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## Lot Size

The lot size (LS) (also known as the replenishment quantity (RQ) or the cycle stock (CS)) is the number of units that arrive in a replenishment lot or are produced in a manufacturing lot (Points 1, 2, and 3 in the figure). The average replenishment quantity (ARQ) is the average size of lot size replenishments derived by dividing the total replenishment quantity over a particular period of time by the number of replenishments received during that time.

## Economic Order Quantity

The economic order quantity (EOQ) is the lot size that minimizes the sum of ordering cost and inventory carrying cost associated with the size of the order (see figure). The higher the order quantity, the greater the inventory level.  However, the higher the order quantity the fewer the number of orders and the lower the resulting ordering cost.

The economic run quantity (ERQ) is the production lot size (or run quantity) that minimizes the total of setup/changeover costs and the inventory carrying costs associated with the inventory produced by the run length. The tradeoffs between manufacturing setup cost and inventory carrying costs for determining optimal production run sizes for a large textiles client are illustrated in the figure below. Note in the example that the optimal run length is 3 or 4 rolls per setup for that particular SKU. As is often the case with EOQ modeling, the total cost curve is fairly flat near the optimal solution. The key, as is often the key, is to make decisions that are at least in the “ballpark of optimal”. Unfortunately we often find that lot sizing is off by 200% or 300%.

The formula to compute the EOQ for a purchased item is as follows:

EOQ = {(2 x FAD x POC) / (UIV x ICR)}1/2

For example, if an item has an annual demand of 3,000 units per year; a purchase order cost of \$300 per purchase order; a purchase price of \$2,100 per unit; and an inventory carrying rate of 30% per year then its EOQ is

EOQ = [(2 x 3,000 x \$300)/(\$2,100 x 30%)] ½ = [(1,800,000)/(630)] ½ = [2,857]1/2 = 53 units

The formula to compute the EOQ for a manufactured item, sometimes referred to as the economic run quantity (ERQ) is as follows:

ERQ = {(2 x FAD x SUC) / (UIV x ICR)}1/2

For example, if an item has an annual demand of 5,000 units per year; a setup cost of \$3,200 per setup; a standard cost of \$85.00 per unit; and an inventory carrying rate of 25% per year then its EOQ is

EOQ = [(2 x 5,000 x \$3,200)/(\$85 x 25%)] ½ = [(32,00,000)/(21.25)]½ = [1,505,882]1/2 = 1,227 units

EOQ is considered passé, outdated, and nearly pre-historic in many inventory circles. Yet, in our work with the most advanced supply chain organizations around the world we are finding great profit, service, and operational improvements with EOQ.

## Unit Fill Rate (UFR)

The unit fill rate (UFR) for an item is the portion of the total number of units requested with inventory available to fill the request. It is distinct from and higher than line fill rate (% of lines shipped complete) and order fill rate (% of orders shipped complete). The target unit fill rate is a decision, not an outcome. It is perhaps the most important inventory planning decision of all.

As discussed previously, the higher the unit fill rate, the lower the lost sales cost.  However, the higher the unit fill rate, the greater the inventory required to provide it, and the greater the resulting inventory carrying cost.  There are many ways to determine optimal target unit fill rates. One method is to choose the unit fill rate that minimizes expected inventory policy cost. Another method is to choose the unit fill rate that maximizes expected GMROI. Still another method is to choose the unit fill rate that maximizes IVA. What do we do? It depends on the financial, service, and operational goals. The ability to visualize and simulate those relationships as demonstrated in the figure from the RightStock™ Inventory Optimization System is the key and often missing piece in the inventory strategy puzzle.

As explained earlier, fill rate requirements go a long way toward determining overall inventory requirements.  Simply put, all things being equal, the higher the fill rate requirement, the higher the inventory level required to support it. The higher inventory levels are the result of additional safety stock inventory.

An example inventory and fill rate analysis from a recent engagement in the health and beauty industry is provided in Figure 2. Note that as fill rate increases (from 50% to 99.95%) the required inventory investment increases accordingly from \$4,646,094 to \$8,644,548. At the same time, lost sales cost declines from a high of \$17,953,234 at a 50% fill rate to a low of \$17,953 at a 99.95% fill rate.

The current inventory investment in the example was \$8,300,000 and the lost sales cost was \$3,949,712. The inventory investment that should have yielded a 99.9% fill rate only yielded an 87% fill rate. The discrepancy turned out to be a major mis-deployment of inventory.

## Inventory Maturity

In a recent project with one of the world’s largest and most critical healthcare providers I was stunned to learn that they did not even measure inventory accuracy, let alone know what it was or have on-going efforts to improve it. On a project with a prestigious industrial conglomerate I helped them uncover the fact that over 50% of their MRP and BOM data was just plain wrong. In a project with a global aerospace company we discovered that over 500 people, some with minimal credential requirements could make multi-million dollar changes to high level production schedules with little to no oversight. In a project with a major high tech equipment company we found that unqualified inventory “analysts” were “tweaking” major inventory set points and true demand in their service parts inventory system. The pre-meditated tweaks were un-vetted, un-supervised and made to guarantee that reported turns coincided with their personal turn targets. In a recent project with one of the world’s largest commodities companies the company balked at my suggestion that they even consider using the word “integrity” in reference to inventory because “integrity” sounded moral. In each case, the companies yearned for and nearly demanded the most sophisticated practices in inventory management, while struggling with, ignoring, flying in the face of, and/or naively overlooking the basis for all inventory improvements – integrity.

Integrity is the foundation for everything related to trust. Trust is the fertile cultural and technical soil required for true inventory optimization. Without it, each element of the supply chain hunkers down into their own inventory protection mode, commonly known as hoarding.

