Failures occurring in each logistic chain node inevitably touch products availability in storage and distribution points, leading to stock-outs and subsequent customer dissatisfaction. Dealing with retailers which sell to final consumers, the economic estimation of the Shelf Out-of-Stock (OOS) loss is notoriously challenging. Moreover, in fashion and apparel stores, information technology is fifty-fifty hard to estimate the size of OOS: due to the fickleness of the shopper, a OOS condition may even non lead to a lost sale. This paper focuses on the verification of the occurrence of out-of-stock events in manner stores, aiming to get a quantitative evaluation of the potential lost sales through the assay of the number of days of products unavailability. The number of OOS events due to early on stock depletion will be consequently calculated, along with their consequences. The proposed procedure has been validated on real data of an important Italian mode company.

Example of an OOS condition

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Proceedings of the Conference "breaking downward the barriersouthward betwixt research and industry". Abano Terme, Padua (Italian republic), 14-16 September 2011, ISBN: 978-88-906319-ii-4

Quantifying shelf-out-of-stock

in fashion & apparel retail stores

C. Battista, D. Falsini, L. Scarabotti, M.Yard. Schiraldi

Department of Enterprise Engineering, "Tor Vergata" University of Rome, via del Politecnico, 00133 Rome, Italy

(claudia.battista@uniroma2.information technology, diego.falsini@uniroma2.it, laura.scarabotti@uniroma2.it, schiraldi@uniroma2.it)

Abstract: Failures occurring in each logistic chain node inevitably affect products availability in storage and

distribution points, leading to stock-outs and subsequent customer dissatisfaction. Dealing with retailers

which sell to final consumers, the economic estimation of the Shelf Out-of-Stock (OOS) loss is notoriously

challenging. Moreover, in fashion and apparel stores, it is even difficult to guess the size of OOS: due to

the fickleness of the shopper, a OO South condition may even not lead to a lost auction. Th is paper focuses on the

verification of the occurrence of out-of-southtock events in fashion stores, aiming to get a quantitative evaluation

of the potential lost sales through the analysis of the number of days of products unavailability. The number

of OOSouth events due to due eastarly stock depletion will be consistently calculated, along with their consequences.

The proposed procedure has beedue north validated on real data of an important Italian fashion company.

Keywords: Shelf-out-of -stock; Lost sales; Inventory Management

1. Introduction

The theme of the shelf out-of-stock is increasingly topical

amid companies that consider customer satisfaction the

chief objective of their business and are oriented to offer

the consumer "the correct product in the right place and at

the right time".

Out-of-stock (OOS) events accept a significantly negative

effect on company's revenues, in that locationfore, to increment

business profitability, it is crucial to quantify this

miracle and the relative lost sales.

Many authors have stressed that OOS phenomenon in

retail stores is the direct symptom of the failures of some

supply processes, such as incorrect estimation of demand,

inefficient distribution of products betwixt different

stores, incorrect replenishment criteria, etc.

In the greatest part of retail business, the only available

data on customer demand derives from sales data:

when a product is out-of-stock then, in that location is commonly no

awareness of the entity of the potential lost sales. This

generates a problem in need forecasting, which should

be the starting point for all operations planning, and plays

a key role in supporting the achievement of company'south

strategic targets (Moon, Mentzer, Smith, & Garver, 1998).

Several literature examples, referring to shelf out-of-stock

events, mainly focus on illustrating the consumers'

reactions and behavior (Campo, Gijsbrechts, & Nisol,

2000; Emmelhainz, Emmelhainz, & Stock, 1991;

Papakiriakopoulos et al. 2008). Indeed, customer

satisfaction is a key parameter to increase consumer

loyalty towards the brand, specifically in fashion and

wearing apparel manufacture: Campo, Gijsbrechts, & Nisol (2003)

estimated the costs incurred past the retailer and the

supplier according to the various reactions that consumers

may have due westhen facing an out-of-stock situation. Surveys

in international large-calibration retail trade have estimated that

the bear on of OOS phenomenon averages 8.three% as a

per centum of the total number of sold items (Gruenorthward,

Corsten, & Bharadwaj, 2002). Emmelhainz et al. (1991) ;

moreover, it has been shown that retailers lose upwards to 14%

of customers due to product out-of-stock when, in plough, a

make manufacturer may lose more than than 50%.

