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Complex real-world scheduling problems often include multiple conflicting objectives. Decision makers (DMs) can express their preferences over those objectives in different ways, including as sets of weights which are used in a linear combination of objective values. However, finding good sets of weights that result in solutions with desirable qualities is challenging and currently involves a lot of trial and error. We propose a general method to explain objectives' values under a given set of weights using Shapley regression values. We demonstrate this approach on the Test Laboratory Scheduling Problem (TLSP), for which we propose a multi-objective solution algorithm and show that suggestions for weight adjustments based on the introduced explanations are successful in guiding decision makers towards solutions that match their expectations. This method is included in the TLSP MO-Explorer, a new decision support system that enables the exploration and analysis of high-dimensional Pareto fronts.