La crisis económica y el “Beer Game”

La situación de crisis que afloró hace ya cuatro años en Europa  y que sigue azotando principalmente a los llamados países periféricos (esta mañana la prima de riesgo en España era de 540 puntos) me recuerda indefectiblemente al conocido “Beer Game” nacido en el MIT de Cambridge.

Más allá de lo que parece, la enseñanza fundamental de este juego de negocios es que la estructura del sistema determina cómo éste se comporta. Por eso, los esfuerzos locales de los “managers” por poner la situación bajo control durante el juego resultan ciertamente fútiles. Cualquier cambio local en el sistema no hace sino aumentar el ruido y crear mayor incertidumbre en el entorno.

Este escenario, mutatis mutandis, es el que hemos vivido en los últimos cuatro años en España con dos partidos en el gobierno de distinto signo político, que se han empeñado, con buena voluntad y no demasiado acierto (es inevitable), en resolver localmente un problema de ámbito global (léase, al menos, europeo). Y para colmo de males, los medios de comunicación amplifican el nivel de incertidumbre en la sociedad anunciando que las decisiones tomadas por los gobiernos (quizá en la dirección correcta) la víspera no han servido para mejorar las cosas, sin dar “tiempo al tiempo”. Beer Game en estado puro. Los expertos en “system dynamics” (otra gran disciplina inventada en el MIT) dirían que los medios de comunicación alimentan un bucle positivo, que no hace sino aumentar aún más el ruido, el nerviosismo y la incertidumbre.

Solamente 1) comprendiendo las razones últimas del problema (mal servicio al cliente o crisis económica galopante según el caso) y 2) poniendo en marcha acciones estructurales adecuadas (sistémicas, como se las da en llamar últimamente) es posible eliminar, o al menos mitigar, los efectos indeseables. Un reto formidable en una Europa (y una España) con demasiados gobiernos e intereses encontrados.


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Bizi-Zaragoza: A Supply Chain View

How to mitigate the “rush hour effect” using Supply Chain Tools

Alejandro Serrano – . Apr 19, 2012 | Spain

Bizi-Zaragoza rents bikes to users who need to ride for short periods of time within the city. Bikes are located in 130+ stations in the city, mainly downtown. To get a bike, a user goes to a station and unlock the desired bike with his or her user card. To return it, he or she has to find a station with an empty slot and identify him or herself again.

Bizi Station. Source:

The idea is very interesting, and has been proved successful in several cities. The system in place, however, is far from perfect, since users face two major challenges. On the one hand, a user looking for a bike may find the nearest station empty (see black dots in the picture below). On the other hand, a user looking for a slot to leave a bike may find the nearest station full (see purple dots). Furthermore, stations downtown tend to fill quickly in the morning and empty in the afternoon/evening. Good on-line information may be helpful to find a bike or a spot, but still the bottom line is that the typical user my find the service unreliable when his meeting with her boss starts at 9am, and he has to plan for extra 20 minutes of safety time to park his bike so as not to be late.

To mitigate this situation, and according to today’s Heraldo de Aragón(*), a local newspaper, Bizi managers constantly check on-line those stations with no bikes, and send vans with additional bikes to “replenish” those empty stations in no more than 10 minutes. Here is some anecdotal evidence that this may not be the case. The following picture (borrowed from the company web site) shows the map of all stations at 10:02:45 am today. There were 13 empty stations (marked in black in the map), mainly in the periphery.

Ten minutes later, the picture was the following

As it can be observed, 12 of those 13 stations were still empty. Twenty minutes later, there was a new picture.

In this case, 8 of 13 stations were still empty. Thirty minutes later (picture not reported) still 8 of 13 stations were still empty. A similar problem can be observed with full stations (purple dots in the maps).

The question that arises next is how to mitigate this problem. A feasible option is to place stock (i.e. bikes) according to demand patterns to obtain a given service level. For instance, let us say that for the last 50 Mondays, between 7:30 am and 9:00 am, station#77 has observed a demand pattern that can be considered normally distributed, with mean 10 and standard deviation 2 (that implies that roughly 2/3 of the days demand is between 8 and 12 bikes). How many bikes are needed to guarantee an average service level of, say, 99%? The answer is

ROUNDUP(10+2*NORMSINV(0.99),0)=15 bikes

Therefore, rather that being reactive, Bizi managers could be proactive by replenishing inventory at night before users go to work early in the morning. The previous analysis is quite simple and can be easily extended for all stations and for full stations. The good news is that the company should have a lot of data, given that users sign in every time they take or leave a bike. To improve forecasting methods, individual patterns can be studied, since the system knows the ID of the user that takes or leaves a bike.

Finally, there is the problem of devoting workforce to move bikes from one station to the other. A potential solution may be to charge more to those users who do not make “return trips” within a day. If so, users have incentives to return bikes to where they were in the evening, significantly reducing the amount of bikes to be moved at night.

