Deterministic and stochastic scheduling with teamwork tasks

Abstract

Abstract:We 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 ϭ F( f 1 (C 1 ), f 2 (C 2 ), . . . , f n (C n )), where f i (C i ) is a general, nondecreasing function of the completion time C i of task i. We show that the optimal sequence to minimize the maximum cost MC ϭ max f i (C i ) can be derived by a simple rule if there exists an order f 1 (t) Յ . . . Յ f n (t) for all t between the functions { f i (t)}. We further show that the optimal sequence to minimize the total cost TC ϭ ¥ f i (C i ) 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.

Deterministic assembly scheduling problems: A review and classification of concurrent-type scheduling models and solution procedures

“…T j Wagneur and Sriskandarajah (1993 2007CA Cai and Zhou (2004) PP DP Table 1: Summary of contributions in Section 4.1 ( * Notation is described in the additional on-line material)…”

“…Regarding general cost functions, Li and Ou (2007) and Li and Vairaktarakis (2007) address the DP 2 → 0 layout with a cost function, for which the authors develop some polynomial time heuristics. Cai and Zhou (2004) study the problem for max-type and sum-type non-decreasing functions of the completion times of the jobs in the context of teamworks. They present some problem properties and a dynamic programming procedure, although this reference is disconnected from the main stream of order scheduling and it partially overlaps with existing works.…”

Coordinated scheduling of customer orders with decentralized machine locations

“…This type of scheduling problems is usually referred to as "customer order scheduling" problems with dedicated machines. Various studies have been conducted on different variants of the problem (see Wagneur and Sriskandarajah 1993, Sung and Yoon 1998, Cai and Zhou 2004, Ahmadi et al 2005, Leung et al 2005a, 2005b, 2005c, 2006b, Li and Vairaktarakis 2006. However, in these "customer order scheduling" models, the machines are assumed to be located at the same location.…”