5.4. Modelling Workforce Management and Factory Production Dynamics
5.4.1. Dialogue About Workforce Management
Figure 5.17 is a stock and flow diagram for workforce management. In this sector, the main policies are workforce planning, hiring and departures. Let's resume the imaginary dialogue between a modeller and factory expert that led to such a picture.
| Modeller: | Tell me about workforce management. |
| Factory expert: | Usuallyasmall committee comes together every weektodiscuss changes in the workforce. If there is a downturn in the business then normally we let workers go by attrition and don't replace them. If there is an upturn then we need more workers. |
| Modeller: | How do you decide the number of workers you need in the factory? |
| Factory expert: | Well that's difficult to pinpoint. We know the weekly build schedule (desired production) and we monitor the productivity of our workers (based on a standard two-shift rota). From those two information sources we can estimate how many workers are needed. |
| Modeller: | So what happens if you have too many or too few workers? |
| Factory expert: | If we have too few workers we hire more. It takes time to fill vacancies because we like to honour employment commitments and that makes us fairly cautious about adding new people. If demand is growing we may be temporarily short of workers, which means we can't always produce exactly to plan. If we have too many workers, then we normally reduce the workforce through natural attrition, avoiding forced lay-offs, consistent with our employment commitments. |
| Modeller: | What causes workers to leave voluntarily? |
| Factory expert: | All factories experience regular turnover. Unfortunately turnover in this factory is high, partly a regional effect. Our human resource department estimates that workers typically stay for about a year and then move on. Of course, some people have been with us for much longer. |
| Modeller (on the next day, having created the stock and flow diagram in Figure 5.17): | Here is a picture based on our discussion. The workforce is increased by the hiring rate and reduced by the departure rate. Departures are proportional to the size of the workforce. The bigger the workforce the more departures, because the normal length of stay is roughly constant – about one year in this case. The hiring rate depends both on departures and a workforce adjustment. In the special case when demand on the factory is steady, then logically the workforce size is steady too, and the only pressure on hiring is from departures – the need to replace workers who leave. The average departure rate is the factory's estimate of the departure rate, measured over an interval called the 'time to average departures'. The workforce adjustment depends on the gap between the desired workforce and the workforce. Any such gap is corrected gradually over a number of weeks, reflecting the factory's traditional caution about adding new workers. This particular attitude to hiring is captured in the 'time to adjust workforce'. The desired workforce depends on desired production (the weekly build schedule) and estimated worker productivity. Here is an important link between production control and workforce management where the factory's production plans are transformed into a need for workers. This process of workforce planning does not happen instantaneously. There is a workforce planning delay to represent the administrative time it takes to reach agreement on the desired workforce. |
5.4.2. Operating Constraint Linking Workforce to Production
To complete the visual model we need to reconsider how the production rate itself is determined. In our 'ideal' factory, we made the convenient simplifying assumption that production is always equal to desired production, but in reality production depends on workers, parts and machines. There needs to be enough of each. In principle, all these 'factors of production' can be modelled, but here we limit ourselves to just one realistic constraint, the effect of workers, and implicitly assume that the necessary parts and machines are always available. The relationship between workforce and production is shown in Figure 5.18. The production rate depends on the size of the workforce and on worker productivity. Notice that these two links are hardwired. They are practical operating constraints, not information flows. The bigger the workforce, the more production is possible, and vice versa. Worker productivity, in terms of output per worker per week, is important too. All else equal, high productivity boosts production and low productivity reduces it.
Figure 5.18. Operating constraint linking workforce to production
5.4.3. Simulation of the Complete Model: A Surprise Demand Increase in a Factory Where Production is Constrained by the Size of the Workforce
To investigate the dynamics of the complete model we again introduce a surprise increase in demand. Open the file called 'Production and Workforce' in the CD folder for Chapter 5. You will see a diagram of the complete factory model. Press the 'Run' button in the lower left of the control panel and watch the movement of the stocks and converter dials as the simulation progresses. Then open graph 1 on the right-hand side of the production sector by double-clicking on the icon labelled 'Graph 1 for step, random and ramp'. The simulated trajectories are the same as shown in the top half of Figure 5.19. Press the page tab in the lower left of the time chart to reveal page 2 of the graph pad, which shows simulated trajectories in the bottom half of Figure 5.19.