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(*) The piece of news is here (in Spanish)

The web page of Bizi Zaragoza is here


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To centralize or not to centralize, that is the question

How much safety stock to hold? A ubiquitous question in supply chain network design

Alejandro Serrano –  Apr 2012 | Spain

When a firm designs from scratch its distribution network, a repetitive question arises sooner or later: should we have a centralized or a decentralized network? In a pure centralized network, a large, central distribution center (CDC) contains all the finished-good inventory of the company. In a pure decentralized setting, inventory for each SKU is splitted among several smaller regional distribution centers (RDC).

One of the key questions mangers usually struggle with when deciding about centralizing inventories or not is how many units of each SKU should be held in each case. It is a relevant question, because holding inventory usually entails significant holding costs, both financial and material.

Let us learn the basics of how to answer that question by means of a very simple example: Assume that the demand of a typical product in the portfolio in a stable market is normally distributed, with mean 400 units/period and standard deviation 80 units/period. The market is divided into four identical regions with independent demand. The firm service level target is 95%, thus in the (assumed current) CDC there should be 532 units to maximize expected profit:

(If it is not clear to you why this formula is used, please bear with me; it will be explained in a subsequent post)

Now consider that your company is planning to change its distribution strategy from centralized to decentralized, and so you consider having  four identical RDCs, one per region. The average demand in any region will be 1/4 of total demand, or 400 / 4 = 100 units. The regional variance will be 1/4 of total variance (assuming demand independence across regions), thus the standard deviation in any region will be

The quantity per RDC is

The total inventory is 166 x 4 = 633 units. The safety stock needed, i.e., the amount of inventory to hold above the average demand is 532 – 400 = 131.5 units in the centralized case and 633 – 400 = 263 units in the decentralized case. Interestingly, the latter quantity is exactly two times the former. It is not a coincidence that 2 is the squared root of 4. In fact, when switching from 1 to n DCs, overall safety stock is multiplied by √n. For instance, had we considered 9 RDCs, total inventory to hold would have been 400 + 3 x 131.5 = 795 units.

Of course there may be more involved scenarios (e.g. constraints or demand correlations across regions) that modify the optimal solution. However, keeping in mind this simple square-root formula as a rule of thumb for safety stock will help make back-of-the envelope calculations when quick business decisions have to be made.

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Adidas to cut its assortment by 25%

How many SKUs should a firm offer?

Alejandro Serrano – . Apr 2012 | Spain

Herbert Hainer, CEO of Adidas AG, announced last Saturday* that the company has plans to cut 25% of its 46,897 SKUs. An argument used by Mr. Hainer to justify their decision is that 20% of the current assortment generates 80% of sales.

If this roughly is the case–which should not be surprising, according to Pareto’s law, it means that 80% of the assortment accounts for 20% of sales. And most likely, within the remaining 80% SKUs, Pareto’s law still holds, i.e., 80% of that 80% account for 20% of the remaining 20% of sales, and so on and so for. Working in this fashion we can prepare the following table for how much the SKUs with the least sales sell.

How much SKUs with the least seales sell according to Pareto's Law

As the last row shows, cutting SKUs by 25% means removing those items that contribute to 0.006% of sales, or $1.2m, since Adidas sells roughly $18b. Remarkably, those 12,294 items  only sell $83 (roughly 1 unit) on average worldwide! Therefore, it makes a lot of sense to remove them from the assortment.

The natural question to ask at this point is why pruning 25% of the items and not more. Should Adidas also remove the second-to-last row items (15,367 SKUs!), which sell $400 on average worldwide? What about the third-to-last row?

These question nicely illustrates the usual trade-off between Marketing and Supply Chain departments in the retailing industry. A marketing-driven organization, like Adidas, argues that adding an SKU to the assortment increases sales. The more variety offered, the higher the chances that the customer likes whatever is on the shelf thus the probability of making one additional sale. The penalty to pay is in the form of, mainly, inventory holding cost and ordering cost. In good times (Adidas increased sales by 10% last year) this penalty tends to be underestimated.

Indeed there is no clear answer to the question posed above, but we can have a look at other industries to shed some light on the issue. For instance, in the telecommunication telephone manufacturing industry,  Apple sells only 2 SKUs (i-phone 4, either black or white), whilst Nokia sells at least one model for each market segment (for instance, it sells 37 different models only in Germany). Other successful companies have followed the same trend of reducing the number of SKUs to focus on reducing supply chain costs. Good examples include Lidl in Germany or Mercadona in Spain.

A holistic view of the company is necessary to make sound decisions when answering the question of ow many SKUs in the assortment are needed. Supply chain costs should be carefully pondered before blindly following the advice of marketing experts.

