![]() ![]() ![]() You current Custom Design window contains your D-optimal design.Īt the center of the design region, the relative prediction variance is 0.53562, as compared to 0.208333 for the I-optimal design ( Figure 5.41). (Optional) Click the Custom Design red triangle, select Set Random Seed, type 383570403, and click OK. In this new Custom Design window, click Back.Ĥ.Ĝlick the Custom Design red triangle and select Optimality Criterion > Make D-Optimal Design.ĥ. In this new script window, select Edit > Run Script.Ī duplicate Custom Design window appears, but with the Design Evaluation outlines closed.ģ. In the Custom Design window containing your I-optimal design, click the Custom Design red triangle and select Save Script to Script Window.Ī window appears, showing a script that reproduces your work.Ģ. To compare Prediction Variance Profile and Fraction of Design Space plots for the I- and D-optimal designs:ġ. In the next section, you generate a D-optimal design, and compare the two. This Custom Design window contains your I-optimal design. This means that for about 95% of the design space, the relative prediction variance is below 50% of the error variance. When the Fraction of Space is 0.95, the vertical coordinate of the blue curve is about 0.5. The Fraction of Design Space Plot appears on the left in Figure 5.44. Open the Fraction of Design Space Plot outline. The relative prediction variance of the expected response is smallest in the center of the design space.ġ0. (Optional) Click the Custom Design red triangle, select Number of Starts, type 8, and click OK. (Optional) Click the Custom Design red triangle, select Set Random Seed, type 383570403, and click OK.ħ. ![]() In constructing a design on your own, these steps are not necessary.Ħ. Note: Setting the Random Seed in step 6 and Number of Starts in step 7 reproduces the exact results shown in this example. You can see this later in the Design Diagnostics outline. Because you added RSM terms, the Recommended optimality criterion changes from D-Optimal to I-Optimal. Quadratic and interactions terms for X1 and X2 are added to the model. In this example, you explore the differences between I-optimality and D-optimality in the context of a two-factor response surface design. Thus, a better understanding of the polyhedral structure of this difficult class of MIPs would be valuable for a number of applications.Comparison of a D-Optimal and an I-Optimal Response Surface Design The disjunctive constraint structure underlying our FLP model is common to several other ordering/arrangement problems e.g., circuit layout design, multi-dimensional orthogonal packing and multiple resource constrained scheduling problems. We are, however, still unable to solve problems large enough to be of practical interest. Using these inequalities in a branch-and-bound algorithm, we have been able to moderately increase the range of solvable problems. Based on the acyclic subgraph structure underlying our model, we propose some general classes of valid inequalities. In this paper we reformulate Montreuil’s model by redefining his binary variables and tightening the department area constraints. In fact, though this MIP only has 2 n( n−1) 0–1 variables, it is very difficult to solve even for instances with n≈5 departments. However, no further attempt has been made to solve this MIP optimally. Montreuil introduced a mixed integer programming (MIP) model for FLP that has been used as the basis for several rounding heuristics. The facility layout problem (FLP) is a fundamental optimization problem encountered in many manufacturing and service organizations.
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