7.6. Policy Structure and Formulations for Capital Investment
At the heart of capital investment lies the question of whether the firm should expand capacity and by how much. As discussed earlier, business leaders take quite different approaches to investment decisions. Some invest according to a vision of future demand while others need hard evidence that the factory is stretched or that the financial return will be high. In this case, we represent a conservative investment policy driven by operating pressures in the factory. The policy is conceived in three parts as shown by the grey areas in Figure 7.18. There is an assessment of delivery delay that drives capacity expansion. Lying behind this assessment is a process of goal formation in which factory managers establish the company's standards for delivery performance. The corresponding formulations are described below.
7.6.1. Assessment of Delivery Delay
From a factory perspective, a high delivery delay is a mixed blessing. On the one hand, it suggests that a product is selling well and is popular with customers. On the other hand, it is a sign that production capacity is inadequate. So a crucial question for factory managers is whether delivery delay is too high. This managerial judgement is captured in the concept 'delivery delay condition', which is defined as the ratio of delivery delay recognised by the factory to delivery delay operating goal. If the ratio takes a value of one then delivery delay is exactly on target and no new net investment is needed. However, if the ratio takes a value greater than one then factory managers sense a need for capacity expansion. Moreover, they have the tangible evidence to justify expansion. However, it takes time to estimate whether goods are being shipped on time and so delivery delay recognised by the factory is formulated as an information smooth of delivery delay indicated, where the smoothing time is set at two months. Note that the factory is quicker to recognise changes in delivery delay than customers.
7.6.2. Goal Formation – Weighted Average of Adaptive and Static Goals
How does the company decide an appropriate operating goal for delivery delay? A simple formulation is a fixed goal, a target that once set does not change, but in reality organisational goals can adapt to changing circumstances. A suitable formulation is a weighted average of delivery delay tradition and delivery delay management goal that allows for either an adaptive or static goal, or a combination of both. Delivery delay tradition is performance the factory has achieved in the past, based on a long-term smooth or average of delivery delay recognised. The time constant in this information smoothing process is 12 months meaning that tradition is heavily influenced by performance achieved over the past year. Delivery delay management goal is a fixed performance target, a goal that management aspires to regardless of past performance. If delivery delay weight is set to one then the operating goal depends entirely on delivery delay tradition, and if the weight is set to zero then the operating goal depends entirely on the fixed management goal. A weight between zero and one allows for a combination of both influences.
Figure 7.18. Policy structure and formulations for capital investment
7.6.3. Capacity Expansion – Fractional Asset Stock Adjustment
Capacity expansion is an example of asset stock adjustment. The firm adds more capacity when there is pressure to do so. However, in this formulation there is not a clear target for desired production capacity to use as a benchmark for corrective action. Rather, we are thinking of a process where factory managers argue for a proportional increase of existing capacity (requesting perhaps five or 10 per cent more over the coming year) and then top management decide whether the case for expansion is justified. Such informal pressure-driven asset stock adjustment is quite common, especially in capital investment where there is ambiguity about how much investment is really needed and competition for limited funds. Accordingly, the capacity order rate is defined as production capacity multiplied by a 'capacity expansion fraction'. This expansion fraction is a non-linear function of delivery delay pressure, in which the higher the pressure the greater the expansion approved. But pressure for expansion is a matter of opinion and the formulation cleverly allows for a difference of opinion between factory managers and the top management team who have the final say on investment. Factory managers report the delivery delay condition and the management team interprets this information according to a delivery delay bias. Delivery delay pressure is equal to delivery delay condition minus delivery delay bias. The bias is set at 0.3, which means that the management team approves less expansion than requested, reflecting a conservative attitude toward investment. The same formulation can also be used to portray an optimistic and pre-emptive attitude to investment by setting the bias to a value less than zero.[]
[] An alternative formulation of delivery delay pressure is to multiply the delivery delay condition by a delivery delay bias. In such a multiplicative formulation the neutral value of the bias is one. A bias of less than one (say 0.8 or 0.9) represents management with a conservative attitude to capital investment, whereas a bias greater than one represents management with a pre-emptive attitude to investment, willing to invest in capacity ahead of demand. In the algebraic context shown, the choice of multiplication or subtraction (with an appropriately scaled bias) makes no difference to the resulting feedback structure and dynamics. A subtraction formulation is used here because it matches the formulation in Jay Forrester's original model.
The non-linear function for capacity expansion fraction is shown in Figure 7.19. The horizontal axis is delivery delay pressure on a scale from zero to 2.5. The vertical axis is capacity expansion fraction on a scale from −0.1 to 0.15, expressed as a fraction per month. Where do you find the data to sketch such a graph? The answer lies in carefully defining the axes, identifying points that logically belong on the curve and using common sense to fill in the gaps. In this case, we define delivery delay pressure of 1 to be neutral, requiring no change of capacity. So the curve must pass through the point (1,0). Common sense suggests the function is upward sloping because the higher delivery delay pressure the greater the need for capacity expansion. The gradient of the line around the (1,0) point defines how much extra capacity expansion is approved for a given change of pressure. Everyday experience suggests that expansion of 20 or 30 per cent per year is common and even 100 per cent or more per year is feasible. Capacity reduction is also possible. Moreover, it is not unreasonable to argue that the gradient of the line increases the more extreme the delivery delay pressure. This kind of logical argument leads to the curve in Figure 7.19.
