5.2. Employment and Production Instability – Puzzling Performance Over Time

To illustrate the modelling process, consider the following dynamic puzzle facing a manufacturer of major household appliances. The company has been experiencing fluctuating employment and production in its refrigerator division. The employment level has varied over a ratio of about two:one with peak-to-peak intervals of two years. Conventional event-oriented thinking might suggest that economic upturns and downturns are responsible for this costly and disruptive behaviour over time. However, the evidence in this case is that the economy has been stable. Something else is going on, but what? Feedback systems thinking will often (though not always) look to internal factors, the way the division is organised, coordinated and managed, to explain dynamic behaviour. Interactions among the firm's operating policies and the practical constraints of production may in themselves explain the puzzling behaviour and also hold the key to future improvements.

The situation is expressed dynamically in Figure 5.5. There are two time charts, both with a timescale of three years. The workforce is on a scale of 100–300 workers and production is on a scale from 0–2 000 refrigerators per week. Both trajectories are strongly cyclical. How could these dynamics arise? A feedback systems thinker knows that a balancing loop with delay is capable of generating such oscillatory behaviour. That is a useful structural clue, but where would such a loop be found among the factory's operations?

The search for an appropriate balancing loop begins in this case with a sector map. Our dynamic hunch is that the factory's performance problems stem from the interaction between production control and workforce management. There is somehow a failure of coordination between these two important activities in the factory. Figure 5.6 shows the main connections. The production control sector receives incoming orders from retailers and makes shipments of refrigerators in return. A key question in our investigation is how the firm translates orders for refrigerators into the number of factory workers needed. Common sense suggests the volume of orders is related to the number of workers, but how? Managers responsible for production control decide the 'right' amount of production necessary to fulfil orders and to ensure reliable supply. The resulting production schedule is then used to adjust the workforce and the resulting number of workers determines the production rate. In the figure, you can already see a closed loop between the two sectors, formed by the production schedule and workforce, and it is this loop we want to examine in more detail.

Figure 5.5. Employment and production cyclicality – puzzling performance and structural clue

Figure 5.6. Sector map for dynamics of factory production and employment

A sector map shows the parts of the business, its recognisable functions, each with its own stock and flow network and its own operating policies. We can find the feedback processes within and between sectors by listing policies in use, sketching the stock and flow networks that belong in each sector and then identifying the influential connections. It is like building a jigsaw puzzle. The pieces are the policies and asset stocks, the connections are the clues for which pieces fit together and the resulting picture reveals the feedback processes. Figure 5.7 shows the pieces of the jigsaw for our factory model. At the top is production control with policies for demand forecasting, inventory control and production scheduling, the kind of routine decision-making processes found in all factories. There is also a refrigerator inventory, an important asset stock that sits between the production rate and shipment rate and signals the current balance of supply and demand. At the bottom of the figure is workforce management. Here the policies are workforce planning, hiring and departures – all those routine processes that influence the size of the factory workforce. The workforce itself is the sector's asset stock that sits between the hiring rate and the departure rate.

Figure 5.7. Asset stocks and list of operating policies in production control and workforce management

5.2.1. Dialogue About Production Control

Figure 5.8 is a complete stock and flow diagram for production control. The three shaded regions represent the main operating policies and within these regions there is a more specific representation of information flows and converters. Why use this particular picture? To understand, imagine the following dialogue between a modeller and factory expert:

Modeller:	I imagine that forecasting is an important input to your production scheduling process. Tell me more about forecasting.
Factory expert:	Well forecasting is essentially how we estimate future demand from retailers.
Modeller:	What information do you use?
Factory expert:	There are many different information sources we could use. There is an annual forecast prepared by the marketing department. There is a factory database containing recent and historical records of retail orders and the shipment rate of refrigerators. General economic conditions are relevant too, whether we are in an economic boom or a recession. Figure 5.8. Stock and flow diagram for production control
Modeller:	OK, but would you say that some of these information sources are more reliable or better than others?
Factory expert:	Forecasts from the marketing department are usually viewed with scepticism in the factory. At least that is our experience in this particular factory (though I can imagine factories in other firms where marketing forecasts are taken more seriously). Realistically the only data we really trust is shipments. That's real demand without any marketing spin or bias, and much more tangible (and therefore believable) even than retail orders. We can actually see and count the number of refrigerators that leave the factory each day and, from the database, have a pretty good idea of how shipments vary from month to month. Hence, we have concluded that past shipments are actually a good guide to future demand.
Modeller's note to self:	In that case I can formulate forecasting as an average of the shipment rate itself, and downplay other influences.
Modeller:	So would it be fair to say that production scheduling is driven principally by a forecast of shipments?
Factory expert:	Yes, that's about right except that we also like to make sure we have enough finished refrigerators in stock to meet unexpected changes in demand. As a result we will sometimes schedule extra production to build finished inventory to a satisfactory level or else cut the schedule to reduce inventory if we think it's too high. It's a form of inventory control.
Modeller:	But how do you decide on a satisfactory inventory level?
Factory expert:	In our case that's just a rule of thumb, nothing too formal. Through experience we have come to the conclusion that it's sensible to carry about four weeks worth of shipments.
Modeller:	So to summarise, production scheduling combines forecasting of shipments with inventory control.
Factory expert:	Yes, that's a reasonable description of what goes on.
Modeller's note to self:	So I can augment the forecast with an asset stock adjustment formulation to represent inventory control.
Modeller (on the next day, having created the stock and flow diagram in Figure 5.8):	Here is a picture of what you've told me so far about the factory. You will see the three main areas we talked about: forecasting, inventory control and production scheduling. There is a refrigerator inventory of finished units at the end of the production line. The inventory is increased by the production rate and reduced by the shipment rate. The rest of the diagram shows how production is coordinated.

