1. Introduction

In the recent era of rapid growing information technology and highly fast evolving computing speed industry leading companies like Samsung, Coca-Cola have been trying to find ways to utilize all the available (collectable) data collected over their supply chain to draw and use the meaningful information for their agile and accurate decision making. 

For example, Samsung collects various market information from their retail customers such as customers’ actual sales quantity, inventory level, order forecast and sales forecast on either weekly base or bi-weekly base. Samsung’s big customers such as Best Buy in North American Market even provides Samsung with real-time POS (Point Of Sales) data and both companies closely collaborate each other to correctly read and forecast the market behavior together. These joint efforts made it possible to achieve the highest forecast accuracy on the item level demand forecast. See Ko [1] for further details on this best practice. 

In early 2009, Coca Cola announced to the media their next generation market sensing tool ‘Freestyle’. The Freestyle is the most intelligent dispenser (drink vending machine) that pours more than 100 varieties of sodas, juices, teas, and flavored waters. This dispenser contains 30 cartridges of flavorings that mix up 100 different drink combinations. Each dispenser contains 30 cartridges of flavorings that mix up 100 different drink combinations. The cartridges are tagged with radio frequency ID chips, and each dispenser contains an RFID reader. The dispensers collect data on what customers are drinking and how much, and transmit that information each night over a private Verizon wireless network to Cokeʼs SAP data warehouse system in Atlanta. The company will use the data to develop reports that assess how new drinks are doing in the market, identify differences in regional tastes, and help fast-food outlets decide which drinks to serve. See Refer Weier [4] for further stories on Freestyle. 

In both cases explained above these companies’ most strong intention behind their efforts is not to lose any potential demand in the future by accurately predicting the market demand. In other words they want to best serve their customers so that they can make their potential customers to fall in love with their products and their brand eventually. 

There exist several different measures which help companies to assess on how well they serve their customers in the field. For the overview of customer metrics please see Lambert and Pohlen [2]. In this paper we would like to study two of such metrics. One is the well-known ‘customer service level’ and the other is ‘in stock ratio.’ The first metric ‘customer service level’ was introduced by researchers who studied inventory management. Once the target customer service level is determined together with the demand distribution over certain time period then the level of optimal inventory can be easily computed. The customer service level is a good barometer of how well a company is meeting its customers’ immediate request or needs. On the other hand the ‘in stock ratio’ percentage can provide a much simpler way of calculating the level of customer service or the level of inventory at the store. Compared to ‘customer service level’ ‘in stock ratio’ does not have any assumptions to be satisfied. In this paper we investigated these two measures side by side to draw some useful management insights for putting these measures into practices. In stock ratio is not a brand new concept. Readers who are interested in checking out other occasions of in stock ratio usage can refer Han and Kim [6]. In that paper authors first defined the new metric ‘in stock ratio’ to describe the product availability and provided the solution procedure for seeking the optimal inventory level for each retail store. 

2. Customer Service Level(CSL)

2.1 Definition

The customer service level has been very popular in real practice for such a long time because it is a good barometer of how well suppliers (retailers) are meeting their customers’ irregular and dynamic requests or demand. The customer service level measures the number of times you successfully serve your customers’ needs. If customers can not find what they want in your store, they would look for them elsewhere immediately. The customer service level, in general, can be defined as following: 

One pitfall of the above form of customer service level is caused by the partial fulfillment of the customer’s request. Should you count the numerator or should you not count when you only have 24 units of product available in stock upon your customer’s request of 25 units. In practice, the partial fulfillment does not add a count towards the improved customer service level.

Furthermore on time delivery often be the necessary condition for adding count towards the improved customer service level in addition to the exact number. Incorporating on time delivery condition the above expression of the customer service level will become:


Example 2.1.1 Suppose that a retailer makes orders for a certain color television model to a electronics supplier over 3 month time period as described in <Table 1>. 

<Table 1> Customer Order History Example.

In this case the customer service level of this supplier for the given period can be computed as :

2.2 Customer Service Level and Safety Stock Level

It will very hard to explain customer service level without mentioning safety stock level. These two are closely linked to each other. It will be the most reasonable statement that one should increase his safety stock level in case he wants to improve his customer service level. Increasing the safety stock level is the first thing he can think of to level up the customer service level. 

Demand forecast is a prediction based on past actual sales history. The future sales of a certain product will probably be similar to this quantity. In this situation safety stock plays a role of buffer for situations where actual sales exceed the demand forecast. In this way safety stock is sort of ‘insurance’ to help ensure that the company can meet up customer requests for a product during the period of time required to complete the product replenishment cycle. There exist two uncertainty factors. One is the demand side fluctuation and the other is the supply side fluctuation. Demand side fluctuation involves the unknown customer demand while supply side fluctuation is linked to the unknown replenishment lead-time, or the time between order placement date and the delivery completion date. In this paper, we will consider the demand side fluctuation only for the efficient explanation on the outstanding topic. Furthermore, we will use the newsvendor model foundation to clearly provide the linkage between customer service level and the safety stock. 