(*) Frankfurter Allgemeine Zeitung. The link to the piece of news is here  (in German)

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Tuitear y Tutear no son el mismo verbo

De cómo algunos creen que las redes sociales no son la sociedad. Alejandro Serrano – . Mar 2012 | Spain

Desde que leo asiduamente entradas en twitter vengo observando cómo algunos usuarios se dirijen a otros que no conocen de nada con una familiaridad asombrosa. Esto incluye tuits a personajes públicos, como políticos o empresarios, que están en las redes sociales porque su presencia en estos foros ha pasado a ser de facto obligatoria.

Aunque muchos de ellos son extremadamente respetuosos (por ejemplo, éste iba dirigido ayer a Mario Conde: “Don Mario, respeto sus fuentes, pero la TV está diciento otra cosa. Ojalá sea cierto lo que dice”) hay otros que traspasan las fronteras del respeto, la educación y el buen gusto, todas a la vez. Tres perlas recientes:

@Jiwert @gaceta_es vosotros no teneis ni p. idea de lo que necesita la educación pública.” (dirigido al ministro de educación, la abreviatura es mía)

@Rubalcaba No tienes vergüenza

@nnn Juan Roig es muy HDP infinito”. (dirigido al dueño de Mercadona, la abreviatura es mía)

¿Cómo es posible semejante atrevimiento? Es cierto que en twitter no hay filtros: por defecto, cualquiera puede opinar, a diferencia de lo que ocurre en muchos blogs, donde los comentarios a las entradas requieren el permiso del autor para publicarse. Esto libera muchas restricciones para expresarse, pero nunca debe eliminar las limitaciones legales o las naturales propias de la libertad de expresión. Parece que algunos usuarios olvidan esto. O quizá lo ignoran. O hacen caso omiso. O se sienten protegidos por un anonimato que es ficticio.

En cualquier caso, opino que no es deseable para la sociedad permitir en el mundo “virtual” de las redes sociales lo que no se permite en el mundo “real”. Como sociedad, debemos protegernos de nosotros mismos. Para no llegar a acostumbrarnos; ni a contagiarnos.


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When too much is as bad as too little

Why your firm should not aim at achieving 99% service level for all products (most likely)

Alejandro Serrano – . Mar 2012 | Spain

Last week I attended a nice talk given by the head of logistics of an e-commerce retailer. His firm holds roughly 10,000 SKUs and serves daily demand to end users from a central distribution center. A characteristic of the industry in which this firm operates is that orders should be satisfied in less than 24 hours. Since suppliers’ lead-times are on the weeks or even months (some are based in Asia), the firm is forced to hold large amounts of inventory to cope with uncertain demand.

The firm has a customer service level goal as high as 99% for all products. This figure, 99%, may be judged as appropriate by some people, but rises at least two questions: 1) why 99% and not, for instance, 90% or 99.9%, and 2) why 99% for all 10,000 products.

The answer to the first question might have to do with the fact that achieving 100% service level is virtually impossible. Therefore (put yourself in the CEO’s shoes,) if you want to provide your customers with an excellent service level, a feasible, close-enough-to-100%, easy-to-remember, and popular figure is 99%. And why not, you want to keep that figure high for all 10,000 SKUs in your warehouse.


A key point that is missed here is the fact that service level that maximizes expected profit should at least depend on the price and the cost of each particular item. In fact, inventory theory (or common sense) says that one should increase service level until the marginal benefit of adding an additional unit be exactly as high as the marginal cost of adding that additional unit. Note why this makes sense: given the cost of an specific item, if its market price goes up, the firm should increase the service level for that item. Why? a higher price implies a higher unit margin, and you want to capture that additional margin with higher probability, thus inventory should go up. Likewise, if given a price, the cost of an item increases, service level should be reduced to avoid a higher probability of holding too much inventory (as measured in moneys,) which is mainly driven by obsolescence, insurance, spoilage, and financial costs.

There are other factors that have an impact on service level above and beyond price and cost, such as the so-called salvage cost or goodwill cost. But as a conclusion,  and without entering into details on how to compute optimal service levels, it should be apparent that 1) There is an optimal service level that depends on the margin of the product, which may be below or above 99%; and 2) service level should be computed for each SKU, or type of SKUs, thus defining it for all items in a firm does not make by and large much economic sense.

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Conocimiento y experiencias logísticas innovadoras

Sesión organizada por el IAF y las Cámaras de comercio en Zaragoza

Alejandro Serrano – Mar 2012 | España

“Conocimiento y Experiencias logísticas innovadoras”

El 19 de marzo participo en esta sesión para hablar de la “Supply Chain and Finance Initiative“, puesta en marcha desde el Zaragoza Logistics Center. Haré una breve introducción de qué es ZLC y en qué consiste esta iniciativa. Después ilustraré con un ejemplo cómo cambia el comportamiento de un comprador cuando tiene que preocuparse por el impacto de sus decisiones no sólo en la cuenta de resultados, sino también en el balance de la empresa.

Más información e inscripciones en este enlace.

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