As was indicated in the introduction the survey work of Grinyer (72) and Higgins and F i n n (77) in the United Kingdom and that of Gershefski(70) and Naylor and Schauland (76) in the States has shown that while there exists many corporate financial models very few are of the mathematical programming type.*____________________
•Grinyer found only one optimising model out of fifty models in his survey while Gershefski suggests that 95% of the models he surveyed were of the simulation type - a result confirmed in the later survey of Naylor & Sehauiaiv
The reasons for this soon emerge if we examine current ideas on the nature of the objectives and of the planning process within an organisation and contrast these with the structure of the objectives and planning process implicit in the two types of financial models.
The objective function normally chosen in most corporate financial mathematical programming models found in the literature is the maxi
misation of the value of the firm. This valuation criterion is in accordance with traditional economic thinking which assumes that the objective of the firm is the maximisation of the long run profits.
However, the inadequacies of classical economic theories in accounting for the behaviour of the firm has led to a series of revisions of tha concept of the firm as a profit maximiser.
One of the first major revisions was by Baumal(5 9) whose observations led him to conclude that firms do not devote all their energies to maximising profits but rather that)as long as a
satisfactory level of profits is attained,a company will seek to maximise its sales revenue. The importance of this hypothesis is that the firm is no longer working towards a single objective
but must balance two competing and not necessarily consistent goals.
Baumol's idea is still primarily a description of the behaviour of the firm in the market place.
A more comprehensive and directly challenging attack on the economic theory of the firm arises from the work of organisational theorists. H.A. Simon(57) argues very persuasively that the omniscient rationality attributed to.economic man bears little resemblance
to reality. A more accurate description of the behaviour of decision making within an organisation is that of a search for satisfactory solutions. In thia model of behaviour the objective function becomes a two valued utility function: good enough or not good enough.
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While most of the models that we have already discussed appear in part to incorporate these ideas by the inclusion of policy
constraints such as a minimum level of return on capital. Simontf (64) interpretation of these constraints is somewhat different. In
his view decisions are not directed towards a single goal but with discovering courses of action that help to satisfy a whole series of constraints. It is these constraints that motivate the decision maker and gui^e his search. In this sense the constraints are more 'goal like' than binding limits on the possible actions. Any planning mechanism ought thus to aid the decision maker to find 'satisfactory1 plans with respect to these constraints or goals rather than to maximise a single critericnand regard the constraints as inviolate.
The foregoing discussion provides a key for the understanding of the high deqree of acceptability of simulation models. The characteristic feature of these simulation models is that they examine the consequence of a decision by producing a series of financial indicators. These indicators range from projected profit and loss statements, balance sheets sources and use of funds statements to merely a few financial ratios. Hence, by having an immediate analysis of the consequence of any decision,the decision
maker can search rapidly through a series of alternative plans hopefully to arrive at a satisfactory solution. Hence, the computer is merely performing, albeit many times faster, analysis traditionally carried by the accountant. Although their high degree of managerial acceptability may well stem from this emulation of traditional accounting methodologies it imposes
unable to provide much guidance in searches for alternative and possibly better solutions. Thus if a particular plan is unacceptable it is left to the user to input another series of decisions in the hope that this will improve the general level of performance. While it is true that certain models do incorporate decision rules*. These rules are usually simple pre-emptive lists such that ifa particular restriction is not satisfied in a period then the restriction is overcome by searching through a pre
ordered list of alternatives. A more sophisticated variation of this is the method of backward iteration (Grinyer and Woller(75)) when previous decisions can be altered to overcome a restriction in a particular time period. Though again this can be seen as a limited search through a pre-ordered list.
In contrast mathematical programming is a very powerful tool. Its main limitation is that before the search is commenced it is necessary to specify a minimum set of conditions which any plan must satisfy together with a single measure of the value of this plan. This prior specification of minimum conditions and a single criterion introduces an unfamiliar and,possibly unacceptable,rigidity into the planning system.
A further contrast between financial simulation models and mathematical programming models is in the nature and quantity of the information flows between the model and the user.
