Strategic Modelling and Business Dynamics: A Feedback Systems Approach

5.3. Equation Formulations and Computations in Production Control

It is common for equation formulations to be organised in sectors and blocks that correspond as closely as possible to the visual model. We begin with inventory accumulation as shown in Figure 5.10. These are the standard equations for a stock and flow network. Refrigerator inventory at time t is equal to refrigerator inventory at the previous point in time t−1, plus the net change resulting from production (the inflow) and shipments (the outflow) over the interval dt between t−1 and t. The initial inventory is set at 4 000 refrigerators, deliberately chosen so that there are four weeks coverage of initial shipments, exactly in line with the factory's rule of thumb. The production rate is identically equal to desired production, a temporary but convenient assumption that says the factory can always produce as many refrigerators as needed at just the right time. The shipment rate is equal to the retail order rate implying there is enough finished inventory available in the shipping bay to fill orders.^[] The retail order rate itself is formulated as a one time step increase, a simple yet insightful exogenous change. The order rate begins at 1 000 refrigerators per week and then, in week 10, rises by 10 per cent (100 refrigerators per week).

^[] In practice some factories temporarily run out of inventory and/or deliberately choose to build to order. Such supply bottlenecks are usually modelled by introducing an order ...