Aggregate Inventory Management
This article is also available on our website: PROACTION – Generating Best Practices. It is an excerpt of a paper originally written by George Miller, Founder of PROACTION. It has been modified and updated by Paul Deis, PROACTION CEO.Overview
In spite of the great advances in industrial management in areas such as JIT, Flow Manufacturing, Lean Manufacturing, MRP/MRPII, ERP and Supply Chain Management, and now, Electronic Commerce, inventory investment management continues to be a major issue for many organizations. Installing the latest software and mouthing the most popular buzzwords is no guarantee of good inventory management. As with almost all Best Practices, it is the effective use of available tools by properly educated and trained people that creates the desired result.
This paper covers how to set up and maintain Aggregate Inventory Management for improved investment and operations management. It is a “macro,” top-down approach that complements a company’s “micro” SKU (part number) level management techniques.
Definition, Goal and Objective
• Definition—the APICS Dictionary defines Aggregate Inventory Management as “Establishing the overall levels of inventory desired and implementing controls to ensure that individual replenishment decisions achieve this goal.”
• How to assess overall investment levels and set targets.
• How to identify inventory investment level “drivers” and help control them
• How to link aggregate inventory management “macro” strategy to “micro” controls and develop accountability
• Performance measurements
• Specific techniques, such as ABC analysis, control parameters, inventory buildup charts, and input-output control.
• Goal—Helps manage assets and make money.
• Objective—Optimize inventory levels within the parameters of service, cost, logistics, process and investment objectives/constraints. Inventory management should be exercised to keep the lowest level of inventory consistent with achieving the objectives. Too much inventory reduces Return on Investment and Return on Assets (lower profits). It also tends to increase expenses, in the form of interest payments, handling and storage, management, damage, loss, obsolescence, tracking, taxes, insurance, etc.
Although most managers, accountants and taxing authorities regard inventory as an asset, treating it as such for operational purposes may create liabilities. You have probably heard stories about factories working to “keep people busy” or maximize “efficiency” and other similar nonsense. If they are making inventory that is not needed now, they are often wasting money. If they work just to keep people busy, they are still consuming material, energy and other resources that may not earn adequate profits. They may use resources that could better be used for more immediate and profitable needs. If inventory is deployed improperly, it may create liabilities. A customer of one of our clients had branch managers who would “hoard” products at their remote branches so that they “wouldn’t run out.” This created an excess of material in the wrong places.
How to Assess Inventory Investment Requirements
First, understand market, customer needs and service expectations; your own company needs, expectations, process, abilities; supplier abilities and mindset; industry norms and mindset; world-class best practices.
From this, you should learn how fast and reliably customers expect to get their shipments, what is involved to get raw materials and production completed, what the best in the industry are doing and plan to do, and what might be possible. For instance, if all competitors are shipping from stock, then you will either need to duplicate that feat, or determine how to manufacture very fast, or convince customers that your product is so great or so cheap that it is in their interest to wait while you make it to order. Or, you might figure out how to procure better or manufacture better in a way that allows you to carry less inventory.
The result of this step is to establish what industry inventory standards might be and what is possible. Make sure you have an “apples-to-apples” comparison: there may be significant differences among companies. For example: One company might stock finished goods, another one may sell it to another division or to a distributor.
Measure Current and Historical Inventory Levels and Performance
Measure current and historical company inventory levels and performance, not just overall statistics, but broken down into levels of responsibility, commodity, area, type (raw material, work-in-process, finished goods, consignment) and market. Do this to help isolate figures down to levels of accountability and to show inventory investment performance by market, process or even product line. You may find that your systems are unable to do that, meaning that it is past time to make changes to them, whether that be to replace them, modify them or put in separate inventory tracking and control systems (recommended as a last resort).
The result of this step is to establish how your own company is doing and has been doing with inventory management.
Establish Performance Metrics
Establish performance metrics – Inventory is usually measured in currency value, such as U.S. Dollars ($USD). Another, complementary way is to measure it in velocity. For example, you might measure it in “turns” which relates to how many times it moves or “turns over” per year. For example, if there was an average of $100 in inventory in the last year and annual cost of sales for the last year was $2000, that would be calculated as cost of sales ($2000)/average inventory ($100)= 20 turns.