*See, for example. Chambers, Singhai, Taylor and Wright (71).
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Financial simulation models are characterised by requiring decision inputs from the user and output the information in the form of the consequent impact on the value of selected financial policy variables (e.g. return on capital, earnings per share). In linear programming models the information
input is merely the data relating to the benefits and costs of various alternatives and the plan is output in the form of a set of decisions. In this case the impact on financial policy variables has to be determined separately. Hence, as currently used mathematical programming models search through decision space for a plan which maximizes a scalar measure of company performance whereas simulation models are used to search, even though that search is unstructured, over a vector of policy variables.
It is the contention of this section of the thesis that the acceptability ol simulation models stems largely ' from their ability to provide an interactive search mechanism over a vector of policy variables. It is thus the aim of the final Chapter of this thesis to illustrate one method whereby mathematical programming algorithms may be used to enhance this search.
The remainder of this section concentrates on the approaches proposed so far in the literature in order to understand why they have failed to provide a viable alternative to either simulation or LP models.
The work of Simon (57 and 64) Cyert and March(63) in
developing a behavioural theory of the fir.n finds its recognition in operational research methodology in the recent development of multi-criteria methods. These methods accept the multi
criteria nature of many planning systemsand attempt to explore the various alternatives in a systematic fashion. Although this approach at first sight would appear to provide the appropriate planning mechanism a closer examination of the two mainstreams of research in this area indicate quite daunting implications for the management user.
The first of these approaches originates from the early work of Charnes, Cooper and Ijiri (63) in goal programing. In this approach the objective function usually takes the form of a weighted linear combination of deviations from a set of goals.
While their formulation is intuitively appealing, its rather simplistic structure can give rise to anomalies caused by solution instabilities*. Another major difficulty is the
* A particularly apposite example is the case of attempting to maximise profits in each of two years where total profits are limited to a fixed quantity. If the problem is formulated as
min (l+£) + z2
s.t. p^^ + S 1
P 1 + P2 * 1
where p^, denote profits in each of the two consecutive years and z2 are shortfalls from target. The ratio 1 + E t 1 expresses a preference for profits in year one over year two. Then the
solution if p = (0,1) for a positive value of £ and p = (1,0) for a negative value. Thus an infinitesimal charge in the weights can completely alter the form of the solution. While this exaraple may seem trivial and unlikely to occur in practice the reverse appears to be true.
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specification of a trade-off function between conflicting goals.
This difficulty is compounded in the case of financial planning models because the goals are usually ratios introducing a non
linearity into the problem.
The importance of ratios is fairly clear from the extent to which they are discussed in standard texts on financial analysis*.
In addition'there have been various publications which give ratio norms for various industrial categories. Although there is a plethora of ratios and their definitions vary widely (Perrin (6f>) ) certain key ratios can be identified as particularly significant in corporate financial planning. Obvious examples are measures of profitability such as return on capital,earnings per share, measurement, of debt levels such as gearing and times covered together measures of growth of sales and profit.
The idea of incorporating financial ratios into mathematical programming methods is not new. Chambers(07) in his paper 'Programming the allocation of funds subject to restrictions on reported results' concludes :
"It became evident in discussions of the first aspect - the effect on published results - that at least in the short run, managers were using several overlapping but distinct criteria to measure the firms' performance and the success of capital budgeting. On the other hand, they did not question the fundamental importance of cash flows which a project could be expected to generate. On the other hand, they were unwilling altogether to neglect the
*See Lev(74),Van Horne (77)
changes which the project would bring about in other parts of the published accounts, derived on the basis not of cash flows but of accruals. They regard the accounting convention of assigning costs and revenues to the periods judged to give rise to them as defining rules of a game in which they wanted a good score."
However, in his particular model these ratios were hard constraints and could not be violated. A more appropriate model according to the organisational theorists would be one where constraints ware not hard and could be broken if it seemed beneficial. While got.1 programming certainly affords such a structurejthe quantification of constraint violations is a
fundamental problem associated with the weights used in goal program
ming. These weights are the relative value that the decision maker attaches to deviation from one criterion as opposed to another and the difficulty of attaching sensible values to these weights in any realistic planning model has led many authors to abandon goal programming formulations for financial models. Such an attitude is characterised by Carleton, Dick and Downes(73) •
"If the objective function in a goal programme has more than one argument, absolute priorities have to be imposed arbitrarily.
