The introductory chapter consists of four sections. In Sect. 1. 1 we reveal the c- rent situation in hospitals that is faced by the management. We address the general issue of personnel scheduling in the service industry in Sect. 1. 2. Then we motivate our research by considering physicians as the scheduling object. In particular, we show the complex nature of physician scheduling in a hospital environment. The focus of the research is presented in Sect. 1. 3. Finally, we conclude the chapter by illustrating the outline of the thesis. 1. 1 General Economic Situation in Hospitals The mounting pressure in the health care industry to reduce costs is forcing hos- tals and related facilities to take a closer look at their staf?ng policies (see [111]). A primary dif?culty in reducing personnel costs, the major component of the budget, is the variability in demand and the need to assign staff to ?xed shifts. Furthermore, government run facilities, especially those in the European Union, are seeing their budgets cut in terms of real dollars despite an aging and more acutely ill patient population (e. g. , see [96]). It has been reported that up to a third of the hospitals in Germanyplan a reductionin staff (see [91]). The schedulingprocess is furtherc- plicated by the generally recognized importance of taking individual preferences intoaccount. Moreattractiveschedulespromotejobsatisfaction,increaseproduct- ity,and reduceturnover(cf. [2]). However,withoutimprovedschedulingprocedures that better match supplyto demand,the level of care that theynow providewill soon become unsustainable. 1.