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A PROJECT ON ECONOMIC ORDER QUANTITY

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EOQ(Economic order quantity)

The amount of orders that minimizes total variable costs required to order and hold inventory.

Economic order quantity (also known as the Wilson EOQ Model or simply the EOQ Model) is a model that defines the optimal quantity to order that minimizes total variable costs required to order and hold inventory.

The model was originally developed by F. W. Harris in 1913, though R. H. Wilson is credited for his early in-depth analysis of the model.

Underlying assumptions

Variables

Formula

Implications

Extensions

Underlying assumptions

1. the monthly (annual) demand for the item is known, deterministic and constant

2. the lead time is known and constant

3. the receipt of the order occurs in a single instant and immediately after ordering it

4. quantity discounts are not calculated as part of the model

5. the setup cost is constant

Note that deterministic does not imply the constancy of the demand. For instance, the sine function is deterministic, but not constant.

Implications

EOQ models provide several key insights. The most important one is that the optimal order quantity Q* varies with the square root of annual demand — NOT directly with annual demand.

This provides an important economy of scale; if demand doubles, for example, the optimal inventory does NOT double — it goes up by the square root of 2, or approximately 1.4.

This also means that inventory rules based on time-supply are not optimal. For example: many inventory managers maintain a "month's worth" of inventory. If demand doubles, then a "month's worth" of inventory is twice as large. As noted above, this is more than is optimal; double demand should increase inventory by the square root of 2, or about 1.4.

Remember that this model makes some important assumptions. If these assumptions are not accurate, then results may differ.

Extensions

Several extensions can be made to the EOQ model, including backordering costs and multiple items. Additionally, the economic order interval can be determined from the EOQ and the economic production quantity model (which determines the optimal production quantity) can be determined in a similar fashion.

Optimizing Economic Order Quantity (EOQ)

Inventory models for calculating optimal order quantities and reorder points have been in existence long before the arrival of the computer. When the first Model T Fords were rolling off the assembly line, manufacturers were already reaping the financial benefits of inventory management by determining the most cost effective answers to the questions of When? and How much?. Yes long before JIT, TQM, TOC, and MRP, companies were using these same (then unnamed) concepts in managing their production and inventory. I recently read Purchasing and Storing, a textbook that was part of a “Modern Business Course” at the Alexander Hamilton Institute in New York. The textbook published in 1931 (that’s right 1931) was essentially a how to book on inventory management in a manufacturing environment. If you’re wondering why I would want to read a 70-year-old business text, my answer would be that the fundamental concepts of managing a business change very little with time, and reading about these concepts in a vintage text is a great way to reinforce the value of the fundamentals. The occasional reference to “The War” (referring to WWI) also keeps it interesting and the complete absence of acronyms is refreshing.

As you may have guessed, this 70-year-old book contained a section on Minimum Cost Quantity, which is what we now refer to as Economic Order Quantity (EOQ). I can imagine that in the 1930’s an accountant (or more likely a room full of accountants) would have calculated EOQ or other inventory related formulas one item at a time in a dimly lit office using the inventory books, a mechanical adding machine and a slide rule. Time consuming as this was, some manufacturers of the time recognized the financial benefits of taking a scientific approach to making these inventory decisions.

Order Cost

Also known as purchase cost or set up cost, this is the sum of the fixed costs that are incurred each time an item is ordered. These costs are not associated with the quantity ordered but primarily with physical activities required to process the order.

For purchased items, these would include the cost to enter the purchase order and/or requisition, any approval steps, the cost to process the receipt, incoming inspection, invoice processing and vendor payment, and in some cases a portion of the inbound freight may also be included in order cost. It is important to understand that these are costs associated with the frequency of the orders and not the quantities ordered. For example, in your receiving department the time spent checking in the receipt, entering the receipt, and doing any other related paperwork would be included, while the time spent repacking materials, unloading trucks, and delivery to other departments would likely not be included. If you have inbound quality inspection where you inspect a percentage of the quantity received you would include the time to get the specs and process the paperwork and not include time spent actually inspecting, however if you inspect a fixed quantity per receipt you would then include the entire time including inspecting, repacking, etc. In the purchasing department you would include all time associated with creating the purchase order, approval steps, contacting the vendor, expediting, and reviewing order reports, you would not include time spent reviewing forecasts, sourcing, getting quotes (unless you get quotes each time you order), and setting up new items. All time spent dealing with vendor invoices would be included in order cost.