The name of the model derives from a newsvendor who must purchase newspapers at the beginning of the day before attempting to sell them at his newspaper stand along the street corner. 

If he purchases too many then he will have some left over resulting additional salvage cost. If he purchases too few then he will lose some of his potential customers to other newsboy. In this way, the tradeoff is between too many and too few. In this case, the extra newspapers prepared in the morning as buffer by the newsboy due to the demand uncertainty is called safety stock. 

[Notation]
r = unit newspaper sales price (p > 0)
c = unit newspaper purchase cost (0 < c < r)
h = unit inventory holding cost per unit period
π = stock out cost per unit shortage
 = unit newspaper demand in the period (> = 0) 

 (Continuous random variable)
φ = cumulative distribution function of demand (= 1 ― φ )
ø = probability density of demand
μ = mean demand
σ = standard deviation of demand
g = stock level after ordering (decision variable)
C.S.L = customer service level

Now, using notations above, the newsboy’s profit function can be formulated as following :
 
where, x⁺:=max(x,0)

Furthermore, the expected profit function can be expressed as :
 

The first two components in above expression represent the profits of the newsboy when he sells copies of newspaper at the price of r while he purchases each copy at the price of c. And the last two components correspond to the inventory holding cost (or salvage cost in this case) and the shortage cost (or opportunity cost for the potential sales). And the optimal solution that maximizes the expected profit of the newsboy should satisfy the following condition :
 

We will not prove the above result on the optimality condition. For readers who want the detailed mathematical proof please refer Porteus [3] or Kim [5]. 

Example 2.1.2 Suppose that a cellular phone manufacturer sells mobile phones to a mobile operator based on weekly operator‘s weekly order cycle. Furthermore, let‘s assume the size of the weekly order made by the operator follows normal distribution with mean of 250,000. and standard deviation of 20,000. And the parameter values required for the Newsvendor Model are summarized in <Table 2>.
 

<Table 2> Parameter Values.

Then, the optimal stock level of the manufacturer can be computed using the equation (1) as :
 

It is notable that the manufacturer’s CSL at the optimal stock level is under 80%. The lower the material purchase cost or the higher the cellular phone price the CSL at the optimal stock level improves, or less likely hit the shortage. <Figure 1> summarizes the required stock levels for meeting the various predefined CSLs. The required stock levels sharply increase as the standard deviation of demand distribution gets bigger and bigger and as the target CSL is moving towards 100%. At 99% target CSL the required stock level is 50% higher than that of 77% target CSL when the standard deviation of the demand is at the largest (= 100,000). In this reason, the target CSL should be traded off considering inventory holding cost and the stock cost as well. For the high-end consumer electronics such as smart phones managing high level of inventory can be a huge risk to both the retailer and the manufacturer. 

<Figure 1> Optimal Inventory Levels at Varying CSL and Demand Fluctuation.

2.3 Discussion

In Section 2 we have revisited the definition of CSL together with the well-known inventory model which is called the newsvendor model. There exist two major difficulties in using the CSL for the real business purpose. Firstly, for the CSL to be used for inventory management it is inevitable to estimate a series of parameters as shown in Example 2.1.2. But in reality, parameter estimation is one of most difficult tasks for any inventory manager of an organization. Secondly, even though the parameter estimation has been done successfully it’s not over yet. these parameters should be adjusted and maintained to reflect the business and market dynamic changes over time. These adjustments job is even more critical than coming up with the a certain parameter estimation procedure. These difficulties keep this measure from being used in the real business fields. 

3. In Stock Ratio(ISR)

3.1 Definition

In stock ratio, in general, can be defined as percentage of stores having any sellable products available in stock among the entire stores. Suppose that a company is selling a certain product. And this company has 100 own stores with 70 stores having sellable unit(s) of this product then in stock ratio of this company for this item would be 70% at the moment of investigation. 

For rigorous definition of in stock ratio the following notations are deployed throughout this paper. 

˚S : Total number of stores owned by the company
˚P : Total number of products to be distributed to stores
˚P(A) : Probability of event A to be occurred
˚P(B|A) : Probability of even B to be occurred given that event A has already occurred 

And the following three assumptions make our analysis on the development of probability statement of in stock ratio more concise and efficient without sacrificing the context of the real world problem. 

(A.1) Upon the completion of the product distribution each product has the same probability to go to any store
(A.2) No two customers can show up simultaneously at each store
(A.3) Any customer exhibits the random pattern in selecting a store to visit. Or there does not exist any customer preferences on selecting stores. 

