PAS mathematical models to achieve alignment
The focus in this chapter is on the component mathematical models of PAS (see Figure 7.1 and Figure 7.2). PAS can only be performed if the system engineers are able to build a mathematical model of the problem situation for each of the pilot studies. In this chapter, I will show that the system engineers were able to do this for all three pilots.
Typically, a subset of the alternative is infeasible. When the feasible set of alternatives can be characterized mathematically, the PFM algorithm can search an optimal alternative within this set (either by an exhaustive search or by sampling, depending on the size of the feasible set). Otherwise, if a characterization of the feasible set is not available to the algorithm, the group decision makers – the stakeholders - can propose possible feasible alternatives for consideration. The algorithm can then rate these alternatives.
This chapter has the following structure:
–– TU Delft pilot for the food facilities in paragraph 7.1;
–– TU Delft pilot for lecture halls in paragraph 7.2;
–– Oracle’s pilot for office locations in paragraph 7.3;
–– Pilot comparison and conclusion in paragraph 7.4.
The mathematical models are explained for each of the pilots as follows: the model structure (first subparagraph), the model formulas (second subparagraph) and the optimization tool (third subparagraph).
Recall, that in step 5 alternatives are generated in two separate ways:
A The group of decision makers self-designs alternatives, use the design constraints to test the feasibility of the design alternatives, and use the PFM algorithm to yield an overall preference score of these feasible design alternatives;
B The system engineer generates feasible design alternatives and uses the PFM algorithm to find the feasible design alternative with the highest overall preference score.
The decision makers are able to design alternatives (step 5a) with the model that is explained in the first and second subparagraphs. The system engineer is able to generate alternatives (step 5b) with the optimization tool is, as is explained in the third subparagraph.
The mathematical models for the pilot studies have been built by the system engineer and the facilitator. The author had the role of the facilitator. The system engineer for the first pilot was Binnekamp, for the second pilot it was Valks with the aid of Barendse, and for the third pilot the system engineers were De Visser with the guidance of De Graaf. Valks and De Visser cooperated in this study as graduate students with the author as their main mentor and Binnekamp, Barendse and De Graaf as their second and/or third mentors.