Safety Stock & Re-order points – simple explanation


Safety stock is the additional number of units of stock held by a company to mitigate several market risks. Without safety stocks, the company could have negative customer experience, lost revenue, lost market share and long-term customer value. However, a higher safety stock strains the organization in the form of higher working capital requirement. Safety stocks help in mitigating several risks as below:

  1. A Sudden spike in demand
  2. Offset inaccurate forecasts
  3. Longer than expected lead times to delivery (from the supplier)
  4. Quality issue rejects of stock, leading to stock-outs
  5. Increase in manufacturing or production time
  6. Transportation strikes or non-availability of transport
  7. Warehouse space issues due to which inbound gets delayed

So, how does one calculate the safety stock needed for an item?

The answer is that there is no one definite way of calculating the safety stock required. One shouldn’t use the available formulas blindly as the specific case of each company x product x market is very different.

Method 1: Let’s start with intuition (I love intuition!).

Intuitively, safety stock is designed to cover for maximum delays in delivery from the supplier. So, what can be the maximum delay from a supplier that you want to guard against – it is the maximum lead time minus the average lead time from the supplier.

So, the most common formula for safety stock is:

(Max Daily Sales * Max Lead Time) – (Average Daily Sales * Average Lead Time)

Re-order Point = Lead Time Demand + Safety Stock

Method 2: EOQ Formula (For a full blog post on EOQ refer this link)

A toys company deals in one single toy and procures from a single supplier and has an annual demand of 4000 units of a single toy. The cost of placing an order is Rs. 50 each time with the annual costs of holding the toy being at 40 % of the purchasing cost. The company purchases the toy at Rs. 120 per unit. How much should the company order at a time?

EOQ= √ (2*C*D)/CH

EOQ= √(2*50*4,000)/(0.4*120)

EOQ= √(400,000)/(48)

EOQ= 28.87 units

Method 3: Formula used in SAP ERP system

A buffer stock or safety stock has to be designed to cover various deviations. A delay in any of the lead times mentioned below affects the procurement pattern.

  • ordering lead time
  • manufacturing lead time
  • transportation lead time
  • stock conversion lead time (inward lead time or QC clearance lead time)

Moreover, the determination of safety stock depends on the forecast accuracy. Higher the accuracy, lower the safety stock requirement. Hence, we have the below

R = Relationship between forecast accuracy and service level (Service Factor)
W = Delivery time (in days) / Forecast Period (in days)
MAD = Mean absolute deviation (parameter for forecast accuracy)

Now, if replenishment lead time is greater than the forecast period by factor W then:

Safety Stock = R x Sq.rt. W x MAD


Safety Stock = R x W x MAD

Method 4: Safety stock should cover supply and demand variability

Safety stock should have two components: supply safety stock and demand safety stock.

Demand safety stock = k*sd(forecast error)*sqr rt(lead time)

k = factor for number of std deviations required for given service level (refer link)

Supply safety stock = k*std dev lead time

Total safety stock = sqrt( demand safety stock + supply safety stock)

As you saw from the above methods, there is no one clear way of calculating safety stocks. It depends on a whole range of parameters such as lead times, forecast periods, order cycle times, forecast accuracy, service levels, lead time variances and others. Therefore, it is very important to test and observe the trends of all variables periodically to ensure that the best safety stock values are used by the firm.

Thank you.




ROI of a distributor or supplier – business turnover, margins and rotations (in e-commerce and FMCG)


Retail excites me a lot because it is a simple business of buying and selling goods and yet it covers almost every complexity under the sun. It has a complex supply chain from raw material to finished goods, yet seeming so simple and convenient when we add items to our shopping cart in offline and online stores. One of the most interesting aspects of retail distribution is the calculation of return on investment by various stakeholders in the supply chain.

If you are a manufacturer, you will witness both suppliers upstream and the distributors downstream investing in your business. Suppliers setup factories, invest in raw materials, labor, technology, etc. for your products. Similarly, distributors or retailers buy your finished products, invest in warehouses, technologies and partner with you in distributing the product to your end customer. Both these stakeholders invest capital in making and/or distributing your products and will look for profits in doing so. While IRR is probably the most sound way of calculating the ROI of an investment, most distributors and suppliers you meet always do a quick back of the envelope ROI calculation and it is never far away from the IRR(internal rate of return) method in its results and is really cool to work with suppliers and distributors on the various parameters that go into it.