To arroyo the above mentioned issues, this newspaper aims

to quantify customer service level in a style & apparel

retail store and to eaststimate the entity of out-of-stock

events, trying to quantitatively evaluate the related

potential lost revenues.

Post-obit an inventory management theory approach,

sales information of selected products in selected stores ha ve been

analysed to point out the stock-out-periods; lost revenues

for each product in each store have then been computed

using sales average and standard deviation.

The discussion volition primarily focus on the major causes

and consequences of out-of-stock events in retail stores,

and will and so concentrate on implementing an effective

method for OOS quantification. Information technology is thus described the

procedure to identify and select appropriate products and

stores to be analysed together with the criteri on to

compute shelf out- of-stock days and the out-of-stock

items number due to an early depletion of the

refurbishment lot: the proposed arroyo has been

validated on anorth important Italian fashion company with

160+ stores in Italy.

2. The Shelf Out-Of-Stock problem

The expression shelf out -of-stock describes the situation

where a consumer cannot buy the desired product from

stores shelves because it is sold out. The major variables

that can affect product availability in the stores and that

Proceedings of the Conference "breaking downwards the barriers between inquiry and industry". Abano Terme, Padua (Italy), 14-16 September 2011, ISBN: nine78-88-906319-2-iv

can be the crusade of out-of-stock have been pointed out past

several authors in literature (see Papakiriakopoulos,

Pramatari, & Doukidis, 2008):

(Anupindi, Dada, & Gupta,

1998)

(Clark & Lee, 2000; Downs,

Metters, & Semple, 2001)

(Gruen, Corsten, & Bharadwaj,

2002)

(Gruen, Corsten, & Bharadwaj,

2002)

(Cetinkaya & Lee, 2000;

Nahmias & Smith, 1994)

Table 1: Variables related to the OOS problem

2.one The major causes of out-of-stock

The above variables can bring, together withursday other problems

linked to supply chain management, the depletion of on-

shelf-production, hence client dissatisfaction and an

increasing probability of incurring into lost sales.

Many companies in contempo years are giving increasing

importance to consumers and to their level of satisfaction ;

this derives, with no doubt, from the availability of

products that want to buy in the stores.

Products on-shelf-availability depends on several factors,

among which nosotros tin can identify:

array: the necessary quantities should be

available for sale, directly on the shelf, at the right

fourth dimension, i.east. when the customer wants to buy them;

products display: the exhibition space defended to

the product should be congruent with the wantd

sales book;

stock list accuracy: the stock listing recorded in the

information systems or in accountancy should

correspond to the physical products availability;

sales forecasts: forecasts of sales should exist accurate,

reliable and related to the promotional process;

gild procedure: the amountain of production needed in a

certain period in a kiven southtore (sales forecast or

refurbishment requirements) should be promptly

reported in lodge to guarantedue east a timely delivery to

that shop;

availability at the supplier premises: product to be

refurbished in the shopsouth should exist available in the

supplier warehouse or, eastwardventually, in the upstream

supply chain;

commitment process: the ordered quantities should be

delivered to the store at the appropriate time, non

before (shop warehouses may be too small) nor after

(which cause OOS).

Unfortunately, inefficiencies and lack of coordination

between supply chain actors are frequently present, generating

delayed deliveries and shel f-out-of-stock problem in the

stores.

two.2 The consumers answer to an OOS

In literature, upwards to xv possible solutions for a consumer

forced to confront an out-of-stock situation accept been

classified; notwithstanding, usually only the top five are

considered (Gruen, Corsten, & Bharadwaj, 2002):

- purchase the particular in another shop;

- delay the purchase (from the aforementioned shop);

- supplant the item with another one of the same brand;

- supervene upon the item with another item belonging to a

dissimilar brand;

- non purchase the item at all.

