"Fostering the use of Operations Research in Development"

Hosted by

The Operations Research Society of South Africa
(ORSSA)

Sponsored by


The International Federation of Operational Research Societies
(IFORS)

Berg-en-Dal, Kruger National Park, South Africa, May 16 – 18, 2001

OPTIMISING THE HOLISTIC MASS BALANCE PERFORMANCE

By L.F. Scheepers (M.Sc.) - Independent Linear Programming Specialist. E-mail address :-

0. Synopsis.

The purpose of this paper is to introduce the concept of the holistic mass balance and its optimal performance. Although the concept may be perceived as philosophical, it is shown that a class of mathematics exists that can find the optimal holistic mass balance performance plan in realistic time periods in practice.

Large integrated mining and metallurgical complexes execute their plans in a holistic fashion, irrespective of whether the plans incorporate analytically all possible combinations of mining the ore reserves, of beneficiation flows and of sales permutations. It therefore follows that the inclusion of "holistics" in the planning processes right from the onset, can only improve overall efficiency and profitability of these complexes.

The chrome operations of the Zimbabwe Mining and Smelting Company are used to illustrate the concepts of optimising the holistic mass balance performance. Linear and Mixed Integer Programming techniques deliver the required functionality and performance levels to enable the execution of complex techno-economic planning scenarios and decision support analyses within the holistic mass balance .

1. Introduction.

Mass balances are subject to computing procedures for two purposes :- firstly, to analyse and accumulate the history of the mass balance performance over the given circuits, and secondly, to plan the future performance of the mass balance with a view to maximising economic utility of the mining and/or mineral processing operations involved.

It is only in the case of the simplest of mass balances, that future performances can be planned with the aid of an electronic calculator - multiple alternative mass balances require complex computer models for this purpose and at present, input-output models are most frequently used. Input-output models contain a variable degree of subjectivity and cannot optimise mass balance economic utility. However, they assist the planner in improving the understanding of the mass balance and they enable the exploration of present and future situations.

Optimisation models, of which Linear Programming (LP) and Mixed Integer Programming (MIP) are most applicable, are certainly able to find the optimum economic utility mass balance performance plan whilst dispensing subjectivity completely.

When it comes to the economic evaluation of the holistic mass balance, which encompasses the ore resources in situ, mining and beneficiation, up to the point of sale of the final products, the optimisation techniques of linear and mixed integer programming are able to determine the optimal performance. This is clearly illustrated by the ZIMASCO LP-model below.

-1-

2. Basic principles and state of the art : conventional mass balance optimisation.

2.1 Basic principles.

The concept of a mass balance originates from the law of conservation of mass, which in general states that mass is neither created nor destroyed, or, in the specific case of the mining and mineral processing industries, the products resulting from a mineral processing operation, have the same mass as the starting materials minus the losses, i.e. if no accumulation takes place.

To control a mineral processing operation properly, a complete mass balance must be determined frequently so that the overall performance of the circuit can be assessed accurately and the input values the plant has, be properly accounted for in order to execute corrective actions. This activity is known as metallurgical accounting. The aim of the corrective actions is to arrive and remain at processing conditions that will yield optimum process economic utility. [1].

In this paper, the term "mass balance performance" assumes that the mass balance is determined on given circuits and therefore refers to the performance of the circuits.

Consider, for example, the following mineral processing circuits:-

Diagram 1above illustrates the case of two sources of ore, at different grades, being fed to a crusher. After crushing, the material is screened and concentrated at two possible separation points :-

  • A : yielding 3t (high mass) of salable material at a low mineral content grade and associated with a low revenue per unit sold, and
  • B : yielding 2t (low mass) of salable material at a high mineral content grade and associated with a high revenue per unit sold.

The conventional mass balance (e.g. diagram 1. above) lends itself to optimisation of economic utility, in that by separating at point B rather than at point A in the concentrator, a higher profit is earned. This is of course under the assumptions of firstly, identical costs, irrespective of the choice of separation point and secondly, that the revenue structures are such that the increase in revenue due to the higher grade B material, more than compensates for the reduction in B material mass, compared to the A material mass and grade.