More turns (or “turnover”) is usually good, provided that cost, service or quality aren’t unacceptably affected. If they are, the answer is not simply to increase inventory, but to try to improve the underlying “drivers” influencing it instead, if possible and cost-effective. There are variations of the turnover (this term should not be confused with the European “turnover,” which usually refers to total sales for a period) formula, mainly in addressing how to calculate average cost of goods sold or inventory.
Sometimes, turns are calculated by comparing full sales value with average inventory cost or even equivalent sales value. To maintain easily comparable figures, state all numbers in fully “burdened” costs, using industry standard overhead/burden calculations, unless this is contrary to the standards of your industry or locality. Hopefully, future standard world accounting practices may help to reduce confusion in this area.
It is becoming more common to measure inventory performance in days coverage instead of turnover. People seem to relate to it better.
Inventory and sales may also be commonly measured in more industry-friendly terms, such as tons (steel), bushels (corn), housing units (construction or real estate) or ounces (gold).
A further refinement is to stratify the inventory by “Quality,” as asserted by Gary Gossard of IQR International. The idea of classifying inventory as active, slow-moving or obsolete has been around for a long time. Constantly track it, to highlight any change in inventory quality or condition, such as a new requisition for an item which is already in excess or obsolete. The active, weighted “good” inventory not exceeding your “days coverage” target, divided by the total inventory, multiplied by 100, it equals the Inventory Quality Ratio (IQR) number. 33-40% is typical for mediocre companies. 66% is considered pretty good.
All of these numbers can be time-phased, to show changes over time, due, for example, to seasonal supply and demand changes, or planned improvements. These can then be applied in still more detail to the appropriate organizations, product lines, trade channels, warehouses, planning groups or other responsible entities and then monitored for results.
The numbers should be capable of being “drilled” down or up, from the entire enterprise level to an individual SKU (Stock-Keeping Unit) transaction or part number. Managers or employees should be able to look at total figures for their areas of responsibility and readily identify specific problem areas down to lower levels and finally to specific items, policies, orders and decisions that accounted for them.
Here are typical Inventory System Metrics, which should be broken down by organization/responsibility, area, type, commodity, market/product, and time phased, with targets and actual values:
• Inventory Turnover or Days Coverage
• Inventory value or other unit of measure, such as tons
• Inventory “Quality,” including IQR and summaries of amounts of each type
• Customer service level, expressed how the CUSTOMER perceives it
Perform an ABC analysis, a simple, common and powerful tool for inventory management. It is based on Pareto’s law of “80-20.” The most common approach is to calculate demand in units, preferably for future periods, then calculate the total usage value at cost for each item (total cost of sales multiplied by units required) for a given future period. If future demand data are not available, the next best thing is to use history, but this won’t work well for items with major swings in demand over time. Sequence these in descending value. Typically, the top 10 to 15% of items account for 75-85% of value (“A” items), the next 20-30% account for 10-20% of value (“B” items) and everything else accounts for the rest, about 60-70% of the items, usually about 5% of the total value (“C” items). Your inventory should be less than these percentages for the “A” items, because they are much more tightly controlled and a little higher for B’s and significantly higher for C’s.
Then compare the list to actual values in inventory, plus actual and planned commitments. The answers will often suggest immediate corrective actions!
An ABC list suggests what to concentrate on to control most of the inventory investment. What it doesn’t tell you is that being short of a $.10 screw might prevent the shipment of a $5,000,000 radar unit, so ensure that there are control systems for all items, just control the expensive ones much more carefully. Err on the side of caution for the cheaper items, allowing a safety stock coverage or “two bin” approach to avoid stock outs, but keep inventory from getting out of control.
Create an Inventory Buildup Chart
Another good analysis tool is the inventory buildup chart. Use a standard x-y coordinate chart. Plot the cost build-up over time, by product group, with cost on the “y” (vertical axis) and time on the “x” (horizontal) axis. Normally, raw material cost accumulates first over time, followed by labor and overhead application. Allow for safety stocks, lot size inventory, transit stock, defects/rework/scrap, and normal finished goods and distribution pipeline stocking. Show the affect of consignment arrangements. Some people also treat accounts receivable as sort of a de facto inventory, until it is paid for. Once this chart is completed, show it around for shock value. Presented correctly, it will really make people think about the effect of constraints and decisions (just another form of constraint) on inventory. Then, work on changing the rules!
