7.1 Block 1: Simulation Model of a Material-Consuming
Boolean logic decides the operating state of the material sink at each time step in the simulation (every minute in the application cases). For the generic operating state logic presented in Figure 38 the implementation is described in detail below and in its Vensim visualization in Figure 71.
The approach used to model the modules of a material sink in a system dynamic software are described below. Readers may refer to the model structures and more comprehensive variable definitions in Appendix A.
Checking if machine is off: A PULSETRAIN function is used to distinguish non-working times (e.g. nights or weekends) from working hours. Since most manufacturers adjust their working hours depending on demand, a second condition, checking the stock of processed parts before starting a day of shift of production is added.
Checking if planned maintenance activities are up-to-date: A stock and flow set is used to model the time since the last maintenance activity (“MaintTickerS1” and “UptimeS1”) (see Figure 72). When the elapsed time exceeds a preset maintenance interval value, the machine enters a
“maintenance overdue status”. In the generic operating logic, the planned maintenance is executed immediately, represented by the elapsed maintenance activity flow, “ElpMaintS1”. After exceeding a constant or condition-dependent duration, the maintenance job is registered as completed. A supporting flow “CompMaintS1” signals the completion and restarts the time-since-maintenance counter flow.
Checking if technical parameters are in order: the occurrence of a technical error is modelled as a PULSETRAIN function with a time-to-failure as the pulse frequency and time-to-repair as the pulse duration. Both functions are modelled as normally distributed random functions recalculated following each failure incident, using a stock as a breakdown counter (“BD Count S1”).
Parameters of the random functions are extracted from company data (in input
model behavior is not contingent on a pseudo-random sequence generated by Vensim™.
Checking if employee is present and ready: Short employee absences (e.g.
bathroom breaks or for supporting activities) are modelled by a PULSETRAIN function. Employee qualification is modelled as a normally distributed random function recalculated each shift. Parameters of the random function are extracted from a company skills matrix. The employee qualification is compared with a minimum employee qualification for the completion of the next production job (see Figure 82).
Checking that material feed and removal are in working order: The machine will idle if there is a technical error either directly upstream or downstream, no material upstream, or the maximum stock for the variant is exceeded (starving and blocking). The material feed and removal are assumed technical systems, with their failure modelled analogously to the technical errors of the main machine. The stock levels, modelled in the stock-management module (see Figure 79), are compared with limits set in this module for each variant.
Checking if an order is open: Based on a schedule in the input spreadsheets (see Figure 81) the system loads a series of jobs each day based on their start date. If no jobs are listed in the schedule, the process will go into idle state. If a job is processed, the machine will complete the job when the processed quantity (“Finished S1”) exceeds the current job quantity (“Current Job QTY S1”) in Figure 74. Alternatively a pull-system can be implemented, where the material sink start to produce a fixed lot size of the product variant with the lowest downstream inventory levels after completing each order. No production schedule is required.
Checking if the current machine configuration is correct for the next order: The required machine configuration for each product variant is specified in the input spreadsheets (see Figure 82). For a new job, the required
configuration is compared with the existing configuration. If these are not identical, a setup of a combination specific duration is completed based on
“Setup Matrix S1” (see Figure 75). To avoid circular logic, a support stock-flow is used to set the current configuration to the desired configuration at the end of the setup.
As soon as the setup time is completed, a work state can be resumed, assuming all other criteria are still fulfilled. In the work state, the specified variant (from the order) is produced at a variant-specific speed. The work state is then ended through the closure of the order after exceeding the order quantity, any incurred quality losses are deducted from the production speed during production. The quality losses deducted are represented by ML M1S1 (material loss through defects) in Figure 74, slightly simplified for transparency.
7.1.2 Depicting Peripheral Waste-Causing Activities
Material waste-causing activities that are not driven by the operating state of the main module are depicted in the peripheral module. One of these is the cleaning of the machine and the removal of material waste, which can either take place in fixed intervals (e.g. daily) or on a needs basis (i.e. when the accumulated waste for the material sink reaches a critical value). For example, in one process clean ups are completed once the accumulation of material waste, “Dirt Accu S1” exceeds a fixed “dirt limit” (see Figure 76). For each clean-up, a fixed rate of cleaning product is consumed. The accumulated cleaning waste counts towards the aggregate material waste.
7.1.3 Accumulated Waste
The accumulated amount of material waste is modelled as a separate flow-stock-flow chain for each material waste type as shown in Figure 77. System dynamics software cannot distinguish between materials in a single stock,
therefore multiple stocks should be used to model different homogenous waste piles. Process defects are modelled as material waste form “1” in all process modules. Unlike other waste forms, the rate of waste accumulated is deducted from the production speed, so that the main module continues to produce until the order quantity of good parts is reached. Aggregate material waste (sums by waste type over all processes) is modelled in the stock management module.
Similarly, from current operating-state dependent material waste rate of each material (“Current Mode MLR S1”) is calculated using the regression model presented in Section 6. The regression coefficients for both cases are located in an ExcelTM lookup (see Figure 82). Values of the waste amplifiers are modelled as random normal functions (e.g. employee qualification, “Local Quali S1” in Figure 78) or as material waste dependent (e.g. ambient conditions, “AC Unsuitability S1”).
Material waste flows attributed to transitions are dependent on the current material waste quantity (“Current Trans MLA S1”). The value of the material waste quantity is only held for one-time step (i.e. transition duration = 1 min).
In all cases the material waste accumulates over time, until it is disposed of by a peripheral housekeeping activity (see 7.1.2).
7.1.4 Modelling Logistical Performance
While the last few sections have focused on modelling the amount and cost of material waste, this thesis strives to identify material efficiency solutions without sacrificing logistical performance. The logistical performance of the system is modelled in the KPI monitoring module (see Figure 80) and briefly described below.
Total material cost is calculated as the sum of the material cost of good parts and the material waste cost (raw material purchase price and the disposal costs). The machine depreciation is modelled linearly over the simulated
period, assuming a write-off period of 20 years. The labor cost is a qualification dependent hourly rate a machine sink that is not in an “off” state, this may be a fraction of an hourly wage in the case of multiple machine operation. The machine utilization for each material sink can be modelled as the ratio of the hours spent in a “work” state to the total number of hours in the simulated period. The cost per piece can be calculated as the sum of all cost stocks divided by the throughput for all product variants.
The average throughput time of the system is estimated by dividing total inventory level of the system by the average daily customer demand, resulting in “days of inventory”. The delivery reliability can be measured by comparing an ideal dispatch flow (based on job due dates) with the actual shipment dates.