The management of planning problems confronting logistics service providers frequently involves complex decisions. For more than four decades now the crew assignment problem (to flights, duties, reserve activities, etc.) of the airlines has captured the attention of the Management and Operations Research community since crew members management is extremely complicated and may generate many problems that hinder the smooth operation, influencing the total company operations profit (Rosenberger, 2001). Therefore for airlines the efficient management of their crew staffs is considered to be a question of the highest economic relevance. In the process of managing airline operations, once the scheduling of flights is performed by the commercial department and once the nominal crew assignment is completed, the problem of scheduling the reserve activities is raised. The latter activity is, first, to scale the size of the crew reserve and then allocate the available crew on reserve activities, taking into account the various constraints. In the case considered here, we assume that the solutions of the crew scheduling problem (CSP) and of the size of reserve problem are already established; thus, we focus our interest only on the assignment of crew to reserve activities. The amount of necessary investments and the high operational costs supported by the air transportation sector as well as its hard competitive environment, has led airlines to pursue a permanent improvement in their management practice at the planning and operations levels. With the deregulation policies adopted by the air transportation administrations of many countries, this goal has gained a major momentum. To meet their daily commitments, airlines assign or reassign their available crew to the scheduled or unscheduled flights and reserve activities while satisfying regulations and other operational constraints. When these assignments are done in an ineffective way, they have to support substantial overcosts which can impair their survival as a firm. The crew reserve assignment problem is then of considerable importance for airlines; and consequently, since the pioneering work of (Simpson, 1969), there has been a lot of research done to improve its solution (Yoshihara & Sengoku, 2000; Sohoni, Johnson, & Bailey, 2004; Liping, 2006). From the point of view of complexity theory, this problem is considered to be a difficult one since it presents a combinatorial choice within time and space dimensions with complicating ingredients from the operational constraints. It appears also that this problem is strongly related to the scheduling problem of crews duties (preventive medical visits, training, license renewal, etc.). Thus, a global solution for the crew reserve assignment problem is requested. In this communication a solution approach based on efficient enumerative methods is proposed to solve simultaneously these related problems.
In most airlines, the crew reserve assignment is established empirically. Sometimes even no crew reserve is planned, and operational problems are solved on time (Gaballa, 1979). The decisions are not optimal and can be very expensive. In fact, some operators spend little time on this task and have focused more on development of crew rostering. The development of crew reserve planning is often based on fixed ratios and the occurrence of specific events and periods (bridges between holidays, vacation periods, etc.). This leads to an availability of reserves approximately equal for each day of the month with the exception of those periods where the size of the reserve is increased. However, an effective crew reserve planning should allow airlines to cope with unexpected operational situations such as: failure of a crew (illness, delayed delivery, absence, late arrival of the crew at the airport, etc.), technical failure generating a change in aircraft type, strikes, and delayed flights (traffic congestion or bad weather) which prevents the crew scheduled for a flight to be available (Gaballa, 1979; Sohoni, Bailey, Martin, Carter, & Johnson, 2003; Sohoni, Johnson, & Bailey, 2004). The programming of crew reserve activities may affects the productivity of the airlines. An unused crew on reserve represents a loss of potential flight hours, but a higher loss is generated when no crew reserve is available and the call for a backup crew becomes unavoidable. The call for a crew who was given a leave is never desirable given the disruption it will produce in his personal life.