Optimizing Shipping Times Using Fractional Factorial Designs Steven Walfish June 6, 2002

2 Agenda Background on the problem. Why optimize shipping times? How do you optimize shipping times? What is the best statistical analysis? How do we improve the analysis?

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4 Why Shipping Times? Inventory management is becoming critical to cost reduction. Vendor managed inventory (i.e. Shipping without a PO) is common. Statistical forecasting and supply chain management tools are integrated into the ERP. Product that arrives too early is as bad as product that arrives too late. It is a game of cash flow. Sometimes environmentally sensitive product is shipped.

5 Background Started as a data mining exercise. Understand shipping patterns. Find an optimum strategy for the supply chain. Develop a predictive model. DOE was an add on. Initially was an 11 factor design, this presentation is reduced to 6 factors for simplicity.

6 Where Do We Start? What is the response variable? How do I measure the response with precision? What are the independent factors? How do I estimate statistical error? Why shipping time? Why not shipping costs?

7 Response Variable Selection Brainstorm possible response variables. Shipping time is easily calculated using on-line tracking information that is available. Shipping time is calculated from when it is picked up till it is delivered at the destination. Shipping costs are not directly correlated with shipping time or quality of shipment (i.e. low shipping costs is not always good!).

8 Flow of Product Raw Materials Manufacturing Ship to a Warehouse Customer Repackaged

9 Independent Factor Selection Choose a design to identify main effects. –Fractional factorial designs. Assume that interactions are not significant. –Allows for a lower resolution design. Use 2 or 3 level factors. –Do not need lots of levels to gain insight. –Levels are usually different options. –Usually a fixed effect model. Rate the factors based on process flow and the impact on days of WIP. –Small versus large boxes. –Packaging material used.

10 Design Considerations Number of runs and data points not an issue. High volume of shipments available. Interactions are truly confounded with main effects. Response variable is not well understood. Need to create a scoring function. Hard to gain an estimate of error (repeatability). Factors are assumed independent. Need to balance optimal shipping with cost structure.

11 The Approach Used an 18 run design with 4 factors having 2 levels each, and 2 factors with 3 levels each. The design is a classic L18 design. Replicated the design matrix 2 times. A full-factorial tests for interactions which have little to no meaning in this context.

12 The Approach Used a “Quality of Shipping” index for the response. Used nonparametric analysis tools. Many times can only use graphic tools. Hard to use classic statistics since there is correlation among independent factors. Create a predictive model to estimate future shipping times.

13 Design Matrix 3 different trucking companies Short, medium and long distance Environmentally Sensitive Shipment (Y/N) Large and small shipments Ship on Monday or Thursday Insured (Y/N)

14 Shipping Quality Index The SQI is not perfect, but it incorporates lost opportunity costs and days to ship. A low SQI is good. Different scoring functions can be used depending on your application.

15 Data

16 Model A mathematical predictive model is derived from the results using simulation Less interested in statistical differences, more interested in “regression model”. Response Surface Methods do not lend themselves to this problem since factors are categorical in nature.

17 Analysis Used the Kruskal-Wallis Test on each factor. Fitted an ANOVA to the data. Used graphical techniques.

18 Kruskal-Wallis Test Used the Wilcoxon Rank Sums and the KW Test to look at differences between factor levels. Assumed independence between factors. FactorK-W P-valueOne-way ANOVA P- value Trucking Co Distance Environmental Package Size Day of the Week Insured

19 ANOVA Fitted a Main Effects Model to the data. Assumed that SQI is continuous. The MSE is used to estimate random error for simulations. FactorANOVA P-value Trucking Co Distance Environmental Package Size Day of the Week Insured0.6244

20 Graphical

21 Comparing Kruskal-Wallis to ANOVA The assumptions for ANOVA might not hold true, especially with a scoring function. The non-parametric models are 1-way analysis. The p-values for the Kruskal-Wallis tend to be smaller than the ANOVA. ANOVA gives you the flexibility to specify interactions if known. Can also use higher resolution designs.

22 Simulation and Prediction The DOE was used to systematically collect data for developing a predictive model. The error term from the ANOVA was used to estimate random error. The expected mean squares were used to estimate factor error. Simulated different delivery scenarios and built a distribution of SQI’s. Derived a function that minimized SQI.

23 Future Enhancements Need to improve scoring function. Look at using Principal Components. Categorical Data Analysis. Develop better “measurement systems.”

24 Conclusions The design of experiment is easy, the analysis is harder. Seeing differences in factor levels not always the most important component of the analysis. Applying DOE to nontraditional applications is becoming more common as optimizing supply chain is popular. It is not easy to measure many responses where data is captured from surrogate markers.