One company had a 14 month buildup curve, which was reduced to 4 months. At another company, the longest lead time material item accounted for only 20% of the product cost, so stocking only that item, instead of finished goods or instead of only reacting to orders, enabled them to radically reduce the response time for orders by 70%. It also added the flexibility of being able to use that raw material to make a number of different end items.
How to Identify and Control Inventory Drivers
Inventory drivers are things that tend to make inventory go up or down. Identify them and you will have some clue of why inventory changes. Understanding them is the beginning of gaining control. I’ve stated things that would drive inventory up, e.g.: more SKU’s. I refrain from stating the obvious: doing the opposite would reduce inventory. e.g.: reduce SKU’s to reduce inventory.
Key Drivers are covered briefly, as follows:
Number of SKUs
The more items you have, the more inventory you will need, in most cases. If you sell 500 widgets a year of A, then replace it with 250/year of A and 250 of B, you will probably need to carry more inventory. Why: demand and supply variability and total economic order quantities are likelier to be higher for 2 items than for one.
The more SKU’s in a product, the harder it is to bring matched sets of parts together at the same time. Because there are multiple items, with multiple vendors, kept and routed through multiple places or paths, with more opportunity for delays, defects, etc, more inventory will be needed.
The more operations there are and the longer that they take, the more inventory you will tend to have. More operations mean a longer supply chain. It may also mean differing lot sizes per operation and more places for delays and defects to occur. Process simplification helps reduce inventory.
The more facilities that inventory passes in and out of, the further apart those are and the harder they are to reach and pass material in and out of, the more inventory you will tend to have.
The more times inventory passes from the control of one system or organization to another and the less efficient the transfer is, the more inventory you will tend to have.
Lot/batch sizes greater than customer order delivery sizes tend to increase inventory. If customers order a product one at a time, but economics, handling or process considerations suggest that you make 1000 at a time, then you will have more inventory available than will be consumed per order, resulting in an accumulation of inventory. If you need to order things in cases, dozens, carloads, tons or weeks’ supply, but they are needed downstream in the supply chain in smaller increments, you will tend to accumulate more inventory.
The longer the lead time, the more inventory you tend to have. If something takes 16 weeks to get instead of 16 days, there is more inventory needed in process to cover the “pipeline” time. Whether it belongs to you or your vendor, it is increasing somebody’s cost, which ultimately will affect your cost and your customer’s cost. Longer lead time also means more chance of running out or having something go wrong out while waiting for it, which is usually dealt with by having additional inventory.
This refers to the cost of owning inventory. Let’s look at what goes into inventory “cost of ownership”, frequently called the “carrying cost” and expressed in terms of percent cost of inventory valuation per year of ownership. For example, a 25% carrying cost (typical) would indicate that it costs about $.25 to own each $1.00 of inventory each year. These costs consist of:
• Cost of money – The cost of capital to the company or, in some cases the “opportunity cost” or return that might be earned on the money by applying it productively elsewhere. The cost of money has ranged anywhere from 6% to 18% in the USA in the last 25 years. Obviously, this has a very significant impact on investment strategy.
• Obsolescence – The risk of inventory never being used, or needing rework to make it usable, needs to be factored into the cost of owning INVENTORY. In theory (and practice), the larger the inventory is, and the longer it is held, the more likely engineering changes, customer preferences and technological changes will render that inventory unusable. In the clothing industry, it is not uncommon to see inventories depreciate as much as 90% when styles change. Certain portions of the electronics industry have problems with inventory becoming obsolete very quickly, due to technological changes.
• Shrinkage – A portion of inventory becomes unavailable to the owner due to loss, damage, theft or spoilage. The longer inventory is there and the more there is, the more likely this is to happen. Steps to prevent it only raise carrying costs in other areas, such as security, climate control, better control systems, recruiting policies, etc.
• Quality Factors – Allowances for yield, attrition, scrap and rework. This is really more of a function of the process than the amount of inventory invested and is more related to throughput, but is sometimes included as part of the aggregate inventory carrying cost.
• Technological or Price Obsolescence – Prices don’t always go up. In fact, in industries such as electronics, prices often plummet due to constantly improving designs, product and process technology improvements. Therefore, it is desirable to minimize inventories in high-risk areas.
• Taxes – There are two dimensions to this: 1) in some areas, a tax is levied on inventories, so the more inventory, the more tax is paid. 2) inventory is regarded as an asset by most accounting and tax rules. Therefore, increasing inventories shows “profits” and profits are usually taxed, usually by multiple government entities.