Possible different existhaviors adopted past consumers

dealing with an out-of -stock state of affairs were also studied by

Fitzsimons (2000), who shows the response in terms of

consumer satisfaction and too in terms of option

behavior. Results suggest that consumers response to an

out-of-stock situation is driven mainly by ii factors: the

difficulty of making an alternative choice and how

important tlid particular out-of-stock item is for the

client: the more consumers are tied to the production, the

more difficult it will be for thursdayem to make an culling

pick.

Moreover, many studiesouthward evidence that an out- of-stock event

is the chiliadost frequent cause of frustration for customers.

The importance of ensuring a high availability of a

product on the shelf is also underlined by researches

(Drèze, Hoch, & Purk, 1994): thursdayey show that the full

corporeality of money spent per visitor in a selling point is

flexible and strongly depends on the number, on the

presence and on the quantity of products available on the

shelf.

2.three. Measuring an OOS

The simplest method to register OOS is pointing out whatever

empty space on stores shelves: these empty due southpaces are

clear indicators of un-replaced products. Obviously, such

procedure should be periodically carried out in society to

obtain more precise information nearly the OOS

phenomenon. The more than oft the due southhelf is checked,

the higher the measurement accurateness will be. Thus, many

resources - in terms of personnel – should exist involved to

continuously inspect and check the shelve south.

A second approach (European OOS Index - EOI) has

been proposed by ECR Europe, after a joint endeavor of

retailers and supplierdue south in the European grocery retail

sector. ECR Europe is a joint trade and manufacture body,

launched in 1994 to make thursdaye grocery and fast moving

consumer appurtenances sector equally a whole more responsive to

consumer demand and promote the removal of

unnecessary costs from the supply chain. Considering merely

fast moving items with depression sales volatility, the divers

Alphabetize monitors daily sales of the corresponding products:

if in a given day a product sells no details (or less than a

predefined threshold), and so it is considered an OOS.

Proceedings of the Conference "breaking downwardly the barriers between research and industry". Abano Terme, Padua (Italian republic), 14-16 September 2011, ISBN: 978-88-906319-2-four

A technology-based approach for automatic-detection of

OOS is through the use of Radio-Frequency Identification

(RFID) technology (Ngai, Cheng, Au, & Kee-Hung Lai,

2005). Using particular-level RFID tags and multiple readers

within the store, it would exist possible to monitor every

item'south position, thus determining its availability. However,

due to complex issues in detail-tagging procedure, costs

and responsibilitiesouth, information technology is expected that it will take many

more years before item-levefifty tagging is widely used by

industry. Thus, this method west on' t be further analyzed in

this newspaper.

three. The proposed approach

The paper proposedue south a new procedure to quantify the

number of OOS days, and, consequently, to estimate lost

sales for each product in the stores of fashion companies,

operating in the habiliment and women air-conditioningcessories industry.

To thursdayis extent, a shelf out-of-stock condition (OOS) occurs

when a product idue south no longer available in a store (thudue south it is

neither in the store warehouse nor on the shelves) and

cannot be sold. Besides, a lost-auction arises when it is

reasonable to expect a product sale (e.thousand. it is probable that

a certain customer could ask for the specific product)

while the product is OOS.

Equally a consequence, nosotros exercise non consider a lost-sale if the

product is OODue south and, at the same time, it is northot reasonable

to expect a client demand (i.east. the production is out-of-

way or information technology has different seasonal characteristics). In gild

to determine if a product is requested from customers

during a certain period of fourth dimension, the following hypothesis

was introduced : a lost sale for OOS may only occur

betwixt 2 successive replenishments so the

quantification of OOS events occurr ed later on the last

array of a product has been ignored (meet Figure 1).

Effigy i: Example of not-OOS condition

This option derives from the awareness that the

distribution of products in retail may stick to marketing

strategies which can exist unrelated to logistic direction;

considering just the OOS occurred between two

successive reorders, the depletion of a product earlier the

next replenishment cannot be regarded as a strategic

option, but as a mere logistics inefficiency (see Figureast 2).

Figure 2: Example of an OOS condition

Figure ii shows the recorded (actual) demand is steeper

than the one estimated, causing the product depletion

earlier the next replenishment; considering that the

production was sold again afterward the replenishment, we

assume that the OOS condition generated lost sales.

