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In this research, based on two deterministic-demand planning models, we established two long-term stochastic-demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic-demand and two deterministic-demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation-based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. usually varies. The projected manpower demand may not reflect the actual manpower demand where stochastic disturbances may occur.A planned terminal manpower supply plan is the basis for the real future operations. Real operations must fulfill the planning objectives by implementing the planned terminal manpower supply plan. Thus, the inter-relationship between the planned terminal manpower supply plan and the real operations must be kept in mind when dealing with real problems with stochastic manpower demands. When these real stochastic manpower demands are not considered, then deterministicdemand models, based on the average (or projected) demand, will tend to use resources too tightly, resulting in an overly optimistic 'optimal' terminal manpower supply plan. Although this terminal manpower supply plan may be shown to be good in the planning stage, it may produce larger variations in performance when applied in real operations, where stochastic demands often occur. In the worst-case scenario, where demand fluctuates wildly during weekly operations, then the planned terminal manpower supply plan could be disturbed enough to lose its optimality. Therefore, to set a good terminal manpower supply plan, not only the related supply but also the stochastic manpower demand fluctuations in actual operations have to be taken into account.In practice, terminal manpower supply plans are usually classified into short-and long-term ones. The short-term terminal manpower supply plan, which involves the current terminal's operations, is usually performed before the beginning of the next period (generally seasonally). On the other hand, the long-term terminal manpower supply plan is usually performed at the beginning of the year (or several years in advance), according to the predicted cargo/manpower demands from historical information. Moreover, the long-term terminal manpower supply plan may have also taken into consideration the terminal's policy in the long run. The constraints in these two types of plans are different. In particular, the available manpower supply for the short-term plan is constrained by the current manpower resource. However, the manpower supply for the long-term plan is generally not constrained and is used as a reference for the termin...

The purpose of this research is to develop two manpower supply planning models and a solution algorithm for mass rapid transit carriage maintenance under mixed deterministic and stochastic demands. These models are formulated as mixed integer programs that are characterized as NP-hard. We employ problem decomposition techniques, coupled with the CPLEX mathematical programming solver, to develop an algorithm that is capable of efficiently solving the problems. The models and the method used currently in actual operations are evaluated by a simulation-based evaluation method. Finally, we perform a case study using real operating data from a Taiwan MRT maintenance facility. The preliminary results are good, showing that the models could be useful for planning carriage maintenance manpower supply.

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In the original article (Chen et al. 2010), the authors inadvertently did not reference their previous work to which this article (Chen et al. 2010) is related. The reference list has been updated with the addition of Chen et al.