Tratados del Perú

As mentioned, various heuristics or exact solution methods have been used within the papers that we have assessed. However, optimizing the proposed objective functions is not necessarily bounded by these set of heuristics. Frequently, we found studies that use a Simulated Annealing (SA) or Tabu Search (TS) approach to optimize their objective (Beli¨en et al., 2009; van Essen et al., 2014; F¨ugener et al., 2014). Besides SA or TS, various other heuristics are also applicable to optimizing the MSS to an objective (F¨ugener et al., 2014). Another example is the study by Dellaert and Jeunet (2017). They use Variable Neighbourhood Search (VNS) to optimize their objective function of an MILP that was initially formulated by Adan et al. (2009). Their proposed version of VNS provided high quality solutions in short computational time in comparison with CPLEX. Van Essen et al. (2014) acknowledged that determining the required number of beds requires a lot of computational time and that SA can requires a lot of computational time. An approach such as SA is known to be able to jump out of (poor) local optima (Kirkpatrick et al., 1983). However, if we use SA with a heuristic that swaps single specialties with each other, it searches its neighborhood and searching the total solution space computational extensive. On the other hand, if we use a heuristic that changes large parts of the solution, local improvements may not be found. Therefore, we want to use an approach that has the ability to jump out of (poor) local optima and has the ability to change a varying size of the solution.

In recent studies of optimization heuristics, the Adaptive Large Neighborhood Search approach (ALNS) is proposed (Lutz, 2015; Ropke and Pisinger, 2006; Pisinger and Ropke, 2010). This heuristic is composed of a number of sub-heuristics that are used with a frequency corresponding to their historical performance (Pisinger and Ropke, 2010). It can be used in combination with the acceptance procedure of SA, which gives it the ability to jump out of local optima. On the base of a degree of destruction, ALNS destroys a varying part of the solution. Therefore, we consider ALNS to be a suitable heuristic to use in our optimization. Furthermore, we found a literature gap in the combination of ALNS optimization and MSSP.

4.6

Conclusions

In this section we presented recent literature reviews that encompass recent literature about oper- ating room scheduling on the tactical level. We explicitly searched for studies that linked the OR with downstream effects at nursing wards. The following research questions and answers conclude this chapter:

5: What kind of approaches can be used to optimize the surgery scheduling?

Many studies within this research field are focused on a single department and thereby ignore downstream effects of OR planning and scheduling. A single department approach leads to sub- optimal results and therefore we narrowed our literature research scope to multiple department approach. In the studies that remain, we found many deterministic approaches. By using a deter- ministic LOS or number of patients, uncertainty within healthcare processes is being ignored. In more recent studies we found studies that incorporate the stochasticity within their program.

6: What approach or model is best applicable?

A stochastic approach that has led to promising results is the approach by Vanberkel et al. (2011a).0 In various studies it has proven to lead to practical results (Vanberkel et al., 2011b; F¨ugener et al., 2014; van Essen et al., 2014). However, their approach is on itself an evaluation tool and it does not optimize the OR scheduling. We found two studies that used this approach and extended it to use it for optimization matters. Both studies compare and use exact approximation and local search approaches. Frequently, an SA approach is used to optimize an objective function. However, we have seen in recent literature that other heuristics are also applicable to solving the MSS problem. We want to be able to search the complete solution space within reasonable amount of computational time. Therefore, we want to use the ALNS heuristic in combination with an SA acceptance procedure. With this heuristic, we are able to search the complete solution space.

Chapter 5

Model Description

In this chapter we propose our approach to solve the Master Surgery Schedule Problem while considering the downstream effects of this planning. We structure this chapter on the base of the methodology by Law et al. (2007). Figure5.1shows a generalized flowchart of the steps the propose for a simulation study. We do not conduct a simulation study, but we consider the framework to be a good guideline for our research. The first two steps of the framework, the problem formulation and literature review, have been done in respectively Chapter 2 and Chapter 4. The conceptual model is presented in Section 5.1. In Section 5.2 we discuss how we gathered the data that is required for our model. In Section 5.3 we formulate our model. After that, a brief description of ward division in our model is given in Section 5.4. The verification and validation of the model is described in Section 5.5. We conclude this chapter in Section 5.6. The experimentation and implementation of the model are handled in Section 6.1and C¸ hapter 7.

Figure 5.1: Steps in a simulation study. Law et al. (2007)