“Across all kinds of investments, ROI is more common than IRR, largely because IRR is more confusing and difficult to calculate.” – Investopedia

As businessman, all vendors, distributors and retailers are interested in the return on working capital employed (ROWCE). After all there is only so much cash in the bank! Distributors and vendors are concerned about two key aspects: profit and cash – maximize profit by minimizing cash requirement. ROI can be increased by increasing profit and by reducing investment requirement. Increasing profit can happen by increasing sales revenue or by reducing expenses and in expenses cost of goods sold (COGS) is the major component that is focused on. However, one has to check all other retail components such as goods returns, payments, transportation charges and other options to reduce costs.

But more important than anything in business is CASH. Vendors and distributors want cash to 1). hold inventory and 2). extend credit in the market. As the turnover starts to increase, the inventory requirement starts to increase and credit requirement in the market increases. This increases the cash requirement for vendors in the market and blocks lot of capital in the market. As inventory requirement increases, there are advantages of ordering full truck loads (FTLs) and holding the inventory for shorter periods of time too, but it depends a lot on category lead times. Therefore, distributors are always on top of their ROI calculations to keep a check on their business situation.

Let us look at various cases to understand ROI calculations:

Case 1:

You are buying a product at Rs.100 on day 1 of the month and you sell it to another stakeholder at Rs. 110 immediately. The stakeholder will give you the Rs. 110 exactly after 1 year. What is your return on this business? Simply put, the answer is Gross Profit/Investment = 10/100 = 10%. The formula is also nothing but (earnings – expenses)/(investment).

Case 2:

You are buying a product at Rs.100 on day 1 of the month and you sell it to another stakeholder at Rs.110 immediately. The stakeholder will give you the Rs.110 exactly after the end of one month. What is your return on this business? You  100 rupees in inventory at the start of every month and you get Rs.110 at the end of the month. So, I make Rs.10 every month and that multiplied by 12 times for 12 months makes it a return of Rs. 120. Return of this business is 120/100 = 120%

The difference between case 1 and case 2 is not in the margin percentage but in the number of rotations of the invested capital. It is actually about margin * number of rotations of invested capital. In the first case, the margin is 10% and the number of rotation of invested capital in one year is only 1 – hence 10%*1 is the return. In the second case, the margin is 10% and the number of rotations of invested capital in one year is 12 – hence 120% return.

But, when you meet a supplier or a distributor, he will tell you that he has invested in a special account manager for you, a special warehouse for you, a special machine for you, etc. So, there are direct and indirect expenses. It is important to break-down the vendor or distributor’s  expenses and account it correctly. The formula comes down to ((Gross Margin)*(Number of rotations of invested capital) – (Expenses direct/indirect))/(Capital Invested)

While the cunning business guys always tell you that they’ve invested in warehouses, human resources and machinery only for you, typically they will always serve more than one customer or vendor. So, it is important to understand their overall business value and your contribution to that and take expenses in proportion to that. If a supplier is supplying to 3 customers and you are contibuting to 40% of their business. It is safe to say that you should take 40% of the human resources, depreciation of the machinery, etc. into the expenses and not the entire expenses of the human resources and depreciation expense.

Case 3:

You are buying a product at Rs.10 and selling it at Rs.11 immediately. The Rs.11 is given to you after the end of the third day of the sale. However, in this business, you have to invest in a machine worth Rs.36 and has a lifetime of 3 years. Return is ((10%)*(number of rotations is 120 because you are getting money every 3 days) – (depreciation expense of Rs.12 for the first year – straight-line depreciation method))/(Rs.10 as capital invested)

The important thing is you don’t take the entire 36 rupees invested in the denominator. Most suppliers and distributors will do this in their calculation when they discuss with you. But, that is sitting as an asset in the balance sheet with only depreciation as an expense coming into the profit and loss calculation.

Case 4:

Let’s take a new case. At the start of the month, you bought Rs.200 value of a stock. You are selling Rs.100 value of stock every month to another stakeholder and that stakeholder gives you Rs.110 at the end of one month. The return of the business is: ((Rs.10 profit*12 times) – (direct/indirect expense))/(200). If I ignore expenses for a moment, your return has dropped from 120% in case 2 to 60% straight. This is because of the Rs.100 capital invested in the stock that has not moved for the entire year. Your return on investment drops by the ratio of the non-moving stock (or non-rotating capital) to the overall stock (overall capital) invested. You might think that the Rs.100 non-moving inventory should not be entered in this calculation and instead, it should sit on the balance sheet (as inventory under assets). However, that is not true for stocks that are not being sold for such a long time. In fact, many companies start taking only 85% of the value once it is not sold for 3 months and 60% of the value once it is not sold for 4 months. This is assuming that one needs to give steep discounts to sell something that is not sold for such a long time and the inventory is losing its value in the warehouse because of natural depreciation, wear and tear, theft and outdated technology. However, this very much depends on business to business and product to product.

