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Although modern location theory is now more than 90 years old, the focus of researchers in this area has been mainly problem oriented. However, a common theory, which keeps the essential characteristics of classical location models, is still missing. This monograph addresses this issue. A flexible location problem called the Ordered Median Problem (OMP) is introduced. For all three main subareas of location theory (continuous, network and discrete location) structural properties of the OMP are presented and solution approaches provided. Numerous illustrations and examples help the reader to be

AbstractIt is often assumed in the facility location literature that functions of the type øi(xi, y) = βi[(xi‐x)2+(yi‐y)2]K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.

The body of thought on location is composed of several contributory JL streams. The best known of these, that associated with the name of Alfred Weber, has concerned itself with the explanation of the choice of production sites by manufacturing industries, and is consequently the stream most closely related to my inquiry.1 However, the Weber school typically pays very little attention to the historical aspects of its subjects; this neglect is apparent both in the nature of the data employed and in the selection of scope, and the placing of emphasis. In the first part of this paper I shall offer an example of a Weber-like analysis or evaluation of the location factors involved in the cotton industry of this country during the past sixty years, as adapted to the purposes of historical inquiry and to the use of historical data; in the second part, I shall apply to some specific historical situations the results of the analysis presented in the first part.

The behavioural location theory emphasises high importance of the limited rationality and the subjective perception of space in selecting of the location for a business activity. The article discusses key competencies from the scope of behavioural location theory. Ac-cording to the Authors, the behavioural location theory is rather complementary than competitive in relation to the neoclassical or modern approach, as it allows to explain the deviations of the decision-makers from the optimisation behaviour.

Business location theory has already been discussed in this journal in various contexts, for example in articles by H. Godlewska-Majkowska, K. Kuciński, A. Rutkowska-Górak, A. Kałowski. However, to our knowledge, the behavioural approach has not yet been presented here and we would like to fill the gap and offer a review of selected authors' works and concepts from this field and hopefully inspire other scholars to develop this promising research direction. In addition, a quantitative analysis of publications on behavioural location theory will be presented.

For the purposes of this article we will define the behavioural location theory as the inclusion of psychological and subjective circumstances of the decision makers into location theory, such as bounded rationality, heuristics usage and subjective spatial perception.

The behavioural approach seems underutilised in location theory despite its potential to explain many of business location decisions which are inconsistent with the profit maximisation principle. According to R. Domański [1995]: so far it has not been satisfactorily examined how the perception of space influences spatial behaviour of people. Nobody objects that many decisions, at least in part, depend on how people perceive the space surrounding them, how they differentiate it and what value they place on different elements of this space.According to W. Dziemianowicz [1997]: the assessment of location factors by decision makers most often depends on specific qualities of the business and qualities of the decision maker. Surprisingly, decades have passed since last important contributions in the field of behavioural location theory.

Location theory has its roots in XIX century, when J.H. von Thuenen offered the agricultural activity location theory in 1826. The interest in location theory revived more than 50 years later, mainly thanks to the works of W. Launhardt [1882] and A. Marshall [1886]. Important dates are also 1909, when A. Weber developed his industrial location theory and proposed the notion of a location factor and 1933, when the first theory of services location emerged, authored by W. Christaller.

Then the development of location theory accelerated, with contributions of such authors as A. Loesch [1939], F. Perroux [1964] or P. Krugman [1991]. It can be argued that thanks to P. Krugman location theory entered the mainstream economics, which neglected spatial issues for a long time.

Different location theory traditions put the emphasis on different aspects. For example, classical approach theorists indicate minimising production cost as the goal of the location decision maker while behavioural approach suggests satisfactory choice as a goal. According to H. Godlewska-Majkowska, there are five approaches to location theory: classical, neo-classical, structural, behavioural and contemporary. Their focus points are briefly explained in Table 1.

There are three similar but distinct terms related to the business location choice: • location factors – specific qualities of particular places which have direct impact on investment volume during building of the company's plant (plants) and the net profitability of business activity run in those places [Godlewska-Majkowska, 2001],
• location virtues – specific qualities of places which contribute to it that identical investments will differ depending on location in terms of investment volume, total production cost, sales revenue and taxes [Godlewska-Majkowska, 2015],

ocation circumstances – internal and external phenomena which transform a location virtue into a location factor. Internal phenomena can be for example: industry, size and ownership structure of the business. External phenomena include among others economic, environmental and cultural issues [Godlewska-Majkowska, 2013]. Clearly, location requirements are different for various sectors. Therefore, location factors are divided into general (those applying to all or many sectors) and sector-specific (those applying to one or few sectors).