  • To evaluate the alternatives presented by a simple conventional mass balance, with the specific view to finding the optimal economic utility, is of little computing significance since a conventional electronic calculator would suffice. However, by :-

-2-

  • increasing the number of participating ores, each with its own mining methods
  • mining rates
  • non-linear mining cost curves
  • transportation costs to the plant
  • chemical analyses
  • increasing the number of separation points to approximate the recovery curve per chemical component contained in the ore
  • differentiating between operating costs at the various separation points
  • including the detailed beneficiation processes, be it of a mineral dressing, a pyrometallurgical, hydrometallurgical, electrometallurgical nature or combinations of these
  • increasing the number of salable grades, each selling into its own territory and signified by different transportation costs, monetary currencies, exchange rates and sales volumes
  • incorporating the price elasticity curves or demand curves
  • including fixed costs, capital expenditures and capital replacement expenditures,THEN, the evaluation of the conventional mass balance, with a view to finding the optimal economic utility balance, becomes a problem of complex and demanding computing significance. See diagram 2. below.

/ Mine
/ ORE / Cost
/ WASTE / Curves

Multiple mineral blocks

Diagram 2 : The holistic mass balance includes all possible

mining, beneficiation and sales combinations.

Multiple Sales Regions

Demand Curves

-3-

2.2 State of the art : conventional mass balance optimisation.

At present, the state of the art in optimising the conventional mass balance is to a very large extent based on input-output models. These models are coded in a computer language or in spreadsheet formats to read the planner's input data and to execute a calculation recipe or algorithm, in order, finally to display the output or results. Implicit to this approach, are the following assumptions :-

  • input-output models do not "know" the limits of the mass balance, other than what was given to them by the planner. The planner excludes parts of the mass balance which he perceives to be of less importance, whereas the next planner may emphasize other sections of the same mass balance and include different sections in his model. The entering of all possible combinations into input-output models can become very complex, cumbersome and time consuming and is hardly ever done by planners.
  • input-output models do not find the optimal economic utility plan - the planner can endeavour to do this by means of the execution of multiple runs of the model, each time changing the input data until a plan is produced that satisfies the planner's requirements and yields the highest "profit" so far. This is termed a "what-if ?" scenario. Unfortunately, the planner has no way of even determining how far the plan is from optimal economic utility, let alone knowing the optimal plan.
  • input-output models are always directed by the planner towards a "good" plan, i.e. in his perception, where "good" is more often than not a, very subjective measure of the quality of the plan.

Having stated these assumptions underlying the input-output model philosophy, it is by no means implied that input-output models are inaccurate or not useful. The purpose of any model is to simplify reality in such a way that it will lead to a greater understanding of the system being modeled and thus provide a means whereby experiments can be made on the model to explore present and future situations. [2].

To a far lesser extent than input-output models, some mining and mineral processing organisations are using mathematical optimisation techniques. These techniques, of which Linear Programming (LP) and Mixed Integer Programming (MIP) are most widely used, differ form input-output modeling in that :-

  • LP-models "know" the limits of the mass balance. The planner can input all possible permutations and combinations of mass balance alternatives into the model as constraints and need not bias the planning results with his perceptions of importance priorities. It is a relatively simple matter to enter the constraints, rather than pre-determining all combinations and then entering them.
  • LP-models find the optimal economic utility plan within the set of given constraints. Should the optimal plan contain a feature that causes a decision of non-implementation, this feature can be relaxed or removed and the model can be re-executed in order to find the next best economic utility plan. The difference between the two economic utility values is indicative of the cost of NOT IMPLEMENTING the best plan. This is a "what is best ?" scenario approach.
  • LP-models direct the planner towards the "best" plan :- it totally ignores subjectivity (company politics, labour relations, career paths, etc.) . It provides a no-bias, optimum economic utility base plan, from which deviations can be quantified in order to ensure that future performance of the mass balance will be at

-4-

an optimum, albeit at the expense of some "soft issues", e.g. a company political compromise. At least from the LP-model runs, the cost of the compromise can be known beforehand. This is known as a "what should be done if ?" scenario.

3. Systems synergism : definition of the holistic mass balance.

3.1 Systems synergism background.

Ackoff described the synergism of systems as : "the systems approach to problems, which focuses on systems taken as a whole, not on their parts separately. Such an approach is concerned with total-system performance even when a change in only one or a few of its parts is contemplated, because there are some properties of systems that can only be treated adequately from a holistic point of view." [3]p7.