Case 5:

You bought Rs.100 of stock at the start of the month and you sell it to another stakeholder. You will get Rs. 110 from that stakeholder at the end of two months from the sale. This means the return is: (10% margin)*(6 rotations) = 60%, a drop from case 2 primarily because of the reduction in number of rotations.

Case 6:

In the above case if the Rs.100 is taken from a loan then the investment is only the interest paid and not the entire amount of Rs.100. Distributors and suppliers would again include the entire amount as a common trick.

A healthier ROI for most suppliers and distributors ranges between 25-40%. From the above cases, we learnt that the product margin is important, but rotations of capital invested in inventory and how much investment is needed matters a lot in retail.

The number of rotations of capital invested in inventory for a period is calculated as 365 divided by (the average number of days of inventory held during that period). In cases where it is complicated to calculate the average number of days of inventory, closing inventory for the period is used as a proxy.

In case 1, you would want to improve in rotations. If your rotations are good, you would want to improve on margins. If both margins and rotations are good, then you would want to improve on overall business volume.So, profits are about the business volume, absolute margins, the number of rotations of capital and the capital in rotation. It is not just about margins, it is about how much money is required to invest and how many times can someone rotate that money.


EOQ: How much inventory to buy? – to stock or not to stock that inventory


Retail Managers are responsible to ensure stock availability to customers by replenishing stocks regularly. At the same time, they are also responsible for profitability of their category or division, leading to questions on – whether we should carry that product and how much inventory should we carry on hand? This is where it gets interesting. Because if you want to cater to all customer demand, then theoretically you must carry infinite inventory so that you cater to all customers who may or may not come. And, carrying infinite inventory is a loss-making proposition, leading to unhealthy inventory and write-offs. Let us understand this through an example below.

Let’s say the product you are going to sell costs $6 and you will sell it at $10, making a profit of $4. However, if you cannot sell that product then you will incur a loss of $6 (product cost).

Therefore, the tradeoff here is between:

a). the profit that you’d earn if the customer walks in and you have it in your inventory

b). the loss that you’d incur if you stock and the customer doesn’t turn up

To make the right decision of whether to hold that extra unit of inventory or not, you need to understand the probability of selling that inventory (say one unit) denoted as Px.

  • If the probability of selling that extra unit is 100% (P100), then you should surely stock it and make a profit of $4.
  • If the probability of selling that extra unit is 25% (P25), then the payoff is

25%*$4 + 75%*(-$6) = -$3.5 (negative payoff). Since this is going to make a negative payoff, you shouldn’t stock that unit of inventory.

  • If the probability of selling that extra unit is 80%(P80), then the payoff is

80%*$4 + 20%*(-$6) = $2 (positive payoff)

  • If the probability of selling that extra unit is 60%(P60), then the payoff is

60%*$4 + 40%*(-$6) = $0 (critical point). So, as long as the probability of selling that extra unit is 40% or above, you should keep stocking inventory. Most auto-buying systems are designed in this way to stock inventory until the probability of selling that unit of inventory goes below the critical point.

Also, the probability of selling that unit is within what time period? It is within the planning cycle (order cycle time plus lead time from PO to delivery). Your days on hand should always be as lean as possible and close to the planning cycle. Credit period is the maximum limit of the planning cycle, but ideally shorter the planning cycle the better the benefit is for the business

The one mistake that we did in the above calculation is we wrongly assumed that profit that we will make out of the sale is only from that particular unit. We should also include the profit that we could’ve made by that particular customer in all future purchases at our store – customer lifetime value (CLV). So, the tradeoff has to be between the customer lifetime value of the customer vs. the loss you’d incur if the customer doesn’t turn up at all. Also, the above calculation should take ‘time’ into account in the form of cost of capital (inventory holding costs) because many times the loss is not the entire cost of the product.

In conclusion, the value of having that inventory in stock changes basis a lot of parameters such as CLV, importance of that category or brand to the image of the retail store, brand equity of the store, type of store and many other business parameters.

The one question that we are yet to answer is: how do we determine the probability of sale?