The process consists of analyzing the inventory build-

upwards diagram per each product in each shop, determining

those products which inventory level reached zero and

which, later on the adjacent replenishment, were sold again.

Among these, just products with statistically significant

information (in terms of sold quantities) were taken into business relationship .

Product past product, comparing the estimated lot coverage

with the actual demand – recorded past the data

arrangement – the number of OOS days and quantities were

computed multiplying the number of OOS days with the

average sales in the same period (i.e. assuming the same

need pattern recorded in the days immediately before

and afterward the OOS event).

It should exist pointed out that using the average auction to

approximate the OOS entity may not be appropriate when

dealing with certain products with intermittent or lumpy

demand pattern. Reliable effects may be obtained with the

proposed method when dealing with large-scale sales

products while findings may non be considered surely

reliable with high-cost tiresome one thousandovers items. Thus, two key

factors need to be analyzed and compared per each

product: mean (μ) and standard deviation (σ ) of sales rate .

The proposed procedure should but be applied with

products with low coefficient of variation c

five

= σ/| μ|.

3.1. The procedure

The procedure is summarized in the following steps:

1) gather the information related to each replenishment policy

for each item in each store, i.e. the replenishment lot,

the expected demand per period, the replenishment

frequency;

two) analyze the sales data for each product in each store

(it would be preferable to collect the data in an

information system) and filter those production which

show a coefficient of variation of the sales in due eastach

store over a certain threshold. The threshold should

exist determined by the analyst according to the needs

of the Company and the characteristics of the

NO LOST SALES

FROM STOCKOUT

Stock size

Time

0

v

10

15

20

25

INVENTORY BUILD-UP DIAGRAM FOR ITEM XXX

NO LOST SALES

FROM STOCKOUT

Stock size

Fourth dimension

0

v

10

15

20

25

INVENTORY BUILD-UP DIAGRAM FOR ITEM 30

Stock size

Fourth dimension

0

5

10

15

20

25

INVENTORY BUILD-UP DIAGRAM FOR Detail 30

STOCKOUT

(in quantities)

STOCKOUT

(in days)

LOT SIZE

ESTIMATED LOT COVERAGE

Proceedings of the Conference "breaking downward the bulwarks between enquiry and industry". Abano Terme, Padua (Italy), xiv-16 September 2011, ISBN: 978-88-906319-2-4

contrasted products: the higher the threshold, the

higher the accuracy; the lower the threshold, the

larger the number of analyzed products.

iii) compute the inventory level for each product in each

store;

4) determine the number of out- of-stock events and the

number of out-of-stock days per each detail in each

store (referring to OODue south event only if a customer

demand is recorded after the next replenishment, as it

has been previously explained);

5) compute the sales average in the catamenia in which the

OOS is recorded;

half-dozen) estimate theastward entity of lost sales by multiplying the

number of days of out-of-stock computed at pace 4)

by the sales averhistoric period computed at pace five);

7) eventually, proceed with the economical evaluation of

the lost sales using the preferred accounting method

(east.g. per each OOS unit, considering a loss equal to

the marginal turn a profit per product).

With regards to step due north.iv), the northwardumber of out-of-stock twenty-four hourss

for each lawmaking was computed considering the number of

days when no southtock was available between two successive

replenishments. Information technology isouth noticeable that thursdayis methodology wasouth

tested on stores assorted with apparel and women

accessories, which by and large follow specific rules of

distribution depending on the blazon of production, on the

season and on the fashion trend: thus, information technology was necessary to

be careful not to consider situations idue north which the product

was absent in the store becaemploy of strategic decisions

coming from distribution planning level. For example, at

the beginning of the flavour, a certain product may not be

present in the stores because its distribution has been

specifically postponed; in this instance, obviously no OOS

should be recorded despite the product inventory level is

zero. For this reason, in order to observe out the number of

OOS days occurred in a givedue north period , the date of arrival

and the date of the last sale for each production have been

necessarily considered.

