In its simplest form, Operations Budgeting may be regarded as a development and sophistication of the budget allocation procedure to take account of a larger number of variables or factors (including variables for which only estimated data is available). For example, unit costs, levels of demand and supply, value-for-money indicators, performance indicators, etc. are usually introduced at this point, either as estimates or as empirical data where this is available.

However, with the incorporation of data on these additional variables, Operations Budgeting provides an analysis of discrepancies between alignment of budget allocations with plans. The same quadratic and dynamic programming techniques are used as for budget allocations.

A significant difference is that whereas in budget allocation, the quadratic programme calculates the optimal feasible financial allocation with other variables adjusted to achieve this, in Operations Budgeting the consequences of budget allocations for the other variables in the plan are calculated and displayed, with allocations adjusted thereafter in the light of decisions about the variables. The method is some­times known as 'n-dimensional accounting'.

The judgement analysis procedure was sufficient to obtain an allocation which is usually more systematic and 'rational' than is attainable through intuitive trial-and-error or discursive discussion and negotiation. The results produced may 'suffice' for the decision-maker's or organisational purposes (Simon, 1960). However, if more reliable results are required, the decision-maker will want to introduce other variables into the equation.

The budget allocations thus far described were derived from decision-makers' priorities. Where past budgets were also used, the allocations also embody an implicit indicator of unit costs. Sometimes explicit unit costs for each budget item (or for a sample of budget items) are available.

These may be incorporated directly into the allocation using the Operations Budgeting procedure. The allocation thus produced may also need to take account of levels of demand (e.g. levels of consumer demand for a product or service), or anticipated supply levels for budget items (e.g. what volume of a product or service it is planned to provide from the budget). These may also be directly incorporated in the allocation using the Operations Budgeting procedure.

The amount of finance allocated to an item in Operations Budgeting thus depends on:

- the decision-makers' priorities (or some other 'internal' factor),

- the demand level (or some other 'external' factor),

- unit costs (where available),

- any other internal or external factor or criterion for which weightings are available for the complete or portion list of items.

The allocation is calculated in the light of these factors, as qualified by decision-makers' weightings of their relative influence. (The allocated finance for each item is further qualified by any adjustments necessary to eliminate any purely logical incompatibilities between the factors). Thus, decision criteria or rules are elicited from the decision-makers for use in the calculations made by the quadratic programme. Uncertainty elements in these rules are modelled by fuzzy logic. Once the operational priority factors are obtained, the final allocation is inversely proportional to unit cost and directly proportional to operational priority.

It should be noted that other relevant variables or factors may also be taken into account - e.g. value­for-money indicators, performance indicators, etc. Moreover, the data used for incorporation of these indicators may be estimates or hard empirically-derived measures. The status and reliability of the results will of course vary according to the status and reliability of the input data; but even if estimated data is used at the Operations Budgeting stage, this may provide the starting point for evolving more reliable results at the Budget Monitoring stage.

The quadratic programme technique allows the relevant variables to be incorporated in a single algorithm and appropriate allocations produced for any required size of budget, level of demand or supply, level of unit cost, or for any requirement in respect of any of the variables. It allows the value of anyone variable to be varied, while holding all the other variables constant, and the optimal feasible allocation to be calculated accordingly.

The allocations thus produced provide a 'synthesized' model of the whole set of the decision-maker's decisions.

The model embodies interactions between priorities and criteria and empirical or estimation data on relevant variables (e.g. unit costs). The decision-maker is confronted with a wider­ranging model of the system than any he/she has previously had to consider in any early stages of the method. Naturally, at this point, the decision-maker's conception of the system may be enlarged and sophisticated by exposure to the results. He/she may make adjustment decisions in the light of predicted effects of the possible items available and of the enlarged conception of the context or system. He/she may then iterate some or all of the process in respect of one or more of the variables, and/or may use the adjustments procedure as a sensitivity analysis to ask 'what if ... ' questions of the system. The decision-maker is then enabled to make adjustments based on his/her enlarged 'system-wide' view-point. Thus, the decision-makers' criteria or rules incorporate data since they are themselves produced from the decision-makers' exposure to past data.

This adjustments procedure may be used after each stage of RN, but is usually found to be particularly effective after the first run of Operations Budgeting. To the extent that the decision-maker decides that the allocations are to be priority-driven, RN becomes a goal­directed cognitive processing model. To the extent the decision-maker decides the allocations are to be demand­driven, then RN becomes a data-driven cognitive processing model (Lindsay and Norman, 1977). To the extent that the decision-maker uses the model to evolve for himself or herself the 'best fit' between goal-directed and data-driven processing, RN approximates to an expert system (Anderson, 1983).

Additional reliability indicators may be used in Operations Budgeting. The decision-maker (or decision­makers) inputs estimated and/or empirical data on the variables or factors to be taken into account. For practical use, a series of error checks are built into the RN program to ensure that decision-makers correct any incompatible data they have entered. These may include logical contra­dictions and absurdities, or any non-absurd constraints which preclude any exact consistent solution to the quadratic programme. A 'model fit' index is obtainable by measuring how 'far' the decision-maker is from an exact consistent solution in respect of the non-absurd constraints. The 'model fit' index is the distance of the decision-maker's implicit model from the nearest 'equivalent' model which can provide a set of financial allocations which is exact, consistent and compatible with the entered data. As with the consistency index for decision-makers' priorities where his/her main inconsistencies were specified, so the 'model fit' index provides a specification of the main variables which do not fit and alternative sets of data adjustments required for an exact, consistent 'solution' to the model.

Operations budgeting involves multi-dimensional scaling procedures (Krushal and Wish, 1978) using a series of 'fuzzy set' techniques (Wang and Chang, 1980; Adlassing, 1980; Shortluffe, 1980; Hersch and Carramazza, 1976). It provides for relative Iv 'soft' subjective data of internal subjective judgements (e.g. priorities) and estimations to be combined with relatively 'hard' empirical data from external pressures (e.g. measured demand) by means of a common scale of terms. This is similar to the process of combining 'subjective' benefits and 'empirical' costs on a single scale as in cost-benefit analysis (Hitch and McKean, 1960; McKean, 1958), or subjective 'utility' and empirically-determined 'probabilities' in decision analysis (Raiffa, 1968), though the 'fuzzy set' technique provides a more reliable, valid metric for this process. The relative hardness/softness of the data is determined so that the scope for adjusting data is defined, since 'soft' data (e.g. priorities) are relatively malleable and adjustable subject to threshold values, whereas 'hard' data (e.g. supply levels) are relatively malleable and fixed for anyone point in time.

The mathematical model evolved from the Operations Budgeting may, under appropriate circumstances, constitute a simulation model of the operational situation. An analogy may be made with the underground map which models the London underground, except that it also embodies the decision­makers' desired route through the system in the form of other priorities and criteria. The simulation model is an assembly point for all the variables and countervailing tendencies which do and/or should affect bl1dgetary decision­makers - the dramatic interaction of a diverse series of happenings, decisions and 'natural laws'. It elicits a discoverable pattern of order underlying financial decisions and actions as they unfold.