Intuitively you know that the probability of selling that first unit of a TV is 100%, the 100th unit is say 80%, 500th unit is 40% and 1000th unit is 10%. Probability changes by quantity.

To get the probability you should simulate a demand distribution basis past historical sales data. Demand in retail scenarios are usually normal distributions. So, we will need the average and standard deviation. It is what we learnt in our MBAs – you will calculate the probability for the random variable (sellout of a TV model) to take the value 500 units and that is P (X=500). One of the ways is for you to calculate the Z value =  (500 – average)/SD and then lookup for that Z value in the Z table to get the probability. This is if the distribution is gaussian or normal distribution. There are other ways too to get this estimate basis various distribution fits such as chi-square, t distribution (for small sample size of 30-100), gamma distribution, beta distribution, pareto distribution and others. Each of these distributions has a method to calculate the probability like the way we have for normal distribution as mentioned above. Typically, in the pre-computer era, because it was so difficult to calculate the area under the curve manually statisticians used to categorize the data they have into one of the 20-30 templatized distributions and use one of the methods to calculate the probability. In the computing era of today, we can actually plot the data and calculate the actual area under the curve with the help of a computer quickly. Therefore, if you don’t know which distribution the plot is looking like it is better to just calculate the area under the curve manually and get the probability. This method is called the ’empirical method’ or ’empirical distribution’. So, if you don’t know which distribution is your data looking like, you can opt for empirical probabilities.

Thank you.

Ways To Reduce Inventory and Improving Service

This post is originally written by Chuck LaMacchia and the link to the original post is here.

Ten Ways to Reduce Inventory, While Maintaining or Improving Service

“Our competitor turns its inventory six times per year, but we’re only at four. We should be able to turn our inventory six times as well!” says the boss. “And get it done quickly!” From that, the inventory reduction crusade is set into motion. What’s the easiest way to lower inventory? Yep, slim down the stock on the medium and high movers. The inventory gets reduced, but expedites go up, and service goes down. You achieved six turns, but at what price?

Why does this happen? Because inventory reduction gets managed in a vacuum. Trying to control inventory independently of the variables that cause it is a no-win strategy. Inventory is a dependent variable based on the inputs of many factors including: demand and demand variability, supply lead time and lead time variability, supply chain design, manufacturing capabilities versus customer purchase characteristics, transportation modes, and desired service levels. In order to achieve sustainable inventory reduction while maintaining or improving customer service, the variables that drive inventory must be improved. Too often, inventory is adjusted to meet financial goals, without corresponding improvements in the variables that drive inventory levels.

Why is inventory the target? Because it shows up directly on monthly and quarterly financials. There’s no line item for supplier lead time, forecasting accuracy, or setup cost reductions. Inventory is usually a big number and in plain view to executive management and the shareholders. It is also expensive. Generally it costs 20% to 40% of the materials cost or COGS per year to store. Some of this cost is based on the value of the product (cost of money, taxes, insurance, scrap); the rest is based on storage (warehouse space, maintenance, utilities, equipment).

Here are 10 approaches to lowering your inventory. The key to sustainable reductions is to focus on the input variables. But remember, the overarching goal of the organization is to maximize long-term profits. Any attempt to reduce inventory should be in harmony with this goal.

Number 1: Pareto your inventory

Gather sales and inventory in dollars by item. Construct two Pareto charts. For the first chart, classify your items into A, B, C, and D (80%, 15%, 5%, 0%) based on sales. Then calculate your inventory for each group. Do your A items represent 50% of your inventory? If not, you may not have enough inventory for these items. A significant amount of inventory on low demand items may indicate problems with product run-outs, transitions, engineering change management, and managing obsolete inventory.

For the second chart, classify your items based on inventory. Then calculate the sales for each group. Again, do your A inventory items represent at least 50% of your sales? If not, inventory may be out of balance. These charts are an excellent way to begin looking at your inventory. After gathering this information, you have the makings of a supply chain data warehouse for further analysis.

Number 2: Reduce replenishment lead times

This can be important for raw material lead time or lead times between your internal tiers of distribution. Break this lead time into three components: the review period, manufacturing time and transportation time. The review period is the time from when the need is identified to when the order is sent upstream. The manufacturing time is the time from when the order is sent until product is available to ship. The transportation time is the time it takes from availability to ship until the material is received and available for use at the next location. Find out how long, and how variable, these three components are.