Nonetheless, this approach leads to an underestimation of

the actual number of out-of-stocks, both at the beginning

of the production distribution menses (a certain store may

have experienced a delay in the first array evangelizey

while other neighboring stores were already supplied, and

this could have locally generated an unsatisfied customer

need) and at the end of the flavor (being no successive

replenishment planned, the sudden stock depletion for a

certain product was not considered equally OOS).

iv. Results from the validation on a industrial case

The analyzed fashion company manages 200+ shopsouthward

selling anorth array of 50'000+ product of women

apparel and accessories in Italy, with a total revenue of

more than 60M€/Y . The sales in 137 stores were analyzed

from 01/09/2009 to 31/12/2009 and 877 diffehire

products were selected (1,7%) amidst those which

registered out-of -stocks and were characterized by a

coefficient of variation less than 6. The total sales of these

products were 7'two 27 units in the analyzed catamenia, and the

proposed procedure estimated lost sales for ii'0 75 units.

Considering each OOS product sale's price, an overall

amount of more than ii00one thousand€ due southales revenues was detected,

but a total acquirement loss of more than threescoreg€ has also been

estimated: this resulted in a potential revenue growth rate

of 28,7%.

ITEMS IN STOCK OUT AND LOST SALES

Total analyzed items with OOS

Total sales of analyzed OOS items

Potential revenue growth rate (%)

Tabular array two: Summary chart of lost sales

5. Conclusions and futurity research

The shelf out-of-stock phenomenon reflects all failures

occurred in the supply chain, such as an incorrect

prediction of the need, anorthward inefficient allocation of

products betwixt different stores of the same company or

an incorrect replenishment system of stores acquired by a

non-logical distribution.

A expert demand forecasting is the starting point through

which all operations can be planned, and plays a key role

in achieving the strategic objectives of a company and of

the supply concatenation logistics as a whole (Moon, Mentzer,

Smith, & Garver, 1998).

Despite this fact, the almost common inventory

management do relies in predicting the demand for

specific items just by studying past sales. If the se items

were always in stock and available for sale, then past sales

and past demand would be the same matter: this event

though, actually never happens, because items go out of

stock from time to time, therefore causing the corporeality

sold to be less than the amount demanded (Wecker,

1978).

As emphasized past Conrad (Conrad, 1977), information technology is important

to distinguish between the number of sales and the

demand of the market. Sales figures substantially reflect

the quantity of a southwardpecific product sold in a particular

period of time: the quantity sold is commonly assimilated past

near companie s to the products demand. Nevertheless,

the number of production auctionsouth is not equivalent to the

products actual demand at all. To perform an accurate

demand forecasting, with the aim of reducing out-of-

stocks and consequently of increasing the customer

service level, it is not enough to simply use historical data:

what really matters isouthward not just the amount of sold

products, only also the actual amount of products

demanded, because it automatically incorporates out-of-

stock events. Analyzing but the number of salesouth, we

would tend to united nationsderestimate the demand for products

Proceedings of the Conference "breaking down the barriers between enquiry and industry". Abano Terme, Padua (Italy), 14-16 September 2011, ISBN: 978-88-906319-2-iv

gone out-of-stock, and we would likewise risk to have an

overestimation of in-stock products demand, since

customers would therefore tend to substitute the sformer-out

product with another in-store particular (Conrad, 1977).

For these reasons, trying to overcome usual incorrect

demand forecasting practices , this paper focused the

attention both on the identification of the OOS days

number and on the quantification of each product'south lost

sales in whatsoever store it was sformer.

The test of the implemented methodology on a real

fashion company case confirmed that OOS events have a

negative effect on the volume of sales; therefore, the

quantification of these eastvents, and of their corresponding lost

sales generated, is both crucial to increase the business

profitability and to heighten the quality of customer service.

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... Many authors have stressed that the OOS phenomenon in retail stores is the directly symptom of the failure of some supply processes, such as wrong interpretation of demand, inefficient distribution of products betwixt different stores, wrong replacement criteria, etc. [3]. In the greater part of retail business organization the only available information pertaining to client demand derives from sales information: When a product is out-of-stock then, in that location is usually no awareness of the entity of the potential lost sales. ...

