for managing inventory become unwieldy and stochastic models (simulations) usually take over.

If you’d like to know how Analytica, the modeling software from Lumina, can help you as an operations research technique for supply chain management, then try a  free evaluation of Analytica to see what it can do for you.

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