Consequently, nonachievability of all the goals, when such is the programme solutions, leaves unanswered the important economic question of how objectives trade off against one another. In other words, finance theory, even applied gently, has something to contribute to management's undertaking of how financial policy requirements fit together. And goal programming is a substantially less powerful tool than linear
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programming for accomplishing this.«
It would appear that If an operationally viable search tool is to be developed goal programming as it currently stands falls some way short.
The second mainstream of multi-objective research is the development of algorithms for the generation of efficient solutions. A solution
is said to be efficient if the performance on a particular criterion can only be improved to the detriment of the performance on some other criterion.* Clearly the decision maker need only consider efficient solutions in his search for the most acceptable one. For linearly independent criteria Benayoun and Tergny(70) have shown that these efficient solutions are situated on the boundary of the feasible region. If the efficient solution lies at a vertex, it is referred to as an extreme efficient solution, otherwise it is referred to as a non-extreme efficient solution. Every multi
criteria LP problem has only a finite number of extreme efficient solutions but an infinite number of non-extreme solutions. Non
extreme efficient solutions can be expressed as convex combinations of extreme efficient solutions, but not all such combinations yield non-extreme efficient solutions.^”
While a fairly comprehensive survey of algorithms for the determination of sets of efficient solutions can be found in
* Mathematically, if y^(x) , i e i denotes the criteria on which decisionx is judged. Then solution x is efficient if and only if there is no other solution Y such than
YityJ^Y^x) vA
and
Yj^y) > Y i (x) for some i e i
^See Yu and Zeleny (73) for a further discussion of this.
Thanassouilis (76)the basic limitation of the approach is self evident on consideration of the details of just two such algorithms. This limitation is a natural consequence of the
fact that efficiency of solutions is a very weak form of comparison, leaving a large number of solutions to be
considered before the final compromise solution can be selected.
For example an algorithm which has been proposed by Yu and Zeleny (73) . centres on the determination of all non-dominated faces. Although strictly speaking such an approach should not be termed an algorithm,since it offers no guidance to the determination of a final solution even given that the
'best' face has been determined,a more disturbing feature is the computational implications of the approach. Thus the method essentially requires consideration of some 2m+n systems of equations where m is the number of constraints specifying the feasible region and n the number of structural variables.
Since the problem posed for solution in the last chapter consists of some 77 structural variables and 48 constraints, this method is seen as computationally infeasible.
Another algorithm,which has been proposed by Evans and Steuer(75) involves the determination of extreme efficient solutions. Briefly the method relies on the cdnnectedness of the efficient vertices and generates the complete series of efficient vertices by moving from vertex to vertes. A check for efficiency of vertex needs to be carried out at each stage and this itself requires the solution of a linear program. Again, such an algorithm proves computationally
Connectedness in this context means that a neighbouring efficient vertex can be obtained from the current efficient vertex in only one simplex iteration.
prohibitive* for most realistically sized problems.
It would seem that on the one hand goal programming methods confront the decision maker with a non determinable prior
specification of trade-offs while the algorithmic searches of efficient solutions present the decision maker with a superabundance of alternatives. Thus,until the informational inputs required of the decision maker in goal programming can be reducedfor ,until the algorithmic approach can be modified to produce appropriate and order subsets of possible efficient solutions^neither method can be considered as practical.
In chapter four a utility framework for goal programming is examined. This framc.'ork provides a powerful and insightful mechanism for the development of the tools necessary for carrying out an interactive search of the set of efficient solutions. In the next section a realistically sized planning problem is proposed to provide the discipline of a precise contextual setting for a thorough test of these search procedures. It will be seen while a natural strategy evolves the essence of the method developed is in its flexibility of response to the decision makers preferences.
In this way, a model is developed which may in the end begin to bridge the gap between mathematical programming models and simulation models.