Are there any ways to reduce the review period? Must you wait until the end of the month to place an order? Long review periods may be driven by system limitations; can these limitations be overcome? Can weekly cycles be reduced to daily? Frequently, a supplier will have minimum order requirements that forces batching of many products with replenishment needs. Can this minimum be reduced so the order can be sent sooner?

The manufacturing time includes a review period for your supplier on top the actual manufacturing time. Generally, the review time is longer than the manufacturing time. Can you work with your suppliers to help them reduce their lead times? Understand their constraints. Possible solutions include: advance notice of upcoming needs, a longer-range forecast, and fixed cycle replenishment.
For transportation time: use faster modes of transport or relieve bottlenecks at shipping/receiving. Shorter and less variable lead times require less inventory. If you carry safety stock, the reduction will be the square root of reduced time. A 25% lead time reduction equals a 13% safety stock reduction. Any transportation reduction also creates an additional direct reduction of transit stock. A day less in transport equals a day less inventory in your pipeline.

Number 3: Revise order cycles/quantities

Smaller and more frequent order quantities translate into less inventory. Is there sufficient capacity to increase changeovers required by more frequent cycles? Can capacity loss be offset by running low demand parts less frequently? Will there be any loss of transportation efficiencies by moving to smaller batches? What does this mean to the labor workload at the distribution centers? Determining order frequencies is one of the key variables of your supply chain. It can affect nearly every aspect of your supply chain. You must have a thorough understanding of your supply chain costs and capabilities before embarking on this strategy.

Options include: reducing setup time and costs, re-evaluating the cost of holding inventory, understanding warehouse storage procedures, and understanding labor, transportation, and inventory cost trade-offs. While the goal is reducing inventory, you may discover that the opposite is true; increasing order quantities on some items may yield substantial overall savings.

Number 4: Improve your forecasting

Many people don’t like the “F” word. But let’s face facts – every make-to-stock or purchase-to-stock company forecasts, admittedly with differing degrees of formality. Even if your production rules are “make what we sold yesterday” or “replenish up to x,” a forward-looking view of demand is implicit in determining how much to buy and keep on hand. While everyone knows the forecast will always be wrong, it is possible to become less wrong. Often, improvement efforts start with the mathematical forecasting method, e.g., – exponential smoothing vs. regression vs. Winters. That should actually be the last step. As the saying goes, “I’d rather be approximately correct than precisely incorrect.” Think of forecast improvement in three segments:

  1. Are the input data the relevant drivers of demand? If marketing or sales are influencing demand through pricing and promotion activity and you don’t take this into account, the forecasting formula doesn’t matter. You must understand and collect the inputs that drive demand.
  2. The data must be accurate. If you forecast from shipments, but shipments don’t reflect true customer order quantity and dates (based on unavailability and backorders), the shipment data are tainted – garbage in, garbage out. Get as close as possible to true demand.
  3. Review the forecasting method. If you have the right inputs and the data is clean, basic forecasting methods will produce good results. If you have limited resources, spend the effort on the first two steps to achieve the best results.

Number 5: Eliminate obsolete stock

How much obsolete stock is kept on hand in your facilities? Is it being kept because no one wants to own up to it? Or is it because the company can’t “afford” an expense hit this quarter to write-off the obsolete stock? Ridding your warehouses of obsolete inventory is a good policy, and good operating policies will result in good long-term financial results. Here, accounting rules can drive poor operating rules. If you don’t address obsolete stock now, it will just continue to grow. So, own up to obsolete stock, get it off the books, and use that warehouse space for productive inventory.

Number 6: Centralize your inventory

In total, distributed warehouses require more inventory than centralized facilities. The key driver of the increased inventory is safety stock. The rule of thumb is: As the number of facilities increase, the amount of safety stock increases by the square root of the facility increase. Increasing facilities by a factor of four will increase safety stock by a factor of two.

If centralization is possible, a reduction in order quantities may be possible. By ordering to only one location, you may be able to increase your order frequency, thus lowering your overall order quantity.

While you may have the ability to centralize some items, large-scale centralization may just not be possible. The centralized vs. distributed analysis is a major supply chain decision and requires extensive analysis from customers’ requirements to suppliers’ capabilities. However, you may be able to take advantage of centralization on a piecemeal basis. Can you hold most safety stock centrally and allow daily replenishments to distributed facilities? Can spare parts be held centrally and expedited in emergency situations? Will customers accept different lead times on some items, thus allowing centralization?