... The stock-out phenomenon is considered as one of the major issues confronting retailers; and retailers that manage it effectively and efficiently stand up to gain a competitive reward. The occurrence of stock-out reflects all the deficiencies in the supply concatenation which include wrong demand forecasting, low replenishment rates, wrong ordering of products and delays on the office of suppliers [3]. Consistent with Battista et al. [iii] the study identifies fundamental determinants of stock-outs. ...

... The occurrence of stock-out reflects all the deficiencies in the supply chain which include wrong demand forecasting, low replenishment rates, incorrect ordering of products and delays on the part of suppliers [3]. Consistent with Battista et al. [iii] the report identifies primal determinants of stock-outs. Notably among them are the educational level of the respondents; the ability of the store owner to utilise ICT to order stock; age and marital status of the respondents; as well every bit the gender of the retail shop owner. ...

This study investigates factors influencing stock-out occurrence in retail shops in Kumasi City in Ghana. The study sampled 2 hundred and forty four retail outlets located in the key business areas of Kumasi City. A well structured questionnaire was used to solicit information from the respondents. Both descriptive statistics and inferential statistics were used to analyse the data. The results of the study revealed that delay in supplier'south items, demand underestimation , and bad back-of-store practices were the master causes of stock-outs. Generally, the study reveals that most retailers are not equipped to use well-nigh of the sophisticated stock control techniques and simply limit themselves to the use of stock books to control stock. Information and communication technology and collaboration with suppliers were considered by the retailers as the master stock control implementation barriers. The report concludes that, although retailers are aware of the occurrence and the causes of stock-outs, many of them had done little to put in place measures to control it; and even the few that have been able to put in identify stock control measures were confronted with implementation challenges. It is therefore recommended that retailers should adopt effective and efficient stock control techniques to limit out-of-stock occurrence.

... Their study resulted that customer reacts by switching shop or quitting or canceling the buy, due to non-availability of their expected product in the store. These reactions by the customers lead to loss to the retailers [16]. A 5 pct reduction in the customer defection rate can increment profits past 25 to 85 percent, depending on the industry [17]. ...

... where d ki (t) is the demand of the k-th detail in the i-th store. Actually, this parameter is difficult to measure; in near cases, in fact there is no awareness of the entity of the potential lost sales since the only available information on customer demand derives from sales information (Battista et al., 2011). ...

Fashion and Apparel (F&A) market, characterized by fast changes in trends and demand, past curt product life-cycles and by broad assortments, requires a responsive/demand driven Supply Chain (SC) focused on products availability, realtime information sharing and speed in matching customers requests (Iannone et al. 2013). In this context, the presented paper shows the results of a three-year research projection by firstly analysing the overall structure and characteristics of a traditional SC in this sector Iannone et al. (2015) in guild to identify the well-nigh disquisitional aspects and processes. From a adventure analysis it emerged that the correct Time Direction, intended as the power of beingness responsive to market fluctuation, is the virtually critical target for way business concern. In this context, the presented work proposes a reference framework for the definition and subsequent optimisation of the physical and informative flows, which is based on a difference assay of demand and an adjusting feedback loop. In last years, the broad spread of east-commerce and mobile purchasing is securely changing the retailing industry leading companied to prefer a new integrated strategy, called Omni-Channel Retailing. The management of both concrete and mobile channels non simply means managing an additional on-line need only requires the bodily integration of all the processes of planning and execution in order to optimize performances. With these perspectives, the proposed framework has been revised and extended in order to represent a visitor implementing this new strategy and, later on the definition of a suitable fix of Cardinal Performance Indicators (KPIs), immune usa to evaluate how information technology may impact on the performances of a traditional SC. The integration of all these analysis and the correct evaluation of the defined ready of KPIs may represent a useful system for supporting fashion companies in the strategic decision making process.

Due to the relevance of stockouts in the retail sector together with their significantly negative effect both on retail and the whole supply chain, this newspaper offers a theoretical review of the stockout definition, rates, its principal causes and consequences.

