Real-world flexible resource profile scheduling with multiple criteria: learning scalarization functions for MIP and heuristic approaches

This article addresses a scheduling problem for a chemical research laboratory. Activities with potentially variable, non-rectangular resource allocation profiles must be scheduled on discrete renewable resources. A mixed-integer programming (MIP) formulation for the problem includes maximum time lags, custom resource allocation constraints, and multiple nonstandard objectives. We present a list scheduling heuristic that mimics the human decision maker and thus provides reference solutions. These solutions are the basis for an automated learning-based determination of coefficients for the convex combination of objectives used by the MIP and a dedicated variable neighborhood search (VNS) approach. The development of the VNS also involves the design of new neighborhood structures that prove particularly effective for the custom objectives under consideration. Relative improvements of up to 60% are achievable for isolated objectives, as demonstrated by the final computational study based on a broad spectrum of randomly generated instances of different sizes and real-world data from the company’s live system.