Number 7: Lower your service level

Heresy, you say. Probably, so let me re-phrase this one: Understand your customers. What kind of service, in terms of lead time and availability, do your customers require? For example, do your customers need their entire order at once? Could you lower inventory by being able to ship half the order immediately, half later this week? Do customers request short lead times just because they can, not because they require it? The best way to meet your customers’ needs is to understand their needs. How do they use your product? When do they know that they need your product? Understanding their needs will help you meet them. However, in today’s competitive environment, you just might find that you have to shorten lead times and increase availability just to keep up with competitors. Whatever the case, understanding your customers’ needs is critical to your success.

Number 8: Reduce SKU counts

Do you have customer-specific SKU’s? Are identical products packaged and stored differently? Postponement is the act of pushing customization until the latest possible moment. If you can store the base item and only customize it when you have the order, you can significantly reduce inventory. This may require packaging or assembly operations at the distribution center, but the savings may well be worth it. You may even be able to respond more quickly to customer orders.

Is there substantial part/SKU proliferation? Do you stock the 2-count, 4-count, 6-count and 8-count packs? Working with sales and marketing, you may be able gain agreement that eliminating one of the packs will not affect sales at all. Any part reduction will help to free up space in warehouse, ease production planning, and reduce inventory.

Number 9: Reduce variability of demand and supply

A tough task, you say. Let’s look at some ways to reduce demand variability. Is it possible to reduce or eliminate large end-of-period buys (that were only to meet quotas)? Breaking this end-of-period addiction is very painful. It will require a quarter of two of decreased sales and profits as customers use up their excess inventories. Also, managing the resultant slack in the supply chain is costly. This is an extremely difficult habit to break and requires support all the way to the top of your organization.

Are there any other ways to smooth customer orders? Study the largest spikes in your historical demand. What caused them? If you can alter these patterns in the future, your volatility will be much less. Or, can you plan them separately if they are driven by discrete events?

On the supply side, do you have suppliers that can commit to tight timelines? A longer average lead time with less variability may be better than a short average lead time with a lot of variability. Generally, you will have to plan for the long end of the spectrum, anyway.

Variability is highly correlated with lead time; shorter lead times generally have less variability. Identifying the volatility and discovering the cause will reduce the variability in the supply chain and lower inventories.

Number 10: Align your metrics

This is a critical (and difficult) step. Does your organization have departmental metrics that are at odds with each other? You might not think so. Even “good” metrics can produce sub-optimization by department. For example, the plant manager gets his bonus based on efficiency. The lower the unit cost, the better, right? The plant manager likes long stable runs so he can get his equipment humming. The inventory planning manager gets his bonus based on finished goods inventory. He likes low inventory in the warehouses. Good for the organization right? And the sales manager wants everything in the warehouse so when he sells that huge new order, everything is available, because his bonus is his commission. Increased sales, good for the organization right?

What happens at our hypothetical organization? The plant manager disregards short production cycles and produces excess stock to get his utilization up. The inventory manager won’t accept the goods at the warehouse because he doesn’t want finished goods inventory going up, so it gets stored at the plant or in trailers. The sales manager inks a deal but the stock is not available at the warehouse, so it gets expedited from the plant. The bottom line: everyone gets his or her bonus but the supply chain is anything but efficient. Beware the metrics – what people get paid to do, they will do.

In conclusion, inventory is the measuring stick of your entire supply chain. It reflects the agility of your supply chain. The only sustainable way to reduce inventory is to improve your supply chain processes. To do this, your organization needs an end-to-end view of the entire chain. You will need to begin breaking down the “silos” across your extended supply chain with communication and understanding. Start internally and then progress upstream and downstream. Finally, remember that supply chain management is a process; there is no finish line.

Good luck!

Top 10 List review:

  1. Pareto your inventory
  2. Reduce replenishment lead times
  3. Revise order cycles/quantities
  4. Improve your forecasting
  5. Eliminate obsolete stock
  6. Centralize your inventory
  7. Lower your service level
  8. Reduce SKU counts
  9. Reduce variability of demand and supply
  10. Align your metrics

Inventory Management, Inventory Costs, Newsvendor vs. EOQ

Different models are used to manage inventory for products that are continually available (like milk) or products available for limited time (like seed).The Economic Order Quantity (EOQ) model determines the least cost level of inventory to carry, as well as costs. News Vendor models are used for products only available for a single period.

EOQ and News Vendor models have proved useful for managing inventory for many years, analyzing tradeoffs among major cost components. These models are robust and easy to customize to particular industries. Their approach to costing is similar reflecting levels of inventory, as well as shipping costs or quantity discounts.