  • Richard Metters Richard Metters

Capacity limitations for manufacturers of seasonally demanded goods create hard problems for both practitioners and researchers. Empirical data propose that practitioner response is far from optimal. Optimal solutions, however, are precluded for realistic issues due to computational complexity. Here, the structure of optimal policies is explored and heuristics based on myopic policies are developed. For uncomplicated problems, the best heuristic deviates from optimality by an average of ii.5% over a variety of weather condition. Heuristics are likewise compared under more realistic business concern atmospheric condition past simulation.

This paper develops an order-upwards-to Due south inventory model that is designed to handle multiple items, resources constraints, lags in delivery, and lost sales without sacrificing computational simplicity. Mild conditions are shown to ensure that the expected boilerplate holding cost and the expected average shortage cost are separable convex functions of the club-up-to levels. We develop nonparametric estimates of these costs and use them in conjunction with linear programming to produce what is termed the "LP policy." The LP policy has 2 major advantages over traditional methods: first, it can be computed in complex environments such every bit the one described in a higher place; and second, information technology does not require an explicit functional form of demand, something that is difficult to specify accurately in exercise. In ii numerical experiments designed so that optimal policies could be computed, the LP policy fared well, differing from the optimal profit by an average of two.xx% and ane.84%, respectively. These results compare quite favorably with the errors incurred in traditional methods when a correctly specified distribution uses estimated parameters. Our findings back up the effectiveness of this mathematical programming technique for approximating circuitous, real-world inventory control problems.

  • Steven Nahmias Steven Nahmias
  • Stephen A. Smith

This paper considers a retailer inventory organisation with Northward first-echelon stores and a single second-echelon distribution center (DC). Client demands at the stores are assumed to be random. When a stockout occurs, customers are willing to look for their social club to exist filled with a known probability. Customers who are unwilling to wait upshot in lost sales. The first and second echelons are both restocked at stock-still, every bit spaced fourth dimension points, where the shop restocking frequency is an integer multiple of the DC restocking frequency. We likewise assume that replenishment quantities at both echelons can be adjusted up to the time of delivery, resulting in replenishment pb times equal to zip. This simplification allows us to decide optimal solutions for the fractional lost sales case, which has proven intractable for two-echelon formulations with lead times. Computational results are given for illustrative examples.

The occurrence of temporary stock-outs at retail is common in frequently purchased product categories. Available empirical evidence suggests that when faced with stock-outs, consumers are oftentimes willing to purchase substitute items. An of import implication of this consumer behavior is that observed sales of an item no longer provide a skillful measure of its core demand rate. Sales of items that stock-out are right-censored, while sales of other items are inflated because of substitutions. Noesis of the true demand rates and commutation rates is important for the retailer for a multifariousness of category direction decisions such as the platonic array to carry, how much to stock of each particular, and how often to replenish the stock. The estimated substitution rates tin can too be used to infer patterns of competition between items in the category. In this paper we advise methods to estimate demand rates and commutation rates in such contexts. We develop a model of customer arrivals and pick between goods that explicitly allows for possible product substitution and lost sales when a customer faces a stock-out. The model is developed in the context of retail vending, an industry that accounts for a sizable role of the retail sales of many consumer products. We consider the information set available from 2 kinds of inventory tracking systems. In the best case scenario of a perpetual inventory organization in which times of stock-out occurrence and cumulative sales of all goods upward to these times are observed, we derive Maximum Likelihood Estimates (MLEs) of the need parameters and show that they are specially simple and intuitive. Notwithstanding, state-of-the-art inventory systems in retail vending provide just periodic data, i.e., information in which times of stock-out occurrence are unobserved or "missing." For these data we evidence how the Expectation-Maximization (EM) algorithm can be employed to obtain the MLEs of the demand parameters past treating the stock-out times as missing data. We show an awarding of the model to daily sales and stocking data pooled across multiple drink vending machines in a midwestern U.S. city. The vending machines in the awarding conduct identical assortments of vi brands. Since the number of parameters to be estimated is too large given the available data, we discuss possible restrictions of the consumer choice model to accomplish the interpretation. Our results signal that demand rates estimated naively by using observed sales rates are biased, even for items that accept very few occurrences of stock-outs. We likewise discover significant differences among the substitution rates of the six brands. The methods proposed in our newspaper can be modified to apply to many nonvending retail settings in which consumer choices are observed, not their preferences, and choices are constrained considering of unavailability of items in the choice set. One such context is in-store grocery retailing, where similar bug of information availability arise. In this context an of import issue that would need to be dealt with is changes in the retail environment caused by retail promotions.

