Question

A retail corporation wants to know how often a customer returns items in a year. The company’s data analytics team analyzed customers’ shopping behavior and came up with three categories of customers. Customers in category 1 do not return items often. Customers in category 2 return some items, and customers in category 3 heavily return items. Suppose that the data analytics team modeled the number of returns in each category of customers according to a Poisson process with rates λ1 = 1 per year, λ2 = 4 per year, and λ3 = 10 per year for categories 1, 2, and 3, respectively. Category 1 customers constitute 30% of the customer base of this retail corporation, whereas Category 2 and 3 customers constitute 60% and 10% of the customer base, respectively.

(a) What is probability that the company gets 10 returned items from a customer during 2019 and 2020 (this time period includes both years 2019 and 2020)? Do NOT calculate a number. Just write an expression for this probability.

(b) Compute the mean and variance of the number of returned items for a customer during 2019 and 2020.

(c) Now consider a category 2 customer. Compute the mean and variance of the number of returned items for this customer (=a category 2 customer) during 2019 and 2020.

(d) Given that a customer returns 10 items in his or her first 2 years, what is the probability this is a category 2 customer? Do NOT calculate a number. Just write an expression for this probability.

Answer 1

a)

As per case study graybar is facing pressure of price reduction. Hence first focus of graybar would be on its supply chain management. In supply chain of graybar there were distributor who is also sharing profit of graybar. Hence graybar has to identify middleman in its supply chain which can be eliminated and make their business more profitable.

b)

Graybar then should focus on its customer relationship management. Gray bar needs to develop strategies, practices which will help them to manage and analyze customer data with the goal of improving and strengthening relationship with customers.

c)

Last focus of graybar should be on ERP. Since current businesses are mostly driven by technologies. Hence in order to be technologically advance graybar should use tools which will increase its productivity and saves time. Enterprise resource planning is a method which help an organization to manage and integrates major part of its business such as planning, inventory management, procurement, marketing, sales ,finance and other areas of business