Decomposition of "BOCR" Models and Modelling Dependencies in "Bipolar" Analytic Hierarchy Process: Application in Mergers and Acquisitions

Xu Jiaxin

Abstract

In many complex real-life decision-making problems, interdependence among the criteria and alternatives are commonly observed. The Analytic Network Process (ANP), proposed by Professor Thomas Saaty in 1980, is a generalization of the very popular Analytic Hierarchy Process (AHP), tackled this problem by utilizing a network of different clusters (goal, criteria and alternatives) with interaction arcs to represent both inner and outer dependency. ANP however, has not been widely used in real life applications due to the high complexity and difficulties faced by the decision makers and the analysts. This is especially true when there is a “Bipolar” situation where there are many sub-networks with different goals within an ANP model. “Bipolar” situation often occurs when users need to decide on whether to undertake a project, which requires investigating the positives (benefits) and negatives (costs) of that project. In this case, the benefit or cost aspects act as criteria and the projects as alternatives. In the software SuperDecisions, where ANP is implemented, outer-dependencies between sub-networks, such as cost sub-network and benefit-sub-network, are not allowed. As a result, only positive dependencies within each individual sub-network can be considered. In addition, the usual multiplicative synthesis of alternative priorities for benefits, opportunities, costs and risks (BOCR) obtained from separate AHP or ANP, can be ambiguous.

This paper proposes two modifications to the ANP model construction process to address these three issues in current ANP. Firstly, a decomposition procedure is proposed to break down a complex ANP model into different sub-networks, followed by reassembling into a modified super matrix in excel. Secondly, re-scaling and re-assessment of the pair-wise comparisons are performed to represent the dependencies between sub-networks with opposite goals. This process will give us a new set of eigenvectors, which are then transferred to the modified super matrix. Lastly, an adjusted incremental benefit/cost ratio analysis used for the synthesis of alternative priorities.

A case application to Merger & Acquisition (M&A) case: Dow’s bid for Rohm’s and Hass, is presented to illustrate how the proposed methods can work in a real-life complex decision-making problem. Proposed decomposition and reassemble procedure will enable users to make connection between different sub-networks within a ANP model. The re-scaling and re-assessment methods enables the ANP model to take account of negative dependencies across different sub-networks. After modifying ANP model, the change of the alternatives’ priority vector can be observed through performing adjusted incremental benefit/cost ratio analysis. Having prospered for decades due to the robust global demand of personal computer, server, industrial and automotive markets, the semiconductor industry will continue to drive the economic growth of Singapore in the manufacturing sector. (Leow, 2018). Scheduling efficiency in manufacturing operations plays the pivot role in maintaining a continued edge in the competitive industry. Several main challenges have been identified about the scheduling complexities in semiconductor industry, including manufacturing complexity, uncertainty and variability, long-time horizons and operational idiosyncrasy. There is currently a large body of research targeting at this intricate but vital field. However, simulation-aided approaching in addressing larger scale scheduling problems have not been widely explored. In this paper, a knowledge-based system (KBS) that aids the simulation model formulation process for semiconductor manufacturing is invented to bridge this gap.