Two‐agent scheduling with linear resource‐dependent processing times

Abstract

This paper considers a two‐agent scheduling problem with linear resource‐dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is NP‐hard in the ordinary sense, and there does not exist a polynomial‐time approximation algorithm with performance ratio unless P=NP; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.

Two-Agent Slack Due-Date Assignment Scheduling with Resource Allocations and Deteriorating Jobs

“…To improve the competition rate, the producer can allocate a certain amount of resources to each job to reduce the processing time. The multi-agent scheduling problem with resource allocation has been studied by Wang et al [17] for a two-agent scheduling with linear resource, for which a FPTAS is proposed for the NP-hard problem. Luo [18] studied the slack due date problem with convex resource, and presented an optimal solution algorithm with time complexity of O(N 3 ) for the two-agent minmax earliness, tardiness, and common decision variable, where N is the maximum number of jobs between the two agents.…”

Distributed scheduling problems in intelligent manufacturing systems

“…In the past decades, a large number of studies on scheduling problems in manufacturing and service systems have been conducted. These problems can be classified as single-machine scheduling [13,14] , parallel-machine scheduling [15,16] , flow-shop scheduling [17][18][19] , job-shop scheduling [20,21] , and their variants [22,23] . In recent years, researchers have proposed a new scheduling method, i.e., distributed scheduling, which aims at scheduling distributed manufacturing systems [24] .…”

Due-window assignment scheduling with learning and deterioration effects

“…Under CONW, SLKW, and DIFW assignments, we showed that these problems can be solved in polynomial time. Further extensions are addressing the above problems in the setting of flow shop and identical (unrelated) parallel machines, considering scheduling with resource-dependent processing times (Wang et al [26], and Wang et al [27]), or studying multitasking scheduling (Xiong et al [30]).…”