Inventory costs fall into three classes:
1) carrying costs of regular inventory and safety stock;
2) ordering or setup costs;
3) stockout costs. Inventory control systems balance the cost of carrying inventory against the costs associated with ordering or shortfalls
Firms carry extra inventory to guard against uncertain events. Known as safety stock, the purpose of this inventory is to provide protection against stockouts. Safety stock is costed just like regular inventory, it is an interest rate times the level of safety stock.
If less is sold than expected during the 10 days or if the shipment arrives early, we will still have inventory on the 10th day and no customer service problems are encountered.
Managing the uncertainty surrounding safety stock is the key to reducing inventory levels.
stockout costs involve lost sales when no inventory is on hand. Such costs fall as inventory (and customer service) levels increase. The relationship between stockout costs and inventory depends upon the accuracy of the demand forecast and the ability of the firm to recognize and react to a change in demand.
One way to evaluate an inventory management policy is to choose a service level target. From this target, the inventory policy will determine the inventory requirements and associated costs of providing that level of service. A higher service level implies that more inventory will be held as safety stock.

Newsvendor Model

From sweatshirts in EOQ to summer dresses in Newsvendor. The big difference is that while sweatshirts were continuous selling items, the demand for summer dresses is limited to summer months. Once the summer season is over, the unsold dresses must be heavily discounted. You are a local design firm that designs northwest-accented summer dresses, sources them from China and sells them through retailers here.

The problem is that for a particular summer dress, total demand during the summer season is hard to predict. All you can do is to make a guess, that is, develop a probability distribution of demand. Let us generate our demand with the throw of a regular dice; it can be any number from 1 to 6, each with probability 1/6.

On the supply side, the lead time from your Chinese supplier is long. There is no possibility of making multiple orders. You make one order before the summer season starts, sell as many as you can during the season and then whatever is left is discounted. Let us say that per unit purchase cost c is $80. For any units that you are able to sell per unit revenue r is $100. For the units you are not able to sell during the season, let us say that you can discount them and are able to sell them at a per unit salvage value s of  $30.

The big decision is the order quantity S of dresses you should order from your Chinese supplier at the beginning of the summer season.

The Trade-off

If you order a very large quantity, there is a bigger chance that you will not be able to sell all of them. There will be excess units at the end of the season that you will have to discount. You will lose money on them. On the other hand, if you order a small quantity, there is a bigger chance that you will be short. That is, there will be some demand you will not be able to satisfy. You will not be able to make as much money as you could have.

The order quantity decision resolves this trade-off between the expected cost of having excess inventory and the expected cost of falling short. We will call the sum of these two costs as Mismatch cost. The optimal order quantity will minimize mismatch cost.

Marginal Costs

To resolve this trade-off, we start with defining marginal costs of excess and shortage.

Marginal Cost of excess Ce  is defined as the cost of  having one unit excess. You bought this unit for purchase cost of c=$80, were not able to sell it during the season and then had to discount it down to the salvage value of s=$30. The cost to you is $80-$30=$50. That is, in this setting, Ce=c-s.

Marginal Cost of shortage Cs is defined as the cost of having one unit short. Had you bought this unit for purchase cost of c=$80, you would have been able to sell it during the season for a revenue of r=$100.  We say, that the cost to you for being one unit short is $100-$80=$20. That is, in this setting, Cs=r-c.

 Service Level

Service level is the chance that you will be able to meet all the demand in a single period (summer season). Suppose you bought an order quantity S=3 units. Recall that demand is any number between 1 and 6 with equal probability 1/6. In this case, you will be able to meet all the demand only if demand is either 1 unit,  2 units or 3 units. That is, the probability that demand is less than or equal to S=3 units. This probability is known as cumulative probability and is given by the sum of the probabilities that demand is 1, demand is 2, and demand is 3 = (1/6)+(1/6)+(1/6)=3/6=1/2. That is, if you buy S=3 units, you will provide a service level of 50%.

Here is a quick table to provide cumulative probabilities in our case:

Demand 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6


1/6 1/6+1/6











Optimal Service Level and Optimal Order Quantity

Single-period model tells us that, given the marginal costs of excess and shortage, Ce and Cs, the optimal service level is given by (Cs/(Cs+Ce). In our case, the optimal service level is equal to 20/(20+50)= 0.2857.

