7.4. Policy Structure and Formulations for Sales Growth
In the light of our discussion on decision making we now return to the market growth model to see how its various policies fit together. Figure 7.14 shows the policy structure behind the reinforcing sales growth loop that links sales force hiring, budgeting, customer ordering and order fulfilment. Before plunging into the detail of the formulations, first look at the broad pattern of connections between the grey areas that correspond to operating policies. Why should sales grow at all? Is the growth engine plausible? To investigate, we start with the sales force and trace anticlockwise. Crucially sales force hiring relies on a signal from budgeting (the authorised sales force) to guide adjustments to the sales force size. Hiring in this organisation is budget driven. Budgeting itself is quite myopic, a characteristic clearly shown in the single information link that feeds in from order fulfilment. Fundamentally, the budget is proportional to the order fill rate – it is not a complex trade-off between competing alternatives. Meanwhile, leaving aside capacity constraints, the principal pressure on order fulfilment comes from the backlog: the bigger the backlog, the greater the order fill rate. Looking down on this company from the perspective of the CEO, we can see there is a causal chain, weaving among the functions, that connects sales force hiring to the size of the order backlog. In addition, the backlog itself is an accumulation of unfilled customer orders. Only one more link is needed to form a reinforcing sales growth loop – the link from sales force to customer orders which is strong in firms that sell high-specification technical products.
Figure 7.14. Policy structure and formulations for sales growth
The policy structure provides a framework within which the equation formulations take shape. In other words, the architecture of the information network is defined and it now remains to explain the equations underlying each operating policy. Again we will begin with sales force at the top of the diagram and work anticlockwise through the formulations.
7.4.1. Sales Force Hiring – Standard Stock Adjustment Formulation
We know that sales force hiring is budget driven. An elegant way to capture this effect is with a standard stock adjustment formulation as shown in the equations below.
The sales force is represented as a stock that accumulates net sales force hiring. Hiring results from corrective action of the hiring policy and depends on the difference between the authorised sales force and the sales force (the gap in head count) divided by the time to adjust sales force. In this case, the head count goal of the hiring policy is the authorised sales force that comes from budgeting. The model is initialised with just four sales people and the time to adjust sales force is set at 12 months. This choice of adjustment time reflects an assumption that the company is reasonably patient in filling any head count gap. Essentially, a shortfall or excess of sales people is corrected gradually over a period of 12 months.
7.4.2. Sales Force Budgeting – Revenue Allocation and Information Smoothing
Budgeting is modelled as a political allocation process driven by precedent and captured in the eight equations shown below. The authorised sales force depends on the ratio of the budget allocated to the sales force and sales force salary. This equation is simply a matter of definition. The bigger the budget, the larger the authorised sales force whereas the higher the sales force salary the fewer sales people the budget will support. We assume that sales force salary is £4000 per sales person per month, including overhead and support. Note that this choice of units ensures dimensional consistency. The most important formulation is the equation representing the budget allocated to the sales force because here are embedded the assumptions about precedent and the politics of budgeting. The budget to sales force is defined as the product of sales revenue and the fraction of revenue to the sales force, in other words a fixed fractional revenue allocation. This one-line equation is surprisingly simple, but captures a lot about the typical shortcuts and compromises that characterise real-world budgets. For example, in a modelling project for BBC World Service (mentioned in Chapter 3) it was found that operating funds were divided into separate components for programme making, programme support and transmission. The proportion of available funds allocated to each of these activities was 70 per cent for programme making, 15 per cent for programme support and 15 per cent for transmission. These proportions, steeped in the traditions of an international radio broadcaster, were not easily changed. Similar rigidity applies to the fraction of revenue available to the sales force in the market growth model. The fraction is set at 0.1, so that 10 per cent of sales revenue is allocated to fund the sales force.
Reported sales revenue is formulated as the average order fill rate multiplied by product price, which is set at £9 600 per system. This equation is more or less an accounting identity that might appear in a spreadsheet model, but for one subtle change inspired by principles of information feedback and the Baker criterion. We assume that data on sales revenue must be gathered and reported before it can be used to inform decision making. Such measurement involves information smoothing. This idea is captured in the average order fill rate, formulated as a smooth (SMTH1) of the true and instantaneous order fill rate observable in the factory. (See Chapter 5 for a review of information smoothing.) The time to average orders is assumed to be one month, representing the typical amount of time required to compile a business report.
7.4.3. Order Fulfilment – Standard Stock Depletion Formulation
Order fulfilment controls the rate at which the factory fills customer orders. At the heart of the formulation is the order backlog, an accumulation of customer orders that have not yet been filled. We assume the product is built to order. Hence, when new customer orders arrive they are added to the backlog and stay there until filled. The average time to fill an order is called the delivery delay. Sometimes, but not always, it is reasonable to assume that delivery delay is constant, in other words the average time taken by the factory to process an order, build the product and ship it is the same no matter how large or small the volume of customer orders. Under this special condition, order fulfilment can be expressed as a standard stock depletion formulation as shown in the equations below. The order fill rate is simply the ratio of backlog to delivery delay. The larger the order backlog, the greater the order fill rate, and this proportionality always holds true given our assumption of constant delivery delay. In this particular case, the delivery delay is set at two months and the initial order backlog is 80 systems, so the order fill rate is 40 systems per month.
More sophisticated order fulfilment formulations are common in which the order fill rate depends on factors such as available capacity, the adequacy of finished inventory or some combination of the two. We will see a good example later in the chapter when capacity is added to the model. For now, a simple stock depletion formulation proportional to backlog is adequate. Incidentally, it is important to realise that, in any of these alternative formulations, backlog does not track individual orders entering and leaving the business in the way one might observe close-up in a factory or in the formulation of a queue in a discrete event simulation model. Instead, there is a volume of orders, so many orders received per week or per month. They flow into the backlog where they are mixed together with no trace of individual identity. Some orders may be for a standard version of the product and others for special product variants that take longer to make. On average, across the product range, these orders reside in backlog for a period of time defined as the delivery delay. This mixing together and resulting anonymity of orders is a good example of viewing the system from the appropriate intermediate perspective, close enough to see the build-up of unfulfilled demand and the resulting pressures on the business, but not so close as to see each individual order.
Surprisingly, the mundane notions of order backlog and order fulfilment reach quite deeply into the philosophy of system dynamics. Backlog is widely used by modellers and is a highly versatile concept broadly applicable to firms, industries and society. Any system dynamics model of supply and demand will, in principle, contain one or more backlogs of accumulated demand waiting to be satisfied. In such dynamical models, equilibrium is not presumed and so supply need not always equal demand. If, in the short-to-medium term, there is a supply shortage, then excess demand accumulates in backlog. From backlog arises (directly or indirectly) realistic pressures for price adjustment, capacity expansion or demand reduction, pressures that reveal the invisible hand of market forces at work, seeking to equilibrate supply and demand.
7.4.4. Customer Ordering
The formulation for customer ordering completes the sales growth loop. Recall that customers in this case are commercial buyers who learn about the product from a professional sales force. The bigger the sales force, the more orders. The formulation is shown below. Customer orders equal sales force multiplied by normal sales force productivity, where normal productivity is assumed to be 10 orders per salesperson per month. So with an initial sales force of four people, the company wins 40 orders per month.
