This study addresses the shift-scheduling problem for nursery teachers. We propose two integer programming models: the shift preference maximization model and shift preference and fairness maximization model. The primary aim is to develop a scheduling framework that not only accommodates individual shift preferences but also upholds fairness, while adhering to stringent constraints regarding labor and facility resources. A key contribution of this research is the introduction of a method to quantify the degree of preference using integer values. The shift preference and fairness maximization model is designed to generate schedules that respect the shift preferences of full-time nursery teachers, considering both the intensity of their preferences and the fairness of these preferences among nursery teachers. A numerical analysis reveals that the proposed models significantly enhance the overall satisfaction levels among nursery teachers, outperforming previous schedules in both short-term and long-term scenarios. In addition, this study elucidates the correlation between the satisfaction of full-time nursery teachers and the associated costs of hiring part-time nursery teachers.
Cross-efficiency-based Malmquist productivity measurement involves both the selection of DEA-optimal weights across Malmquist states and the aggregation of heterogeneous peer assessments. This study develops the Inertial Cross-Efficiency Malmquist Productivity Index (I-CEMPI). The method retains the state-specific primary-optimal weighting sets and coordinates the four Malmquist states through minimum intertemporal adjustment, yielding a unique and reproducible weight representation while preserving primary DEA optimality. Peer Cross-Malmquist assessments are subsequently combined through strategic-perspective-balanced geometric aggregation, which preserves the multiplicative decomposition into efficiency change and technical change. Applying I-CEMPI to 440 listed Chinese SRDI “Little Giant” enterprises over 2019–2024 shows substantial scope for intertemporal selection within the empirical optimal sets. Perspective balancing produces larger changes in aggregate productivity assessments than intertemporal coordination, while comparisons with the standard MPI and a published Cross-GMPI show high overall agreement together with differences in a subset of firm-level classifications. Innovation productivity contracts over most horizons, with technical change accounting for the larger share of cumulative contraction. Strategic perspectives differ more clearly in their efficiency-change and technical-change compositions than in persistent aggregate productivity rankings.
With the development of e-commerce, there are many scenarios of trade-in in online channels. According to customers’ heterogeneous preferences, platforms can choose different combinations among timing of rebates (instant, deferred, and mixed rebates) and forms of rebates (cash and gift-card rebates) to maximize their profits. We derive the platform’s optimal rebates and profits for five different scenarios: instant rebate, deferred cash rebate, mixed cash rebate, deferred gift-card rebate, mixed gift-card rebate. Furthermore, we show that the platform should choose the deferred rebate strategy when the waiting cost of impatient consumers is relatively low, otherwise, they should choose the mixed rebate strategy. When the cross-selling profitability is relatively low, the cash rebate strategy is dominant, otherwise the gift-card rebate strategy is dominant. Finally, the platform is more inclined to choose the mixed rebate strategy under the cash rebate strategy, and the deferred strategy under the gift-card rebate strategy. The findings provide guidance to platforms on how best to choose the trade-in programs.
Fixed-sum output data envelopment analysis (DEA) models are extensions of DEA and have been widely used to measure the performance of decision-making units (DMUs) with fixed-sum outputs. Considering the opinions of other DMUs, a cross-equilibrium efficient frontier (EEF) efficiency method was proposed to rank DMUs, where each DMU can choose a favorable EEF to evaluate itself and the others. However, in some cases, the favorable EEFs of the DMUs are multiple. Multiple EEFs produce multiple cross-EEF efficiencies. To eliminate this flaw, this study proposes an interval cross-EEF evaluation model that allows DMUs to select all favorable EEFs to evaluate themselves and others. All DMUs with interval cross-EEF efficiencies can be fully ranked by applying the stochastic multi-criteria acceptability analysis approach. Finally, we demonstrate the effectiveness and feasibility of the proposed method using a dataset of 32 companies in the vehicle industry for the year 2022.
Conditional value-at-risk (CVaR) is a widely used measure for quantifying and controlling tail risk. In many applications, however, the loss distribution varies with observable contextual information, giving rise to contextual CVaR, which evaluates tail risk under a context-specific conditional distribution. Rather than estimating the conditional distribution from historical data, we exploit the Rockafellar-Uryasev representation to formulate both contextual CVaR estimation and optimization as optimization problems involving conditional expectations. Based on this formulation, we develop a unified data-driven predict-then-optimize framework. For a broad class of smoothing methods, the predicted objective admits a context-dependent weighted empirical formulation. When the weights are nonnegative and normalized, they induce a context-specific empirical probability distribution and preserve the convexity of the optimization problems. We study three representative methods, k-nearest neighbors, kernel smoothing, and kernel ridge regression, and establish consistency and explicit convergence rates for both estimation and optimization, thereby providing theoretical guarantees for the proposed framework. Numerical experiments in portfolio and inventory applications demonstrate the effectiveness of the proposed framework and support the theoretical findings.