Figure 7.19. Graph for capacity expansion fraction
As delivery delay pressure rises from 1 to 1.5, the capacity expansion fraction increases from 0 to 0.2 per month (24 per cent per year). As pressure rises even further to 2 (meaning that top management believe that factory deliveries are taking twice as long as normal) the expansion fraction increases to 0.7 per month (84 per cent per year). Extreme pressure of 2.5 leads to fractional expansion fraction of 0.15 per month (180 per cent per year). The reverse logic applies when delivery delay pressure is considered to be too low. As pressure falls from 1 to 0.5, the expansion fraction decreases from 0 to −0.2 per month (a capacity reduction of 24 per cent per year). When pressure reaches zero (meaning that both demand and backlog have also fallen to zero) it is plain to the management team that demand has collapsed and drastic action is needed to shed capacity. The capacity fraction decreases to −0.7 per month leading to capacity reduction of 84 per cent per year that, if sustained, would lead to closure in less than two years.
There is a lot of meaning packed into these few equations for fractional asset stock adjustment. Effectively, the organisation 'searches' for the right amount of capacity needed to supply the market, but without setting a specific target. In terms of the Baker criterion such a policy is myopic but also versatile. Pressure for expansion is able to filter through to those who have the power to invest. They are not concerned with the detail of investment but rather the appropriateness of the proposed expansion relative to existing capacity. Providing there is a good case, capacity expands. Interestingly, this policy leads to reinforcing feedback in capital investment. The bigger the factory, the greater the absolute investment, leading to an even bigger factory.
7.6.4. Production Capacity – Two-Stage Stock Accumulation
Production capacity is represented in the aggregate. It is the total output achievable by the factory, measured in systems per month, using all the available equipment. As always perspective is important. We are not so close to the factory as to see individual machines, conveyors and assembly lines, but we are not so far away as to be unaware that capacity constrains factory output and can be changed only gradually. When investment is approved there is a substantial time lag before new capacity is actually operating. Equipment needs to be built, delivered and installed. These aggregate characteristics of capacity are portrayed in a two-stage stock accumulation process shown in Figure 7.18 and captured in the equations below. Stage one is a stock of capacity being built but not yet available for production. This pipeline of latent capacity is increased by the capacity order rate and reduced by the capacity arrival rate (i.e. final delivery to the factory). The capacity arrival rate is defined as the ratio of capacity being built to capacity lead time. This ratio is a standard stock depletion formulation where the time to build new capacity is assumed to be 12 months. The bigger the pipeline, the greater the arrival rate. We assume the initial value of capacity being built is equal to the capacity order rate multiplied by the capacity lead time, in other words there are 12 months worth of orders in the pipeline to begin with.
Stage two is a stock of production capacity already installed in the factory and available for use. This fully operational capacity is an accumulation of the capacity arrival rate. The factory is initialised with a capacity of 120 systems per month which, at normal utilisation of 50 per cent, is more than enough to fill customer orders of 40 systems per month generated by the initial sales force of four people. Note there is no explicit representation of obsolescence or capacity reduction. When disinvestment occurs it is treated as negative capacity arrival. Accordingly, the capacity arrival rate in Figure 7.18 is shown as a bi-flow to signify that capacity can either increase or decrease. This simplification really means that investment and disinvestment are treated symmetrically. Just as it takes time to add new capacity, so it takes time to dispose of surplus capacity once an approval for disinvestment has been agreed. Incidentally, if this kind of approximation is unsatisfactory (and results in formulations that contradict the guidelines in Figure 7.5) then capacity obsolescence and discard should be represented separately.
Multi-stage stock accumulations are widely used in system dynamics in any situation where there is a significant lead time in building organisational resources. The structure applies to capital investment of all kinds (equipment, buildings, infrastructure). It is also appropriate for skilled human resources where people take time to train, to master skills on the job and to be fully assimilated by the organisation. For example, an airline model to investigate the dynamics of service capacity might distinguish between stocks of rookie staff and experienced staff with a flow rate between the two stocks to represent on-the-job training. The training rate would be a standard stock depletion formulation defined as the ratio of rookie staff to the normal training time. Occasionally more than two stages are needed. For example, in Chapter 9 a hospital model to investigate the quality of patient care shows stock accumulations for medical students, junior doctors and consultants, with standard stock depletion formulations controlling the flow rates from student to junior doctor and from junior doctor to consultant. Intangible asset stocks can be represented in multiple stages too. A model to investigate knowledge development by firms engaged in an R&D alliance might show stock accumulations for incubating knowledge and applied knowledge, connected by a knowledge transfer rate.