# Dual Market Facility Network Design under Bounded Rationality
## 1 Introduction  
Globalization has brought about large scale integration of regional economies and culture through effective transportation and communication. International trade has been the central attention of major firms in last couple of decades. Economic globalization has led to major changes in how the companies deal with the market. Any attempt towards a competitive advantage at an international level has far reaching benefits to the company. Even supporters of globalization agree that the benefits of globalization are not without risks--such as those arising from volatile capital movements. With the recent global meltdown, capital flows reversing and international trade shrinking, getting into a non-imitable market advantage that has assumed the prime importance [1]. In this work, the focus is on firms that are present in many markets across the globe. With Asian countries like India and China gaining importance in the international market, there are issues that globalization still has to iron out before we can really see homogeneity across the globe. Low income countries are slowly gaining ground in the recent globalized world. On one hand, these countries offer huge market opportunities, with large gain in the labor cost, but it has itself associated with increased logistics cost and foreign trade barriers. Considering these paradoxical factors simultaneously, this paper works on quantifying the decision of off-shoring production facilities, modeled by taking into account the real life uncertainties and response variances. In particular, we consider the case of two economies served by a firm manufacturing two products at two localized final assemblies, using a common component which can either be produced locally or transported from a central setup which would also cause the company to incur respective transportation costs. Each of themarkets has respective demand characteristics, selling price, and assembly costs. We intend to maximize the total profit of the firm, by optimally deciding where to locate the common component manufacturing setup, and also the individual transportation quantities. This situation is analyzed using the Newsvendor Model. The notion of bounded rationality in operation management was taken from the economics literature. Initially, the \"bounded rationality\" term was introduced by [PERSON] (2006) to denote the decision-making behaviors where the decision maker finds the alternatives. Later, scholars constructed diverse model frameworks to cover agents' bounded rationality by the quantal response model. To account for the limitations in the normative approach adopted by a traditional Newsvendor Model, which assumes that decision makers are perfect optimizers, the descriptive approach of bounded rationality is incorporated. The decision model of bounded rationality is basically based on classical quantal choice theory ([PERSON], 2008). Considering all possible utility generating alternatives to be the candidates for selection, decision makers try to choose much captivating alternatives (obtaining greater utility) because their probability of selection is high. For this purpose, the analytically convenient logit choice model can be used where selection probability of alternate \(j\) is proportional to \(\exp(u_{j})\)([PERSON], 2008). The quantal choice models take into account that decision makers may commit errors. It is not necessary that one always makes the best decisions; better decisions are made frequently. Thus, we formulate the problem with the framework of bounded rationality for the multi-market network design. The resulting formulation leads to a quadratic objective function with linear constraints. Since the constraints are not all equality constraints, it is not simple to reduce the problem into linear system of equations. The problem is solved through a novel approach of Frank-Wolfe linearization method along with Generalized Benders' Decomposition method. The results are compared with standard gradient search method and the superior convergence is empirically proved.