Figure 5.19. Simulation of an unexpected 10 per cent increase in demand. The view in production control
Once again the retail order rate (line 1, top chart) increases by 100 refrigerators per week in week 10. Now, however, factory production is constrained by the size of the workforce. As a result, the production rate (line 4) rises slowly. In fact, there is virtually no change in production in the four weeks immediately after the hike in orders. However, the factory still ships to order and, since production remains low, the only way to fill the extra orders in the short term is to deplete inventory. The refrigerator inventory (line 1, bottom chart) plunges to 3 000 by week 24 and here is where the coordination problems for the factory begin. The steady decline of inventory over a period of 14 weeks creates enormous pressure from inventory control to boost production. This pressure is most clearly visible in desired production (line 3, upper chart) that soars to almost 1 250 by week 26, a planned increase of 250 refrigerators per week against an increase in demand of only 100. The knock-on consequences are serious, because desired production is the signal that guides workforce planning.
Figure 5.20 shows simulated trajectories in workforce management (which can be found on pages 3 and 4 of the graph pad). To begin with, workforce (line 1, top chart) is equal to desired workforce (line 2, top chart) and the factory has just the right number of workers (200) to produce the required 1 000 refrigerators per week. After the hike in orders, the desired workforce rises in response to desired production, reaching a peak of almost 250 workers in week 30, an increase of 40 per cent. The hiring rate (line 1, bottom chart) increases to fill the gap, but not all at once because factory managers are cautious in their approach to hiring. Hence, the workforce rises only gradually. As a result there is a sustained shortage of workers and it is this shortage that curtails production and then feeds back through inventory control to amplify desired production and desired workforce. Here we see in action a balancing loop with delay, creating havoc with factory planning and coordination.
Figure 5.20. The view in workforce management
How does the confusion resolve itself? To investigate return to the production control variables in Figure 5.19 and review the situation in week 24. By this point in time the production rate (line 4) has finally caught up with the retail order rate (line 1). As a result, the refrigerator inventory stabilises and so too does desired production. However, there is still a need to rebuild inventory, a task that justifies the growing workforce. By week 42, refrigerator inventory is back on target and desired production is equal to demand, but now the consequences of past hiring come back to haunt the factory. The workforce is still near its peak and production is much higher than orders and shipments. Inventory therefore continues to grow, beyond desired inventory. The resulting excess inventory puts downward pressure on desired production and desired labour leading eventually to a reduction in the workforce and production. By week 72, inventory is back in line with desired inventory, but now the production rate is too low because the workforce has been allowed to shrink too much (through departures). However, the factory is gradually getting closer to matching production and shipments, while at the same time bringing inventory and the workforce in line with their targets. Another round of adjustments in the interval between weeks 70 and 130 brings the factory into long-term equilibrium. The simulation shows that equilibrium is hard to achieve, even in the seemingly easy case where demand increases permanently in a one-time step. In the face of a more variable demand pattern, the factory may never achieve the right balance and find itself locked in a syndrome of production and employment instability similar to the problem experienced by the real refrigerator manufacturer on which this example is based.[]
[] The cycles in the factory model are slightly shorter than the two-year periodicity we set out to explain. It is a useful exercise to identify the parameters that determine periodicity and to adjust them for a better fit.
5.4.4. Pause for Reflection
This chapter has shown the typical steps in going from problem articulation to a feedback representation and simulation model. Most models start from a dynamic issue in terms of performance over time that is puzzling, dysfunctional, unintended or maybe just difficult to foresee. The modelling process is creative and iterative. The modeller begins with a hunch about which feedback loops are capable of generating the dynamics of interest. The hunch is underpinned by a philosophical view that dynamic behaviour arises endogenously from feedback structure rather than from external and uncontrollable events. The search for feedback loops then begins in earnest and can progress along a variety of different paths as outlined in Figure 5.3.
The factory dynamics model began as a sector map, which was then developed into a stock and flow diagram – a very common path in my experience. Sector maps show the main interlocking subsystems or functional areas in which feedback loops are to be found. They also convey a clear impression of the model boundary and assumed level of aggregation. Inside sectors are operating policies that guide asset stock accumulation. The operating policies depict decision-making processes and the information flows on which they depend. Feedback loops emerge by stitching together stock accumulations, operating policies, information flows and other practical operating constraints.
The factory model contained policies for forecasting, inventory control, production scheduling, workforce planning, hiring and departures, as well as a production function depicting the operating constraint of workforce on production. These six policies and single production function jointly guide the accumulation of workforce and finished inventory. At the heart of this coordinating network lies a powerful balancing loop with delay. Simulations of the factory model (in response to a one-time increase in demand) show cyclicality in production and workforce broadly consistent with the problem encountered by the real factory. By probing the way factories manage production we have found a credible feedback structure that offers an explanation of the instability phenomenon. We have transformed our vague dynamic hunch into a well-defined dynamic hypothesis.