3.2 Convergence Characteristics of In Stock Ratio

Suppose there exist S stores and P products for company A. When one of the customers visit one of company A’s stores to buy just a product then the probability that the customer finds the product available can be written as :

Then this probability statement can be rewritten as :
 

The probability P(Customer fails to find the product | Customer visits a store) can be easily calculated under the assumptions (A.1), (A.2), and (A.3). The total number of possible ways in assigning P products into S stores is SP. Furthermore, the total number of possible ways in assigning P products into (S-1) stores is (S-1)P. Using these two conditions we have the following expression on In Stock Ratio: 

where S represents the total number of shops owned by the retailer and P is the total number of products available to place to S stores. 

Having the form of In Stock Ratio derived as in (2) it is interesting to note that In Stock Ratio converges as the number of shops increases. We can use the following ratio, which we call ‘Product Shop Ratio’ or simply ‘PSR’, to show the occurrence of convergence :

where C is set to P/S, Product Shop Ratio. Using the fact from elementary calculus that,


the limit associated with the In Stock Ratio expression in (3) can be reduced to :

as S increase increases to a sufficiently large number. In other words, when PSR is held at a certain constant the In Stock Ratio converges to a constant number. 

Example 3.2.1 We consider an illustrative case with 9 different combinations of product number and shop number as shown in <Table 3>. To illustrate the actual convergence of In Stock Ratio as the shop number increases while the Product Shop Ratio is held at a constant, say 1.5 the corresponding in stock ratios are computed at different values of the number of shops. 

<Table 3> ISR with Varying #Shop Under the Fixed PSR(= 1.5)

It is shown in <Figure 2> that the In Stock Ratio converges to 1 ― e ^―1.5  = 77.7(%)  as the number of shops increases. 

<Figure 2> Convergence of ISR.

3.3 Inventory Management using In Stock Ratio

Now we can compute the inventory level which accomplishes the target In Stock Ratio. Consider a retailer with 1000 shops nation-wide. If the target In Stock Ratio is 98% then the required inventory level can be computed as:

The resulting inventory level is 3,910 units when the number of shops, S, is equal to 1,000. 

<Table 4> ISR with varying PSR Values.

3.4 Discussion

Compared to the CSL it is much straight forward to apply the ISR to come up with the appropriate inventory level which satisfies the pre-defined target ISR. The inventory manager in this case, just needs to remember the number of shops where they can sell their products. Contrary to the CSL measure the parameter estimation process is not required at all with ISR measure. But still there exist several weak points with ISR measure. The first weakness is that ISR does not reflect the size of demand for each time period. No matter how big is the customer demand the ISR will be computed as 100% as long as all shops carry at least one unit of inventory for the outstanding item. This means that 100% ISR not necessarily represents the sound status of the inventory level. In other words, ISR measure should be adjusted using some additional information to overcome this kind of weak points. The second weakness is the ambiguity on determining the replenishment quantity and replenishment time. The value of ISR measure will change whenever any shop’s inventory level hits zero even during the same day. In this context, for the ISR measure to be effective in the field the value of ISR should be updated in real-time between shops and warehouses. In addition the replenishment quantity and replenishment schedule should be computed and executed within very short time frame such as daily or weekly at least. In such cases where the replenishment schedule is updated biweekly or monthly then the value of ISR won’t change even after shops’ inventory levels hit zero while customers keep visiting their shops for the stock-out product. In other words, the value of ISR no longer provides meaningful insight on the customers’ behaviors. 

4. Conclusion

In this paper we have investigated two measures for evaluating the degree of customer service. Furthermore we studied how these two measures are linked to manage the desired target inventory level of product manufacturer or retail company. Then which measure will be more intuitive and more practical in reality? The answer is the In Stock Ratio. There exist two major reasons for this answer. Firstly, they don’t prefer to adapt mathematical models which require many complex assumptions. Especially, they don’t want to invest their time and efforts for estimating various model parameters or for validating complex model assumptions. Secondly, not like CSL measure adapting ISR does not require mathematical background such as demand distribution function, cumulative probability etc. But as explained in Section 3 and Section 4, adapting ISR measure only can be insufficient and ineffective in drawing exact replenishment quantities and computing the efficient replenishment time. Deploying ISR measure only can capture the limited part of the entire market dynamics. In order to capture the holistic aspect of market dynamics following questions should be answered. Which items are hot in the market at the moment? What are the actual daily (or weekly) sales for past several says (or past several weeks)? What are the recent inventory status trend at stores? Answers on these questions will be sufficient to make the strong analysis on sales and inventory trend leading to effective way of understanding customers’ preference on products. Finally this result can be used to derive competitive sales and inventory management policies. Extended to months or years the trend analysis will allow companies to realign their business structures or let them know on which business to focus or to ignore. It will be an interesting future research topic to design the business process, in pursuing higher customer satisfaction, by combining ISR measure and short term trend analysis with or without possible partner collaboration opportunities. 

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