Question

Part 1

John, the supply chain director, explains to the management team that product availability does not only depend on production capacity, but also on proper DC operations.

The company has one DC in Kansas that has the potential to face disruptions due to natural phenomena (usually tornadoes). John has gathered data from past 52 years on how many times a year the DC has faced disruptions and had to stop its operations (Table 1).

Table 1: Number of disruptions per year at DC in Kansas .

Year	# of disruptions
1968	2
1969	4
1970	1
1971	1
1972	2
1973	1
1974	0
1975	0
1976	1
1977	5
1978	0
1979	5
1980	5
1981	0
1982	3
1983	3
1984	0
1985	4
1986	0
1987	0
1988	0
1989	3
1990	5
1991	1
1992	4
1993	5
1994	5
1995	2
1996	3
1997	0
1998	2
1999	4
2000	1
2001	0
2002	0
2003	1
2004	2
2005	1
2006	4
2007	3
2008	4
2009	3
2010	0
2011	1
2012	4
2013	5
2014	2
2015	4
2016	5
2017	4
2018	4
2019	4

1. Based on the empirical data in Table 1, what is the probability of having 4 or more disruptions at this DC (Kansas) next year?
2. Based on the empirical data in Table 1, what is the probability of having no disruptions at this DC (Kansas) next year?

Part 2

The company owns another DC in Montreal (Canada) that also faces disruptions sometimes during the year due to snowstorms (that block the roads). The number of disruptions, in this case, follows a Poisson distribution with an average of 4.4 disruptions per year.

1. What is the probability that the number of disruptions next year at this DC (Montreal) is equal to or less than 4?
2. What is the probability of facing no disruptions at this DC (Montreal) during next year?

Part 3

The time (continuous) taken by any of the DCs to recover from a disruption follows a uniform distribution with a minimum of 5 and a maximum of 15 days.

1. If a disruption happens, what is the average time the DC will be closed for?
2. If a disruption happens, what is the probability that the DC will be closed for more than 7 days?

Answer 1

1)a) Probability of 4 or more disruptions= no. of years where disruption is 4 or more/total no. years=19/52

b)Probability of having no disruptions = no. of years where disruptions are 0/total no. years=12/52=4/13

2)A) It follows a Poisson distribution with pmf=, where m is the parameter and here =4.4

Probability disruptions less than or equal to 4= = 0.5518

B)probability of facing no disruptions= =0.01228

3)A) It follows a uniform distribution with pmf= where b=15, a=5

Average time DC will be closed == 10

B)Probability that DC will be closed for more than 7 days= ==15-7/15-5

=0.8