• Insurance – The cost of carrying insurance on inventory needs to be considered, as well as insuring the space, equipment, people and other resources needed to control it.
• Space – Costly storage space sometimes occupies 25-30% of the total facility, when one considers raw material warehouses, stockrooms, work-in-process storage, receiving, shipping, outside warehouses, MRB and residual storage areas. Inventory reduction campaigns can help companies avoid the need to move to large facilities, or permit them to shut down or cut back existing facilities.
• Manpower – All of this inventory needs people to order, receive inspect, record, move, count, store, retrieve, post it to the ledger, etc. People are the largest or second largest expense (behind material) for most manufacturers.
• Record Keeping Systems – Software, procedures, equipment and paper must be used to track and control inventory.
• Material Handling/Storage Equipment – Conveyors, fork lifts, bar code readers, scales, automated storage and retrieval systems, trucks, carts, bins, racks, shelves must all be purchased, leased, maintained and cared for.
• Physical Inventories, Reconciliations – Must be conducted to ensure that inventories are properly accounted for and maintained.
• Transportation – Must be provided to move inventory in and out of the facility, to vendors, within the facility, to different workstations and storage areas.
• Energy – Heat, light, humidity control, air conditioning, refrigeration and fuel must be consumed to make all this happen.
• Inappropriate Lot Sizing – In inventory formulae, the carrying cost of inventory is often expressed as a flat percentage of the inventory value, for convenience of computations, but that is an oversimplification of reality. For instance, consider material handling/storage costs. Just because a dollar of inventory is added, doesn’t mean that carrying costs go up, say, $.02. In reality the costs would not usually go up in a direct proportion at all, but only when we had to pay for an additional expense, or make the next capital investment in equipment or space to accommodate the inventory. So actually, most of these costs are step functions, rather than continuous curves.
We urge caution in the use of so-called EOQ (Economic Order Quantity) formulae in planning. While these can be useful guidelines in some cases, they can easily go awry and are hypersensitive to changes in carrying costs and order costs, which are usually no more than guesstimates, at best. We smile in amusement at PhD’s made or lost on the study of such arcane calculations, often failing to consider basic realities such as; how much space and money do we have, anyway? You can refer to Paul’s book, Production & Inventory Management in the Technological Age, pages 137 to 139 for a detailed explanation of why this lot sizing method is weak and should be used with caution.
• Supply variation—refers to the reliability of the supplier to deliver the desired units in the needed quantity, at the right time, at an acceptable quality level. If this can’t be done reliably, then companies tend to carry a buffer (safety) stock to make up for the deficiencies in the supply system.
• Demand variation – refers to the ability to reliably forecast what the customer will require (whether that is an internal or an external customer). Lower reliability tends to encourage buffer (safety) stocks.
• Defects —Extra inventory is often carried to allow for probable rejections. This is just a specialized form of safety stock for supply and demand buffering.
• Logistics constraints/transportation costs – This also sometimes falls under the heading of supply and demand variation and it certainly can affect it. For example, one of our clients transports parts by ocean freight to a plant in Portugal, or at least they do that if they don’t have to ship by air to get them there faster. Because ships traveling between economical ports only leave every few weeks, a 20 or 40 foot long container is the most practical shipping size. A certain amount of time is required for packing, transportation to the terminal, Loading, transport, unloading, customs and transport to the consignee. These are very real logistics constraints that must be built into the “pipeline” portion of the inventory model.
Another company studied ships fresh flowers from Latin America to the U.S. Air freight is the only feasible way to handle shipment, due to shelf life and care issues. It results in a shorter “pipeline” and higher transportation costs, which end up either directly costed to inventory, or get rolled into overhead, or cost of sales—same ultimate effect.
As unit costs rise, so will inventory, but the turns, or days coverage, will remain the same.
How to set Inventory Targets
After considering the current situation, drivers, and external situation, estimate what inventory levels should be, given certain sets of circumstances. There are impressive supply chain modeling tools to help you do this. Our experience is that developing an accurate detailed inventory behavior model is quite a chore to create and a major task to maintain, so we usually don’t. Normally working on projects with limited budgets, we study past behavior and focus on the main drivers, seeking to change a few with the greatest potential impact to achieve assigned objectives- sort of a “delta’ approach.
