Abstract
We have a big database of point of sale for one of the major
convenience-store chain in Japan. We can observe who bought what, where,
when by using the database. We focus on a product life cycle. Generally, the
cycle is surprisingly short. For example, sale of about 65\% product of
rice balls is discontinued within three months. We show that the cycle
depends on a number of repeat customers.
Fig.1 shows time series of market share. Both products are plum rice balls.
The product A has been bought since the release date t=40. However, the
market share of the product B was immediately lost after the release date
t=25.
In order to investigate a difference between the product A and B, we
introduce a conditional probability, P$_k$(N$_i,t$=1$$N$_i,t -
1$=1). Here, N$_i,t$ is 1 when a customer i buy a product k in t-th
shopping of rice ball. Therefore, P$_k$(N$_i,t$=1$$N$_i,t -
1$=1) expresses a probability that the product k is chosen continuously.
The product A with long life cycle indicates a high probability,
P$_A$(N$_i,t$=1$$N$_i,t - 1$=1)=0.5. However, the product B with
short life cycle expresses a low probability, P$_B$(N$_i,t$=1$
$N$_i,t - 1$=1)=0.2. As shown in Fig.2 we can find that there is a
correlation between the life cycle $$ and the probability $łeft
P \right_ $. In this conference, we show the probability
in more detail and describe it by applying Logit model.
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