There are also other classifications of location factors. The importance of subjective factors in the location choice is reflexed in the classification by Grabow et al. [1995] into soft and hard location factors, on the basis of H. GodlewskaMajkowska [2015]. Hard factors are more traditional, have direct influence on business activity and are easily measurable, while soft factors have indirect influence on business activity and are difficult to quantify.

It is worth to note that authors of this classification consider both kinds of factors as equally important and find even the soft factors as ones, which can be parametrised, measured and compared. Figure 1 presents the classification in a more detailed way.

In our view, Grabow et al. [1995] showed an excessive scepticism when it comes to measurability of some factors. For example, the local government attitude towards investor may be measured by places in investment attractiveness rankings, such as 'Gmina na 5!' conducted every year by Institute of Enterprise at Collegium of Business Administration at Warsaw School of Economics. Apart from it, the classification should be considered to be validated as more than 20 years had passed since its publication and made more precise, because as H. GodlewskaMajkowska [2015] points out, some factors seem to overlap – social climate is presented as separate factor than local government attitude towards investor, but in fact the former includes the latter.

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Each business has to choose its location and the effect of business location selection is called location decision. Location decision may be the result of a more or less formal procedure. There is a consensus among scholars that business location decision is important for entity's economic performance. At the same time, it is acknowledged in the literature that subjective factors (such as bounded rationality) play a non-negligible role in location choice. As R. Domański [2004] outlines, location decision makers usually have limited knowledge and incomplete information and in many cases the decision maker does not behave like the homo oeconomicus. Sometimes he has limited or biased information about his decision situation and at the same time he assessed the incomplete information in a subjective way.If the situation is complicated, he has to simplify it by using intuitional rules in decision making. He does not try to achieve the optimal result but rather a satisfactory one. Such statements suggest R. Domański finds bounded rationality model convincing.

According to classical, neoclassical and contemporary business location theory the decision maker undertakes the optimal choice, while heterodox approaches such as behavioural location theory claim making an optimal choice is impossible. The classical, neoclassical and contemporary theorists assume decision makers are homo oeconomicus, a person with perfect information about the present and the future, able and willing to make complicated calculations and not prone to psychological biases.

Behavioural economics accepts different set of assumptions about the human nature: limited (imperfect) knowledge of the decision maker, limited ability to process the knowledge and searching for satisfactory result rather than optimal. Decision maker who behaves in line with those assumptions is purposefully called homo satisfaciendus.

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Homo satisfaciendus is the concept of decision maker used in the bounded rationality model created by H. Simon [1955], which is fundamental for behavioural economics, including behavioural location theory. In the model it is assumed that the decision makers do not aim to maximise utility from choice made (making an optimal decision) but rather search for a good enough (satisfactory) option and once they find such an option they also stop search. In practice, it means that typically a decision maker will accept the first location that meets his minimum criteria, the so called aspiration level and will not even check alternative locations. Simon points out that people may use so called heuristics, which are decision making patterns simplifying their decision problems but he did not elaborate on it.

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The gap has been filled by D. Kahneman and A. Tversky [1975] who singled out three famous heuristics: availability, representativeness and anchoring. H. Godlewska-Majkowska [2016] argues that such heuristics are used to assess location virtues of places which a location decision maker had visited within business location decision making process.

The bounded rationality model has served as the basis for the A. Pred [1967] behavioural matrix, which linked information availability, investor's information processing ability and profitability of chosen business location. The general rule is that the more information (or information processing ability) one has, the more profitable location one chooses, caeteris paribus. An adapted version of Pred matrix is presented in Figure 2. Point A represents homo oeconomicus, who has perfect information and perfect ability to use it, so he or she will choose the optimal location. All other decision makers make suboptimal decisions and the extreme is reached in point B, where the decision maker has little information and low ability to process it, so he or she will choose a poor location that may result in a loss.