Six Sigma Case Study (DMAIC)

by Crystal Ball on 1st October 2006

provided by

Oracle Crystal Ball

In a paper and accompanying model, we show how this opportunity is formulated as a Six Sigma project and showcase how Crystal Ball Professional Edition is used within each of the DMAIC (Define, Measure, Analyse, Improve, Control) process phases to deliver responsiveness to the customer and financial results to the business.

As with most business situations of this nature, we are seeking the best (or most profitable) tradeoff between conflicting actions or strategies. This example specifically balances responsiveness to customer needs (higher levels of inventory given uncertain demand) against efficiency for the business (lower cost of goods sold). Of particular interest in seeking this optimal balance is how we can improve the solution and account for the effects of uncertainty in the key process input variables (KPIV’S). This method (stochastic optimisation) enables us to specify objective functions (Y’s) and requirements (constraints on X’s) in terms of likelihood of occurrence (i.e., maximize profit and provide at least 90% certainty that our total inventory costs would not exceed $169,000).

Background:

Fortune 1000 organisations have realised immense success by implementing the Define, Measure, Analyse, Improve, Control (DMAIC) methods made famous by Six Sigma practictioners. These practitioners can maximise their project results (e.g., cost savings and defect reduction) by incorporating real variability and uncertainty in their processes and into their process models or spreadsheets.

Simulation, optimisation, and forecasting can be used throughout the DMAIC process. In this case study, a company that sold perishable inventory used Crystal Ball Professional Edition software within the Six Sigma process to create and maintain an optimal balance between lost sales and wasted inventory. In the recent past, this company all too often turned away customers due to unanticipated demand and a lack of inventory. This problem was identified and handed off to a Six Sigma project team for resolution.

Define:

The first step in the Six Sigma project was to clearly define the defect and our project objectives. A defect was defined as any instance in which we turn a customer away because we do not have the materials to complete their order. In the past few years, these instances seem to have been happening with increasing frequency. We tracked the number of orders declined for the past ten years, and we saw an annual increase in the number of customers turned away. As you can see in Table 1, last year we turned away a record 1631 orders due to lack of inventory.

Crystal Ball DMAIC Case Study Historical Lost Sales

Using the historical sales data and CB Predictor, we forecast the number of lost sales given no change in our current processes. CB Predictor calculated an expected (mean) value of 2113 lost sales for this year (Figure 1). The output was saved as a normal probability distribution that described the uncertainty of the forecast.

Crystal Ball Predictor Results for 2004 Lost Sales as a distribution

We next used the CB Predictor results and Crystal Ball to forecast our losses due to inadequate inventory at $100 per lost sale. Crystal Ball created the forecast using Monte Carlo simulation, which used the probability distribution in Figure 1 to randomly select different possible values for the total number of lost sales. The results are shown in Figure 2.

Crystal Ball Chart of Predicted Total Cost of Lost Sales

Based on our forecast, we expected to lose $211,000 this year due to lost sales, with a minimum loss of $166,000 and a maximum loss of $258,000. While we wanted to reduce the cost of lost sales, we needed to balance this with our need to control the cost of perishable materials discarded due to expiration. Our project goal was to reduce the defect by 75% without increasing our inventory costs (cost of orders, cost of discarded materials, and cost of lost sales), which were $169,000 last year. In order for this project to be deemed a success, we needed 408 or less lost sales for the year and total inventory costs of no more than $169,000.