High levels of inventory integrity develop from high levels of inventory accuracy; reliable base data including leadtimes, MRP records and BOM records; measured and persistently improved forecast accuracy; and consistent, disciplined participation, follow-through, and accountability by key players in inventory decision making meetings and processes.

Once a high level of inventory integrity is established, the next phases of inventory management maturity are attainable. Level 2 is inventory stability, where predictable cause and effect outcomes are the rule as opposed to the exception in inventory behavior. Level 3 is inventory optimization, where the SKU portfolio, forecast, leadtimes, lot sizes, deployment, visibility, inventory carrying rate, inventory turn rate, and fill rate that meet required service levels and maximize financial performance are determined and implemented. Level 4 is inventory integration, where inventory optimization incorporates cross-functional participation in and accountability for inventory decision making. Level 5 is inventory collaboration, where sharing inventory levels, forecasts, and planning with key suppliers and customers is commonplace.

Inventory Management Maturity Phases

Inventory integrity and its elements including inventory accuracy, SKU record accuracy, putaway accuracy, forecast accuracy, and lead time accuracy are all measured, monitored, included in personnel incentive plans, and relentless improved via root cause analysis and corrective action.

## Inventory Malfunctions

The inventory conundrum is exacerbated by many complicating factors. Those factors can be categorized into five major malfunctions:

• Data Discrepancies
• Problematic Perspectives
• Misaligned Metrics

Data Discrepancies

1. Base Data Errors. In many companies the base data used to control and plan inventory and to support inventory decision making is just plain wrong. In a recent project with one of the world’s most prominent HVAC firms we discovered that more than 50% of the MRP, bill of materials (BOM), and on-hand inventory records were wrong. In a recent engagement with a large engine manufacturer we found that inventory planners were regularly manipulating historical demand, set points and parameters to conjure the turn rate they wanted.
2. Un-vetted Changes. It is not unusual to find hundreds of people, qualified and unqualified, with and without accountability, making un-vetted changes to schedules, demand, supplier data, and MRP data. We recently came across a client situation where more than 500 people had access to make changes to multi-million dollar assembly schedules. With a large retailer we found that more than 300 people had clearance to modify multi-million dollar store order replenishment schemes.

1. Untrained Planners. Based on my experience I estimate that less than 30% of inventory planners and analysts working with inventory systems have any formal education in inventory management. During a recent project I asked to see the resumes of the inventory planners. Less than 10% had any formal training in the decisions they were making. Many people pulling inventory triggers don’t know how to use the gun.
2. Faulty Fundamentals. Because so few inventory planners and managers have inventory training and education, there is widespread misunderstanding and misapplication of inventory management fundamentals. During a recent engagement with a large healthcare company I asked about their inventory accuracy. They said that it was well above 98%. I was suspicious, so I asked them how they defined inventory accuracy. They said it was the portion of demand shipped from inventory. I explained that that was fill rate, not inventory accuracy. I then asked what their inventory accuracy was. They didn’t know.

Problematic Perspectives

1. Conflicting Perspectives. Every inventory decision impacts financial, service, and operational performance. However, very few individuals understand all three and very few decision support tools consider all three. As a result, different inventory levels appear high or low depending on the glasses you are wearing. Those views need to be reconciled; a major point and objective of this book.
2. Irreconcilable Interdependencies. Decisions made in customer service, inventory management, manufacturing, sourcing, transportation, and warehousing all work interdependently to impact inventory levels. However, very few individuals understand those interdependencies and very few decision support tools consider them.
3. Operations Myopia. Inventory is typically viewed as an operational or tactical outcome. It is rarely viewed as a strategic contributor to an overall supply chain strategy which in turn serves as a part of an integrated business strategy.
4. Misplaced Accountability. Many people influence inventory levels but often no one is accountable. I like to ask our clients early on who is accountable for inventory. The answer is revealing and quickly highlights the organizational and measurement root of inventory and/or supply chain issues.
5. No Microscopes. Every SKU has a unique demand pattern, supply pattern, and dimensional profile. Individual SKUs are bought, sold, and slotted. Yet, most companies resist individual SKU inventory optimization and planning. Even in cases with 100,000+ SKUs we have developed individual SKU strategies and rolled those up into category and business unit inventory strategies. Inventory strategy is a top-down AND bottom-up endeavor. Wide angle lens AND microscopes are required and available.

Misaligned Metrics

1. Traditional Accounting. Traditional accounting treats inventory strictly as an asset whereas operationally and philosophically inventory is popularly considered a liability.
2. Conflicting Metrics. Metrics used in the five supply chain logistics activities – customer service, inventory management, sourcing, transportation, and warehousing – often work at odds with one another and yield excess inventory.

1. Procurement “Cost Avoidance”. In the name of “cost avoidance”, procurement is still looking for the cheapest first price that may cost much more in related excess inventory carrying costs.
2. Lean. Lean literature and previously idolized supply chain operators often veil the fact that their inventory turn advantages typically come at the expense of suppliers further up the chain.

Were it not for poor fundamentals, grasping for silver bullets, limited education, misaligned metrics, myopic perspectives, misplaced influence and accountability, misalignment with corporate strategy, and false prevailing paradigms: developing inventory strategy would be a piece of cake.

During a recent client workshop the chief supply chain officer noticed that I was becoming discouraged as they bemoaned their inventory ills. He said, “Dr. Frazelle, don’t get discouraged. We don’t. We just keep our heads down, keep making stuff, and hope it turns out OK in the end.” Fortunately he was joking. Unfortunately many live in a world with their heads down, making and buying stuff, and hoping it turns out OK in the end. There has to be a better way.