Presented topics were:
Vogel, J. and R. Stolletz (2018). Does the future matter? Optimization of time-dependent service systems.
A service provider of complex services can adjust the time spent with a customer due to subjective completion criteria. Physicians for example can increase the rate of serving patients by reducing the time spent with questioning the patient or by refraining from additional tests. Working at a high service rate decreases the quality provided to the customers but reduces the congestion in the service system. Furthermore, many service systems are faced by time-dependent demand changes.
Even though the trade-off between quality and speed has been extensively studied in the literature, no publication considers time-dependent demand. We present models to optimize time-dependent service rates based on forecasted demand patterns that minimize quality costs and waiting costs. An integrated optimization model is developed that approximates the time-dependent performance with a deterministic fluid approach or a stochastic stationary-backlog carryover (SBC) approach.
We present analytical and numerical results for the optimal service rate under stationary and time-dependent assumptions. Insight on the anticipation of demand changes in deterministic and stochastic systems are presented.
Schwarz, J. A. and R. Stolletz (2018): Structural properties of time-dependent flow production systems
Flow lines process workpieces sequentially on multiple stations. The processing times are often stochastic, hence buffers are installed to decouple the stations. For these systems, structural properties characterize the relationship between design variables such as buffer capacities and the performance measures expected throughput and expected work in process inventory. The identification of structural properties is important because of their algorithmic consequences for flow line design approaches. We review structural properties of flow lines with constant processing rates that have been proven or are numerically observed under steady-state conditions. Moreover, new monotonicity results for systems with time-dependent processing rates are introduced. These properties are based on sample-path arguments for the case of exponentially distributed processing times and supported by numerical evidence for general distributions.