7.5. Policy Structure and Formulations for Limits to Sales Growth
Although the sales force is vital for generating orders, we also know that product availability is a very important consideration for buyers. Even the most successful sales force cannot sell a product that is not available. Intuitively, we might expect customer orders to be limited by production capacity and therefore write the following equation to capture that constraint (where MIN is a logical function that selects the minimum value of the two expressions in parentheses).
However, a moment's reflection reveals this is not a good formulation. It fails the Baker criterion because it implies that customers know the factory's production capacity and ignore the efforts of the sales force the moment the limit of production capacity is reached. Figure 7.15 shows a much more realistic and subtle formulation in which customers respond to delivery delay and where delivery delay depends indirectly on both production capacity and the utilisation of capacity. The beauty of this formulation is that customers know delivery delay (from experience or rumour) and regard it as very important in their ordering decision, consistent with our earlier discussion of the customer ordering policy. Moreover, the formulation is dynamically interesting. In the short-to-medium term, it allows the freedom for customers to order more than the factory can produce rather than arbitrarily imposing a rigid balance of supply and demand.
Figure 7.15. Policy structure and formulations for limits to sales growth
7.5.1. Customer Response to Delivery Delay – Non-linear Graphical Converter
In Figure 7.15, customer orders now depend not only on the sales force and its productivity but also on the effect of delivery delay on orders. It would be reasonable to assume that the longer the delivery delay, the fewer orders are placed. What is the strength of the effect and how would you estimate it in practice? Normally, modellers sketch such relationships in consultation with the management team, either on a whiteboard or direct on the computer screen so the shape is visible for inspection and comment. Notice that the corresponding equation for the effect of delivery delay is expressed as a GRAPH where the shape of the function is contained in terms of coordinates that lie along the line.
A plausible function is shown in Figure 7.16. The horizontal axis is delivery delay recognised (by customers) defined on a scale from zero to 10 months. The vertical axis is the effect of delivery delay on orders defined on a scale from zero to one. The numerical values in the table on the right of the figure correspond to the shape of the function. The general shape is downward sloping – gradual at first, then steep and ending gradual. For comparison, a straight dotted line is superimposed to show a linear relationship. When delivery delay recognised is less than one month then customers are satisfied and the effect takes a neutral value of one, or very close. As delivery delay rises, the effect becomes stronger. A delay of two months reduces orders to 87 per cent of what the sales force could otherwise sell. A delay of three months reduces orders to 73 per cent while a delay of four months reduces them to only 53 per cent. A delivery delay of 10 months is completely unacceptable to most customers and reduces orders to only two per cent of what could otherwise be sold, thereby rendering the sales force ineffective.
Figure 7.16. Graph for the effect of delivery delay on orders
7.5.2. Customers' Perception of Delivery Delay – Information Smoothing
Delivery delay recognised represents customers' perception of delivery delay. It takes time for customers to build an impression of delivery delay from their own recent experience of deliveries and from rumours circulating in the industry. The natural formulation is information smoothing. The equation is written as a SMTH1 function of delivery delay indicated, where the time constant of the smoothing process is called the 'time to recognise delivery delay' and is set at 10 months. Think about this formulation for a moment in terms of the Baker criterion – what do customers know and when do they know it? What they know and use as the basis for ordering is delivery delay recognised. Customers form this impression by averaging, over a period of 10 months, their day-to-day experience of 'delivery delay indicated'. This measure of delivery delay is the actual time it takes the factory to fill orders, defined as the ratio of the order backlog to the order fill rate. A brief spate of late deliveries, lasting just a few weeks, will do little harm to demand and customers will continue to order in the belief that normal delivery will be resumed. However, if the factory is slow to deliver for months on end then customers begin to think that is the norm. As a result some will stop ordering and place their orders with rivals instead.
7.5.3. Order Fulfilment and Capacity Utilisation
Order fulfilment from the perspective of a customer looks like a time delay. Orders are placed with the factory and some time later the corresponding products are delivered. The factory is a black box, but step a bit closer and the operating constraints of the factory become apparent. From the perspective of a CEO or factory manager, the order fill rate depends broadly on production capacity and the utilisation of capacity. A big factory can supply more than a small one and a factory working flat out, three shifts, 24 hours a day can supply more than a factory working a single shift. These common-sense facts about factory output are captured in the equations below. The order fill rate is defined as production capacity multiplied by the utilisation of capacity. But what determines utilisation? The formulation below, taken from the market growth model, is particularly insightful. Utilisation of capacity depends on 'delivery delay minimum'. This new concept is an estimate of how long it would take to clear the order backlog if the factory were working flat out with no glitches. It can be interpreted as a measure of the load on the factory, a kind of informal metric likely to be known by experienced factory managers.
The longer delivery delay minimum, the greater is the load and the higher capacity utilisation. The relationship is shown in Figure 7.17. The horizontal axis is delivery delay minimum on a scale from zero to five months. The vertical axis is capacity utilisation on a scale from zero to one. For light loads, when delivery delay minimum is between zero and one month, utilisation increases linearly from zero to 50 per cent. The dotted line shows a continuation of this linear trend. Utilisation of 50 per cent represents a factory working normally between one and two shifts. As the load increases to three months, utilisation continues to rise to 80 per cent, but less quickly than before because the busier the factory the more difficult it is to squeeze out extra production. Finally, as the load increases to five months the curve flattens out and utilisation gradually approaches its maximum value of one corresponding to uninterrupted three-shift production. The assumption is that factories very rarely work flat out and only the most extreme load can induce the managerial pressure needed to sustain such high output.
Figure 7.17. Graph for capacity utilization
