Question

Jimmy Lube is a 3-bay Oil and Lube garage in London Ontario. Jimmy Noborsky, the owner of Jimmy Lube is contemplating on whether he should offer economical oil change, which requires him to use refined motor oil. This type motor oil is produced in Sarnia Ontario and supplied by small petro companies that refine the pre-used motor oil and mix it with petro-additives for enhanced viscosity. Jimmy is very concerned about supply disruptions, so he has chosen to use three suppliers no matter what. He has two options. For option 1, the suppliers are well established and located in the Petrolia. Jimmy calculated the “unique event, namely 402 snow-closure” risk for each of them to be 4%. He estimates the probability of a regional economic event that would knock out all three suppliers to be 2.5%. For option 2, the suppliers are newer but located in three different regions. Jimmy calculates the “unique event” risk for each of them to be 20%. He estimates the “super-event” probability that would knock out all three of these suppliers to be 0.4%. Purchasing and transportation costs would be $1 000 000 per year using option 1 and $1 010 000 per year using option 2. A total disruption would create an annualized loss of $500 000 for his garage.

Jim has also been experiencing breakdowns of the hoists in his garage for the past couple of years as shown in the table below.

Number of breakdowns	0	1	2	3	4	5
Breakdown frequency	2	2	2	6	7	1

Each time a hoist breaks down, the garage loses about $2,000. If Jimmy implements preventive maintenance, he will be able to reduce the number of breakdowns to one per month. Preventive maintenance costs would be $500 a month. The maintenance mechanic offers him a deal that for the next 3 years any breakdowns will be covered, so long as the mechanic can come in every month to do preventative maintenance for which Jimmy would have to pay $50. 30

To make the right decisions Jimmy has asked for your help by answering the following questions:

1. What is the probability that all three suppliers will be disrupted using option 2? (5marks)
2. What is the total annual purchasing and transportation cost plus expected annualized disruption cost for option 1? (5marks)
3. What is the total annual purchasing and transportation cost plus expected annualized disruption cost for option 2? (5marks)
4. Which option is best and why? (5marks)
5. Is preventive maintenance a cost-effective option? (7marks)
6. If Jimmy predict the likelihood of a breakdown being 25% without the maintenance, how much must a breakdown cost for him to prefer the preventative maintenance? (8marks)

Answer 1

Answer a)

Let, P(X) = The probability that all three suppliers will be disrupted using option 2 =?

S = Probability of 'Super Event' that would disrupt all three suppliers = 0.4 % = 0.004

U = Unique Event Risk = 20% = 0.2

Formula:

P(X) = S + (1-S) (U^3)

∴ P(X) = 0.004 + [ (1-0.004) * (0.2) ^ 3]

∴ P(X) = 0.004 + [ 0.996 X 0.008]

∴ P(X) = 0.004 + 0.007968

∴ P(X) = 0.011968

Answer b)

Step 1: Find The probability that all three suppliers will be disrupted using option 1

P (D) = Probability that all three suppliers will be disrupted using option 1 = S + (1-S) * (U)^3

Where

S = Probability of 'Super Event' that would disrupt all three suppliers using option 1 = 2.5 % = 0.025

U = Unique Event Risk for option 1 = 4% = 0.04

∴ P(D) = 0.025 + (1-0.025) * (0.04)^3

= 0.025 + (0.975 * 0.000064

= 0.025 + 0.0000624

= 0.0250624

Step 2:

Let

T = The total annual purchasing and transportation cost plus expected annualized disruption cost for option 1

PT = Purchasing and transportation cost per year for option 1 = 1000000 $

A = Annualized Loss = 500000 $

P(D) = 0.0250624 (As calculated in the previous step)

Formula:

T = PT + [ P(D) * A ]

∴ T = 100000 + (0.0250624 * 500000 ]

= 1000000 + 12531.2

= 1012531.2 $

Answer c)

Let

T = The total annual purchasing and transportation cost plus expected annualized disruption cost for option 2

PT = Purchasing and transportation cost per year for option 2 = 1010000 $

A = Annualized Loss = 500000 $

P(X) = The probability that all three suppliers will be disrupted using option 2 =  0.011968  (As calculated in answer a)

Formula:

T = PT + [ P(D) * A ]

∴ T = 1010000 + [ 0.011968 * 500000 ]

= 1010000 + 5984

= 1015984 $

Answer d) As we note that the total cost is lesser in option 1 ( $ 1012531.5) as compared to total cost of option 2 ( $ 1015984), option 1 is more cost effective and thus it is the best option.