This study aims to design a safe and sustainable food supply chain with food safety mechanisms so that confidence-dependent demand can be positively affected by centralized, decentralized and combined supply chain contracts. To determine the optimal order quantity, buy-back price, rebate/penalty and sales target with the proposed framework, we derive the optimality conditions of corresponding models and use the results to analyze the lard oil supply chain. It is found that supply chain contracts together with the food safety mechanism can drastically improve food safety, consumer confidence and the resulting profits of a food supply chain. What differentiates our work from earlier research efforts is that only few studies have focused primarily on food safety mechanisms that embed a closed-loop supply chain to benefit all stakeholders of a supply chain and we attempt to bridge the gap. Further improvements can be developed based on the models developed in this study.
In the transportation industry, crew management is typically decomposed into two phases: crew scheduling and crew rostering. Due to the complexity of scheduling and rostering, bus transportation is not an exception and many relevant studies do not consider both procedures simultaneously. However, such a decomposition can yield inferior schedules/rosters. To address this issue, this paper proposes an integrated scheduling and rostering model for bus drivers and devises a branch-and-price-and-cut (BPC) algorithm to solve the complex problem. The proposed solution framework is empirically applied to real-world instances with various problem sizes whose data is collected from H Bus Company located in southern Taiwan. To validate the effectiveness and evaluate the efficiency of the proposed solution framework, this paper compares the solution obtained from the BPC algorithm with that of a benchmark optimization package. The results show that the proposed BPC algorithm can solve problems with large real-world instances within a reasonable computational time. Moreover, in the numerical experiments, this paper finds that the scheduling and rostering results of the bus drivers are more sensitive to the rostering constraints. Also, the proposed integrated framework can yield a better solution than the solution from a conventional two-phase approach, which demonstrates the advantage of the integration in this paper. The proposed method provided can be employed to deal with the challenges in driver planning for bus companies.
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