Presented topics were:
Vogel, J. and R. Stolletz (2018). Does the future matter? Optimization of time-dependent service systems
In many service systems the service time of tasks is set according to the service worker's subjective standards. Such services are termed customer-intensive (Anand et al., 2011) or discretionary tasks (Hopp et al., 2007). Empirical studies show that the value for the customer increases with the service time due to a higher quality of the provided service (Oliva and Sterman, 2001). At the same time, however, long service times lead to congestion in the system. Thus, a trade-off between quality and speed has to be analyzed. The management of service systems faced by the quality-speed trade-off is discussed for example for physicians diagnosing patients, imaging tests in health care units, up-selling in inbound call centers, and personal care.
We consider a single stage service system modeled as an M(t)/
In the last ten years, research extensively studies the optimization of customer-intensive services for endogenous and exogenous demand. (i) Papers that consider the optimization of service rates for endogenous demand do not consider future changes in the initial demand (Anand et al., 2011). (ii) For exogenous but stationary demand, Hopp et al. (2007) consider the service rate optimization of an M/
We develop integrated optimization models that solve the stationary and time-dependent optimization problem. First, closed form solutions for the optimal service rate in the stationary system are derived. Second, for time-dependent systems a stationary backlog-carryover (SBC) approach is presented. Since the service rates are the decision variables in this optimization model, we develop an iterative SBC (iSBC) approach that calibrates the period lengths to the result of the optimization. The resulting non-linear optimization models are solved numerically.
The analytical solution for the stationary systems show that the optimal service rate is not necessarily increasing in the demand if the sojourn time is considered in the objective function. For small and increasing arrival rates the service rate is decreasing because in those cases the increase in the service value exceeds the increase in the waiting cost. For the time-dependent model, a numerical study shows the reliability of the iSBC-approach compared to a period-wise stationary approach that applies the stationary closed-form formulas in each period of the planning horizon.
As a managerial insight in the time-dependent model it is found that the optimal service rates depend on later changes in the demand. For decreasing demand for example, the service rates decrease significantly before the demand decrease. After the demand change, the optimized service rates decrease smoothly until they reach the new steady-state value. It is demonstrated that customer-intensive services can be improved by considering information of demand changes in the decision.
Schwarz, J. A. (2018). Sales and operations planning for product rollovers with finite production capacities