Manuskripte Aus Den Instituten Ff Ur Betriebswirtschaftslehre Der Universit at Kiel Audit{staa Scheduling by Column Generation

When scheduling its audit{sta , the management of an auditing rm encompasses a number of decisions. These may be grouped into several categories which di er markedly in terms of organizational echelon involved, length of the planning horizon and the planning periods, degree of aggregation of the audit tasks, degree of detail of the required information, and decision objective. In this paper we consider the medium{term problem the focus of which is to assign teams of auditors to the engagements. It constructs a schedule by determining the workload per auditor and week over a planning horizon of between three and twelve months. The objective of the model is to maximize the sum of the preferences of all assigned teams. As restrictions job completion, precedence and resource constraints have to be met. The problem is formulated as a set partitioning problem. We solve the LP{ relaxation of the set partitioning problem by column generation in order to compute tight upper bounds. Fortunately, the upper bounds obtained with the column generation approach are much tighter than those obtained by solving the LP{relaxation of a `standard' project scheduling model formulation. Furthermore, the column generation process is an order of magnitude faster than solving the LP{relaxation of the standard model formulation. Finally, the optimal solution of the continuous relaxation of the set partitioning problem is integral frequently and, hence, we have an optimal solution of the overall integer programming problem.