Forecasting relies principally on information about the shipment rate and is essentially an average of past shipments (on the grounds mentioned that past shipments are a good guide to future demand). It matters how quickly this average responds to variations in the shipment rate. Forecasting should distinguish between routine day-to-day variations in shipments on the one hand and systematic trends on the other. This ability to discriminate is captured in the concept 'time to average ship rate', something that will need to be quantified in the algebraic model and has an important influence on the dynamics of production. The average shipment rate (or forecast) is used in two different ways to guide production planning. It feeds directly into production scheduling where it is one component of desired production. It also influences inventory control. The diagram shows four concepts used to capture the typical nature of inventory control. There is a 'desired inventory', which is an amount of inventory the factory aims to hold in order to avoid 'stockouts'. This desired inventory depends on the average ship rate and normal inventory coverage, consistent with the observation that it is good to carry about four weeks worth of shipments. By comparing desired inventory with the current refrigerator inventory, factory managers decide whether to boost or cut production to ensure that the right number of refrigerators is in stock. The correction for inventory captures this managerial judgement and incorporates a concept called 'time to correct inventory' that represents the urgency with which factory managers correct an inventory shortage or surplus. Production scheduling then combines information on the average ship rate with the correction for inventory to arrive at desired production.

5.2.2. Thought Experiment: a Surprise Demand Increase in an Ideal Factory

To test this part of the model, suppose the retail order rate increases unexpectedly and permanently by 10 per cent from 1 000 to 1 100 refrigerators per week. Will the factory be able to keep-up with demand? Assume for now that the factory can always produce at a rate equal to desired production. In Figure 5.8, this temporary simplifying assumption is shown by connecting desired production directly to the production rate. The link portrays an ideal factory with no constraints on production. Although the situation is deliberately simplified, it is still worth investigating as a stepping-stone to understanding sources of variability in production.

Figure 5.9 is a simulation of this ideal factory generated by running the model called 'Production' in the CD folder for Chapter 5. Press 'Run' and watch the screen icons. Then open Graph 1. For the first 10 weeks, the factory is in perfect equilibrium, as though the retail order rate had been rock steady for a long time. In the top half of the figure, the shipment rate, retail order rate, average ship rate and production are all equal at 1 000 refrigerators per week. In the bottom half of the figure, the refrigerator inventory is equal to desired inventory. Then in week 10, the retail order rate (line 2, top chart) increases permanently by 10 per cent, consistent with our demand assumption. If you look very carefully at the time chart, you will see that the shipment rate (line 1) follows exactly the same trajectory as the retail order rate and is in fact superimposed by it. Thus, the factory is able to fully satisfy demand at all times, despite the unexpected increase in demand. The factory achieves this perfect supply by depleting inventory in the short run and then subsequently by expanding production to meet demand and replenish inventory.

Figure 5.9. Simulation of a 10 per cent unexpected demand increase in an ideal factory

The story of factory adjustment begins in the bottom chart. In week 10, when demand increases, refrigerator inventory (line 1) starts to decline. Now look at the top chart. In the interval between weeks 10 and 15 the shipment rate/retail order rate (line 2) exceeds the production rate (line 4). In other words, the outflow of refrigerators exceeds the inflow, so the inventory must decline. Meanwhile, production is quickly catching up to shipments and by week 15 they are exactly equal. Inventory stabilises, but the factory is not yet in equilibrium. Inventory control calls for more production to replenish inventory. Notice that desired inventory (line 2 in the bottom chart) rises in proportion to the average ship rate (line 3 in the top chart) because of the factory's rule of thumb to hold four weeks coverage of shipments. Hence, there is an interval between weeks 15 and 55 when production exceeds shipments. During those 40 weeks, the factory is producing for stock as well as for shipment. As inventory is gradually replenished the production rate falls until it equals the retail order rate and the factory is back in equilibrium. The important dynamical feature of the simulation is the factory's inevitable need for 'surplus' production, above and beyond the real increase in demand. This outcome is not intuitively obvious from the operating policies alone. It requires simulation to reliably trace the consequences.