Oliver is a procurement manager and he is trying to work out the likelihood that a supplier fails to deliver to the warehouse two days in a row. Which of the following methodologies should Oliver use?

The Poisson distribution is the most appropriate methodology. It is a discrete probability distribution used to model the number of times an event occurs within a specified interval of time or space. In this scenario, the 'event' is a supplier's failure to deliver, and the 'interval' is a two-day period. The Poisson distribution is ideal for calculating the probability of such occurrences, assuming they happen independently and at a constant average rate. It is a standard tool in operations and supply chain management for modeling events like equipment failures, customer arrivals, or, as in this case, delivery failures.

A. value at risk: This is a financial risk management tool that measures potential monetary loss on an investment, not the probability of an operational failure.
B. normal distribution: This is a continuous probability distribution used for variables that can take any value, not for discrete, countable events like the number of delivery failures.
C. binomial distribution: This models the number of successes in a fixed number of independent trials (e.g., defective items in a batch), not the number of events over a time continuum.

1. Chopra, S., & Meindl, P. (2016). Supply Chain Management: Strategy, Planning, and Operation (6th ed.). Pearson. Chapter 12 discusses the use of probability distributions for managing safety inventory, where Poisson is cited for modeling demand or failure events over time.

2. Stevenson, W. J. (2018). Operations Management (13th ed.). McGraw-Hill Education. In the chapter on "Queuing," the Poisson distribution is presented as the primary model for the arrival rate of events (e.g., customers, jobs, or failures) in a system over time (Section 18-3, pp. 798-799).

3. MIT OpenCourseWare. (2006). 15.762J / ESD.262J Supply Chain Planning. Fall 2006. Lecture notes on "Inventory Management I" introduce the Poisson distribution as a model for demand when it is intermittent or involves a low number of discrete units per period, analogous to modeling failures.