Aristotle's statement, "the whole is more than the sum of its parts", was the initial impetus to systems analysis. [3]p5. Von Bertalanffy's comment on Aristotle's dictum was : "the properties and modes of action of higher levels ("the whole") are not explicable by the summation of the properties and modes of action of their components ("the parts") taken in isolation. If, however, we know the ensemble of the components and the relations existing between them, then the higher levels are derivable from the components". [3]p12. So even though the problems of "SYSTEM" were ancient and had been known for many centuries, they remained "philosophical" and did not become a "science" - because mathematical techniques were lacking. The quest for a new "gestalt" mathematics was repeatedly raised a considerable time ago, in which not the notion of quantity but rather that of relations, would be fundamental. In this regard, Lotka proposed systems of simultaneous differential equations; Volterra developed Volterra's equations; von Bertalanffy outlined "dynamical systems theory" [3]p13 and Ackoff in his classification of systems, makes reference to goal-seeking systems. [3]p32. The techniques of Linear Programming and Mixed Integer Programming certainly fall into this class of a new "gestalt" mathematics and are at the same time excellent goal-seeking systems.

3.2 Definition of the holistic mass balance.

The above philosophies and viewpoints, have the one concept of HOLISM in common, being the tendency in nature to produce a whole from its parts [4]p402 and [5]p354. With this as background, the definition of the "holistic" mass balance is put forward.

The "holistic mass balance", is that mass balance, which encompasses the ore resources in situ, through mining and beneficiation to the physical point of sale of the final product(s).

The "holistic mass balance performance" is that mass balance performance which is determined over ALL possible combinations of plant, equipment, machinery, circuits, men and money in the planning process of exploiting the ore body :- ore resources in situ, through mining and beneficiation, up to the physical point of sale of the final product(s).

The "optimal holistic mass balance performance" is that holistic mass balance performance which yields optimum economic utility.

-5-

The above definitions imply that each and every ton of ore in the ore body, irrespective of grade, spatial location or exploitation cost, at least stands a chance of being included in the optimal holistic mass balance. It also implies that each and every possible route that any given ton in the ore body could follow, up to point of final product sale, as well as every possible way in which that given ton could have been affected during the mining and metallurgical processes, are known; and further has been evaluated from a mass balance and economic perspective in order to be able to determine the optimal holistic mass balance.

Furthermore, the techniques of LP and MIP are able to determine the optimal holistic mass balance performance and in that sense meet the quest for a new "gestalt" mathematics. LP and MIP techniques are goal seeking techniques and are therefore able to find the optimal solution. The integer search algorithms take care of evaluating resource exploitation and allocation where discrete combinations of plant, equipment machinery, circuits, men and money are involved.

3.3 Comparison : conventional and holistic mass balances.

In practice, the performances of conventional mass balances in large integrated mining and metallurgical complexes are seldom conducted explicitly in the holistic way. Every unit manager is responsible for the metallurgical accounting of his unit, and is seldom involved in the upstream or downstream effects that the throughput and operating fluctuations of his unit may cause. It is normally the responsibility of the group production manager in conjunction with other senior members of management, e.g. the marketing manager, to synchronise and consolidate the production budgets from the various units. This is more often than not done rather subjectively as senior management is subject to all kinds of company political and other kinds of influences. It is also often done under great pressure due to nearing budget submission deadlines. The fact that the group production manager consolidates the production budgets from the units, illustrates that there is no escape from holism : "the tendency in nature to produce wholes from parts". Unless of course, an organisation is not concerned about improving efficiency and profits e.g. maximising shareholders' returns.

An example :- during a recent consultation, it was shown to a senior member of a mining and mineral processing organisation, responsible for group logistics, that with the aid of the LP-model it was detected that the mine concentrates despatch budget, differs from the smelter concentrates receipts budget. The reply was that profits are not made on paper, but by observant and responsible managers who timeously order more or less concentrates according to the smelter's demand.

This example shows that the holistic approach is adhered to in any case, even though the organisation may not officially plan it that way. It shows that top management still expects an "holistic execution" of the plan, even if the planning was not conducted to maximise the behaviour of the "whole".

So given that there is no escape from holism in the execution of the plans in large integrated mining and metallurgical complexes, the following philosophical question remains unanswered :- why do senior managements of most of these large integrated complexes not officially implement holistics in their planning processes ? If complexes operate profitably with no holistics or "soft holistics" in their planning, how much more profitable would they not be if planning was done holistically right from the onset ?

-6-

Integrated mining and metallurgical complexes which plan holistically, are able to budget and plan according to real world constraints, and not to an arbitrary rule of , e.g. "last year's budget plus ten percent". They find the optimal answers to the "what is best ?" and "what should be done if ?" questions, rather than answers to the repetitive input-output "what if ?" model question, which in any case contains a degree of subjectivity.

The only way for large integrated mining and metallurgical complexes to realise their full economic potentials, is to optimise their holistic mass balance performance planning and to implement these plans accordingly. Only then will the proper management of all the other business economic functions pay off optimally and in the right context.