Suchergebnisse

AbstractWe study a class of new scheduling problems which involve types of teamwork tasks. Each teamwork task consists of several components, and requires a team of processors to complete, with each team member to process a particular component of the task. Once the processor completes its work on the task, it will be available immediately to work on the next task regardless of whether the other components of the last task have been completed or not. Thus, the processors in a team neither have to start, nor have to finish, at the same time as they process a task. A task is completed only when all of its components have been processed. The problem is to find an optimal schedule to process all tasks, under a given objective measure. We consider both deterministic and stochastic models. For the deterministic model, we find that the optimal schedule exhibits the pattern that all processors must adopt the same sequence to process the tasks, even under a general objective function GC = F(f1(C1), f2(C2), … , fn(Cn)), where fi(Ci) is a general, nondecreasing function of the completion time Ci of task i. We show that the optimal sequence to minimize the maximum cost MC = max fi(Ci) can be derived by a simple rule if there exists an order f1(t) ≤ … ≤ fn(t) for all t between the functions {fi(t)}. We further show that the optimal sequence to minimize the total cost TC = ∑ fi(Ci) can be constructed by a dynamic programming algorithm. For the stochastic model, we study three optimization criteria: (A) almost sure minimization; (B) stochastic ordering; and (C) expected cost minimization. For criterion (A), we show that the results for the corresponding deterministic model can be easily generalized. However, stochastic problems with criteria (B) and (C) become quite difficult. Conditions under which the optimal solutions can be found for these two criteria are derived. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

ABSTRACTWe consider a problem in which a distributor purchases fresh products from multiple supply sources for subsequent sale at a wholesale market. Due to uncontrollable factors such as traffic congestion or bad weather conditions, the time taken for the product to be delivered from each production origin is uncertain. As the wholesale market is open for trading only in a fixed‐time window, any fresh products arriving earlier face the risk of decay, and any arriving later cannot be sold. The market demand for the product is random and follows a general distribution. We formulate the basic problem as a multi‐source selection model with random yield, taking into account the trade‐off between purchasing cost and other costs such as deterioration loss arising from delivery uncertainty. We derive the optimal order quantities from different origins and propose algorithms to search for them. We also investigate the effects of delivery uncertainty on service level and transport mode selection. Finally, we examine two extensions. One considers a capacity limit in each production origin, and the other incorporates information updating. For the first extension, we propose algorithms to compute the optimal solution based on its structural properties. For the second problem, we derive the optimal purchasing policy according to updated information such as details of the arrivals of previous orders.