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In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities.

Bus bunching could seriously damage the stability of transit system. This resultant instability always causes a dissatisfying performance of transit system. Traditional bus bunching control methods (e.g., holding control strategy) add slack to schedules or adapt cruising speed. The control methods can alleviate bus bunching in theory, but it is difficult to apply to actual operation, especially in busy traffic. The short-turning strategy only deals with spatial concentration of demand in the existing literatures. We find that the short-turning strategy is also very effective in alleviating bus bunching. In this study, based on the passenger arrival rate of each stop and the spatial-temporal running time, a short-turning model with bunching penalty is developed, and the waiting time of passengers and the operation cost are also considered. Based on data from Beijing Transportation Information Center, we take the Yuntong 111 bus line of Beijing as an example. Compared with the currently used timetable, it is found that a 46.78% reduction in bus bunching is achieved by using the optimal timetable, and there is no increase in operating costs.

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