Don’t let us talk you out of sophisticated modeling tools, though. They have their place. When there are very large amounts of money involved and/or tricky constraints to work around, modeling tools will sometimes help. Many of the detailed control methods presented below contain elements of modeling.
Warning: Calculating or modeling inventory behavior solely by using the rules and parameters will nearly always be wrong. Why: If, for example, you assume that inventory will be an average of ½ times the order quantity plus safety stock, you’ll most often be wrong. Actual supply and demand variability will differ. Defective items/customer returns may result in buildup. Unmatched sets of parts due to shortages will result in buildup. Generally, it is higher than the model would indicate.
Even the best laid plans can go off track if something changes unexpectedly- a major customer cuts orders, unexpected defects occur, requiring ad-hoc reaction, rather than careful, deliberate, advanced planning.
There are two major directions to approach inventory management from—Top-Down and Bottom-Up. Most successful companies use a combination of both.
• Top-Down — this is the “macro” approach. Start with a goal, objectives, ABC (Pareto) analysis of estimated or historical usage, knowledge of overall processes and lead times. Set overall targets, by business unit at a minimum, preferably at a lower level, so that middle managers or even individual supervisors, work teams or administrative control personnel might be held more accountable. It takes more effort as the control is moved to a lower level.
Establish a tracking system, such as actual inventory versus target level. Compare numbers to actual sales, forecast. Monitor commitments and production plans against targets… Hold managers accountable for results and make them come back with reasons why targets cannot be met and solutions to the problems. Motivate them to solve underlying problems. Help them with problems outside of their scope of authority.
Another good tracking tool is Input-Output Control. Simply build a time-phased table of planned starting and ending inventories, showing starting, input, output and results. Then task employees to make the “delta’s” happen and track the actual values per period.
• Bottom-Up—Look at each item- determine cost, lead times, supply and demand reliability/variability, defect rate, transportation, storage, set-up/batch size considerations, buffers, process, handling considerations. Then set the proper planning methods and control parameters, to either default down from the enterprise, product line, commodity or department level to default down, or just establish them at the item/part level.
This takes a lot more effort than merely exercising Top-Down control, but it can deliver better results.
Educate and train people in inventory management and control approaches.
How to Control Inventory
After you do all your research and analysis, set targets and establish your control system, then you get to the hard part – actually making it happen.
Quick hits – Simply establishing the aggregate targets, understanding drivers, educating and training, setting up responsibility, establishing accountability and tracking results usually has significant effects. I have seen greater than 50% reductions from this alone. This can be the cheapest, fastest way of making some change happen, but it has a limited effect, because the approach lacks detail and won’t make major permanent changes in the ways that the business works without additional actions.
What is “Control?” – Control means to make something happen or to know why if it doesn’t, so that something might be done about it. Using that definition, there is no such thing as an uncontrollable situation. Someone once told me that he couldn’t control service inventory, because of unreliable vendor lead times. Nonsense! Unreliable lead times might be controlled by several strategies, such as: multiple sourcing, re-sourcing, safety stock, exhorting supplier to improve performance, ordering sooner, improving your own planning and reaction times, changing designs, alternate routing, training customers to order differently, having vendors stock raw materials. At least some of these would work in almost any situation.
Detailed Control Methods
Most of the detailed control methods that follow have some inventory management rationale built in, but it must be properly set-up and tuned for best use. Provide and implement control tools such as:
• Order on demand- Order only to fill customer orders. This is the most direct, intuitive method and tends to avoid excess inventory. It will only work if it can meet customers’ lead time and cost expectations. It works best for custom ordering and when it will result in delivery service meeting customers’ expectations.
In most cases, organizations must anticipate customer wishes to be successful. This often involves committing inventory in advance, to be able to deliver in time and to produce in economical quantities. So other techniques are often used, such as:
• Reorder point- Keep a certain amount available and on order to help ensure that it is available when needed, but not in excessive quantities.
• Min-max- This is a modified form of order point, with upper and lower limits established.
• Kanban- This is a more sophisticated type of reorder point. Instead of having a single order point, with a relatively large and lumpy order quantity, one replenishes a smaller quantity every time it is consumed. This method was popularized by its success at the Toyota Motor Company in Japan.
• MRP (Material Requirements Planning) – formalized in the 1950’s by Dr. Joseph Orlicky, MRP uses a master schedule developed from a demand analysis of orders, forecast and production plans. It then considers available inventory, parts requirements calculated from the bill of materials, then factors in open purchase orders, lead times, logistical considerations, safety stock and other ordering rules, to develop a materials purchasing and factory schedule to meet planned and actual demand.