This newspaper investigates the impact of retailer stockouts on whether, how much, and what consumers purchase in a category during the out-of-stock menses. Information technology adds to previous literature by investigating the stockouts' touch on purchase quantities, by uncovering the pattern of inside-category shifts triggered by them, and by analyzing dynamic furnishings on incidence, quantity, and choice decisions. Although essential for an authentic assessment of stockout implications, these aspects of out-of-stock (OOS) behavior take received little attending and then far. Moreover, while most of the previous literature on stockouts relies on surveys measuring reported or intended behavior, this research examines revealed stockout response in a natural store environment. To this cease, traditional purchase incidence, quantity and option models are adapted to account for various stockout furnishings, and estimated based on scanner panel data for two product categories. While tractable, the models capture various aspects of stockout reactions within the store, assuasive to trace the implications of stockouts for specific SKUs and household (segment)s. The estimation results demonstrate that out-of-stocks tin can affect all three purchase decisions: they may reduce the probability of purchase incidence, lead to the buy of smaller quantities, and induce asymmetric, non-IIA choice shifts. Simulation of aggregate implications farther suggests that, on the whole, retailer losses from stockouts remain express, while manufacturer losses tin can exist quite substantial, depending on the stockout particular and the store's array composition.

  • S. A. Conrad

The differences between sales and demand are discussed. For the newsboy problem the probability distribution of demand is determined from sales data, under the assumption that customers arrive at random. The optimum stock level is shown, in general, to be different from that in the literature.

  • Thou.A. Emmelhainz
  • James R. Stock James R. Stock
  • Larry Westward. Emmelhainz

2,810 consumers were interviewed regarding their response to 5 items (removed from the shelves past the researchers) that were out of stock. 375 Ss could non detect the specific items they wanted. 32% of these Ss purchased a different brand, 41% purchased a different size or variety of the same brand, 13% delayed purchase, and 14% went to another shop. Perceived production risk, urgency of need, and produce usage were factors in the conclusion to substitute. Repeat make purchase patterns did not influence the decision to substitute simply did influence the specific substitution fabricated, if an item was substituted for what was out of stock. In those cases where no commutation was fabricated, store loyalty influenced the decision to delay the purchase or to become to some other shop. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

  • Sila Çetinkaya
  • Chung-Yee Lee

Vendor-managed inventory (VMI) is a supply-concatenation initiative where the supplier is authorized to manage inventories of agreed-upon stock-keeping units at retail locations. The benefits of VMI are well recognized by successful retail businesses such equally Wal-Mart. In VMI, distortion of demand information (known as bullwhip effect) transferred from the downstream supply-chain member (east.g., retailer) to the upstream member (east.g., supplier) is minimized, stockout situations are less frequent, and inventory-carrying costs are reduced. Furthermore, a VMI supplier has the liberty of controlling the downstream resupply decisions rather than filling orders as they are placed. Thus, the approach offers a framework for synchronizing inventory and transportation decisions. In this paper, we present an analytical model for analogous inventory and transportation decisions in VMI systems. Although the coordination of inventory and transportation has been addressed in the literature, our particular problem has non been explored previously. Specifically, we consider a vendor realizing a sequence of random demands from a grouping of retailers located in a given geographical region. Ideally, these demands should be shipped immediately. All the same, the vendor has the autonomy of belongings small orders until an amusing dispatch time with the expectation that an economical consolidated dispatch quantity accumulates. As a effect, the actual inventory requirements at the vendor are partly dictated by the parameters of the shipment-release policy in use. We compute the optimum replenishment quantity and dispatch frequency simultaneously. We develop a renewaltheoretic model for the case of Poisson demands, and present analytical results.

  • William East. Wecker

The effect of stockouts on prediction accurateness is analyzed. The forecasting bias that results and the effect on the prediction error variance are explored and are seen to depend on the frequency of stockouts, the coefficient of variation of demand, and the serial correlation of demand.