We present an approximate dynamic programming approach for making ambulance redeployment decisions in an emergency medical service system. The primary decision is where we should redeploy idle ambulances so as to maximize the number of calls reached within a given delay threshold. We begin by formulating this problem as a dynamic program. To deal with the high-dimensional and uncountable state space in the dynamic program, we construct approximations to the value functions that are parameterized by a small number of parameters. We tune the parameters of the value function approximations using simulated cost trajectories of the system. Computational experiments demonstrate the performance of the approach on emergency medical service systems in two metropolitan areas. We report practically significant improvements in performance relative to benchmark static policies.
We present an iterative cutting plane method for minimizing staffing costs in a service system subject to satisfying acceptable service level requirements over multiple time periods. We assume that the service level cannot be easily computed, and instead is evaluated using simulation. The simulation uses the method of common random numbers, so that the same sequence of random phenomena is observed when evaluating different staffing plans. In other words, we solve a sample average approximation problem.We establish convergence of the cutting plane method on a given sample average approximation. We also establish both convergence, and the rate of convergence, of the solutions to the sample average approximation to solutions of the original problem as the sample size increases. The cutting plane method relies on the service level functions being concave in the number of servers. We show how to verify this requirement as our algorithm proceeds. A numerical example showcases the properties of our method, and sheds light on when the concavity requirement can be expected to hold.
The recent development of intensity modulated radiation therapy (IMRT) allows the dose distribution to be tailored to match the tumour's shape and position, avoiding damage to healthy tissue to a greater extent than previously possible. Traditional treatment plans assume that the target structure remains in a fixed location throughout treatment. However, many studies have shown that because of organ motion, inconsistencies in patient positioning over the weeks of treatment, etc, the tumour location is not stationary. We present a probabilistic model for the IMRT inverse problem and show that it is identical to using robust optimization techniques, under certain assumptions. For a sample prostate case, our computational results show that this method is computationally feasible and promising-compared to traditional methods, our model has the potential to find treatment plans that are more adept at sparing healthy tissue while maintaining the prescribed dose to the target.
We consider the problem of minimizing staffing costs in an inbound call center, while maintaining an acceptable level of service in multiple time periods. The problem is complicated by the fact that staffing level in one time period can affect the service levels in subsequent periods.Moreover, staff schedules typically take the form of shifts covering several periods. Interactions between staffing levels in different time periods, as well as the impact of shift requirements on the staffing levels and cost should be considered in the planning. Traditional staffing methods based on stationary queueing formulas do not take this into account. We present a simulationbased analytic center cutting plane method to solve a sample average approximation of the problem. We establish convergence of the method when the service level functions are discretepseudoconcave. An extensive numerical study of a moderately large call center shows that the method is robust and, in most of the test cases, outperforms traditional staffing heuristics that are based on analytical queueing methods.
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