In current times, a company’s MRP system is often a subset of its ERP (Enterprise Resource Planning) or Supply Chain Management System, which incorporates MRP as only one portion of an overall “Enterprise” level system. MRP is not always the most appropriate approach for all environments. In recent years, it has been modified successfully, by incorporating techniques of Kanban, JIT, Lean Manufacturing, Repetitive Scheduling, Theory of Constraints and others.
• DRP (Distribution Requirements Planning) — this is a specialized form of MRP, for distribution networks. It uses the same principles, but may also consider the dynamics of multi-level distribution networks, service level planning, cross-docking, shipment staging, truck loading, inventory deployment optimization and other considerations.
• Supply Chain Planning/Optimization- This is the next level of sophistication for MRP and DRP. It creates a model of the supply chain, which may include suppliers, manufacturing, various levels of distribution and even monitoring of inventory through one or more levels of customer ownership.
• Repetitive scheduling- Designed for continuous flow production.
• Process monitoring/control – Control of an ongoing, often continuous, process, usually by monitoring and controlling process parameters, such as raw material properties, desired attributes, temperature, pressure, speeds, viscosity, finish, byproducts, etc.
• Safety stock/safety lead time – Most of the above techniques might be enhanced by building in supply and demand buffers to allow for fluctuations/uncertainty of what will be needed and when and what supply will arrive and when. It can be done by adding on a fixed quantity or time coverage. The trouble with this approach is that people tend to make the wrong allowances, usually on the high side. This inflates inventory, may actually confuse priorities and use up needed capacity, by working on things not actually needed. The best approach is to try to reduce process variation for supply and demand, so that less safety stock is needed.
• Vendor-Managed Inventory – a form of delegation that is proving to be quite popular and sometimes very successful. One provides the supplier with demand and logistics data and makes him responsible for ensuring that the right quantities are available at the right time and place for you to meet demand. It needs cooperation, monitoring and common interests and objectives to be successful.
• Input/Output – Don’t forget to implement the input-output method, described earlier as a tool to help make reductions.
Pitfalls of using control parameters
With the use of MRP, MRPII, ERP and now “Supply Chain Management ” systems, there are more opportunities to improve inventory management, but also more chances to lose control! Unless there is a clearly stated Aggregate Inventory Management approach imbedded in the system, through education, training and parameters, yes- I said parameters!, you will likely fail.
War story from George Miller: “Years ago, I worked for a specialty niche MRPII/ERP company. After I left for the consulting world, a customer of that company called to inform me that the “software wasn’t working” and summoned me to come and help them. After only a day on site, I told them that the problem was that the system was carrying out their instructions at the speed of light, spewing forth recommendations to acquire inventory, based on their unrealistic parameters. You see, most of these systems have various ‘gauges’ and “levers,” to set control parameters to tailor the operation of the system to the company, products and process. These might be set, for example, system-wide, but can usually be overridden at the business unit, plant, department, product line and/or part number level. Each level normally defaults down to the lower level, unless you override it.
“For example, they used unrealistically long process times in the item master planning records and had safety stock and scrap factors planned at multiple levels in the bill of material, “pyramiding” (increasing) demand calculations considerably. No surprise then, except to them, that they were well upon their way to doubling their inventory investment in record time, without significant benefits. The prescription was:
1.The management team to get personally involved in setting the system parameters.
2.Educate employees in inventory management concepts and train them in proper use of system tools.
3.Establish and monitor a special report to assess the effect of “order modifier” parameters, such as safety stock, scrap and attrition factors, order planning method, order quantity rules, order multiples, lead time, review time, inspection time.”
Conclusion: Inventory can be systematically managed. It doesn’t happen on its own. Needed is a rationale, a plan, education, training, organization, tools, policies, procedures and management willpower.
1.APICS Dictionary, 7th Edition, APICS, Falls Church, VA
2.Production and Inventory Control, Second Edition, George W. Plossl, Prentice Hall, 1985 (originally 1967)
3.Production and Inventory Management, Second Edition, Fogarty, Blackstone, Hoffman, Southwestern Publishing, Cincinnati, Ohio, 1991
4.Inventory Reduction, George Miller, 1990.
5.IQR Manual, IQR International (Proprietary document), San Juan Capistrano, CA