Decision of Uncertainty
March 5, 2012
Decision of Uncertainty
E & J Gallo Winery ships wine and spirit products to their regional distribution centers (RDC) for distribution to their retail outlets. The shipment methods used are truck, rail, and intermodal. The number of in-transit damage claims continues to increase for the products shipping to the Georgia RDC via railcar using the Route A transportation template. The Winery leverages the Burlington Northern Santa Fe (BNSF) and Union Pacific (UP) railroad carriers. The decision of uncertainty that the Global Supply Chain Logistics Group wishes to address is should the Winery continue ...view middle of the document...
No claims were filed against the Union Pacific rail carrier. BNSF leverages multiple routes to the Georgia RDC; however BNSF transports 85% of the rail cars to the Georgia RDC using the Route A transportation template, and the remaining 15% of the railcars shipments use other templates. The damage reports were sporadic throughout the year and were not concentrated in any specific month or quarter, so the research team did not focus on seasonality or any specific sample time frame within the 2011 shipment population.
Interpretation of Data using Bayes’ Theorem. Bayes’ Theorem also known as Bayes’ Rule is a useful tool for calculating conditional probabilities (Stat Trek, n.d.). Gallo will leverage Bayes’ Theorem to determine the probability of a random railcar transporting product to the Georgia RDC via the BNSF rail carrier using the Route A transportation template incurring in-transit damage. The annual shipments to the Georgia RDC by BNSF in 2011 were 400 rail loads. The Georgia RDC reported 27 of the 400 railcars arrived with damaged product. The analysis conducted by BNSF revealed that the Route A transportation template was utilized 85% for the railcar shipments to the Georgia RDC from Modesto, California. The sample space is defined by two mutually-exclusive events – in-transit damage is reported or in-transit damage is not reported. Additionally, a third event occurs when the shipment is transported via Route A. Notation for these events appear below (Stat Trek, n.d.).
* Event A1. In-transit Damage Reported.
* Event A2. In-transit Damage Not Reported.
* Event B. Using Route A transportation template.
In terms of probabilities, we know the following:
* P( A1 ) = 27/400 =0.0675 [27 out of 400 rail cars report damage.]
* P( A2 ) = 373/400 = 0.9325 [373 out of 400 trains report no damage.]
* P( B | A1 ) = 0.85 [Damage occurs, and route A is taken 85 percent of the time.]
* P( B | A2 ) = 0.15 [No damage occurs, and route A is taken 15 percent of the time.]
We want to know P( A1 | B ), the probability that damage is reported when the route A transportation template is used. The answer can be determined from Bayes' theorem, as shown below.
P( A1 | B ) = | P( A1 ) P( B | A1 ) P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 ) |
P( A1 | B ) = ...