Optimal order quantity S* is the minimum size of the order that will be able to provide the optimal service level. Going by the above table, if you buy, for example, S=1, you will be able to provide a service level of 1/6=0.1667 which is less than the optimal service level we wish to provide. If we buy 2, service level is 2/6=0.3333 and we will be able to satisfy the optimal service level requirement of 0.2857. Therefore S*=2.

Rule: compute optimal service level and find the minimum value of demand for which cumulative probability, for the first time, equals or exceeds optimal service level. That is the optimal order quantity.

Summary of Formulas for Continuous Demand: Normal Distribution

The demand distribution we considered above is a discrete distribution because demand can only take a limited number of values. In some real settings, it is easier to work with the assumption that the demand follows Normal distribution with a given mean and standard deviation. Normal is a continuous distribution because demand can take any value. In this case, we can use the following formulas:

Given per unit revenue r, per unit purchase cost c and per unit salvage value s:

Marginal cost of excess Ce=c-s; Marginal cost of shortage Cs=r-c.

Optimal service level = Cs / (Cs+Ce)

Given a normally distributed demand with given mean and standard deviation

compute z = spreadsheet function Normsinv (required service level)

Order quantity that can provide required service level = mean + z*standard deviation


Alternatively, given an order quantity S, the service level it can provide =

Spreadsheet function = Normdist (S, mean, standard dev., TRUE)


For Normal distribution, we can also compute the following:

Expected shortage = Std. Dev.*{ Normdist(z,0,1,false) -z +z Normdist(z,0,1,true)}
Expected excess = S – mean + Expected shortage

Expected mismatch cost = Cs*Expected shortage + Ce*Expected excess

Expected profit = (r-c)* mean – Expected mismatch cost

How much to order and when to order?

One of the major objectives of any supply chain is to cater to the demand in the most efficient manner. One of the ways of having achieving such efficiency is: cater to the demand by minimizing the inventory levels as much as possible.

Essentially, there are two fundamental decisions that help us manage inventory. They are:

  1. How much to order?
  2. When to order?

 How much to order?

Newsvendor Model

We decide on how much to order depending on the cost of over-stocking and the cost of under-stocking. For example, say you are company that sells cakes. A cake costs you $1.24 to prepare and you sell the cake at $2.49. But, if you cannot sell the cake within 24 hours, then you have to sell it to another local vendor at $0.99. In this case, the

Cost of under-stocking (Cu) is: $1.25 (the profit that you lose in not being able to sell the cake)

Cost of over-stocking (Co) is: $0.25 (amount that you lose because you have to sell at a discount to a vendor)

The optimal service level (SL*) is: Cu/(Cu+Co). The optimal quantity that you need to order is the smallest quantity Q at which the service level exceeds the optimal service level (SL*).

How can I get the service levels? You can get the demand distribution and the service levels from the past data.

The above formula is also called the newsvendor formula. This is used when the product has a limited shelf life and inventory cannot be carried over.

Economic Order Quantity Model

The other approach to determine quantity is called the Economic Order Quantity model.

Let us make two assumptions:

  1. Demand will be steady (no variance)
  2. Lead time for delivery order is zero. The order is immediately delivered whenever an order is issued.

In such a scenario, I will always order whenever the inventory goes to zero. Immediately the order comes and my inventory reaches Q again. The rate at which inventory goes to zero is the throughput rate (R) itself.

So, the time between two orders is Q/R

Therefore, the order frequency is R/Q.

Every order has certain fixed costs associated with it. For example, even if you order 1 unit of an AC there will be some $2000 of fixed costs (assume fixed cost will be a step cost). So, therefore you want t order as many units as possible so that the fixed costs of an order are spread over large number of units.

But at the same time, if you order more number of units then you have to bear more costs for the inventory carrying costs. Let’s look at what is an optimal solution for under this trade-off situation.

Fixed cost paid per period = S*R/Q (S is the fixed cost for every order)

Cost of holding inventory (H) = cost of keeping one unit in inventory for a certain period

The sum of both fixed cost and the cost of holding the inventory has to minimum. Under such conditions the optimal quantity to order is the Economic Order Quantity (Q*) = sqrt (2RS/H). If you centralize your inventory, then it helps in inventory optimization because: if demand increases by 2 then quantity increase by only sqrt(2).

This can be rounded off to the nearest packaging standards that are required for your supplier.

Now, let’s negate one of the two assumptions we made in the EOQ Model.

Let’s say we have a lead time of 3 weeks before the order comes.


A table for reference to understand which order quantity is better