Common Due Window Assignment Scheduling with Proportional Linear Deterioration Effects

In this paper, single-machine scheduling problems with proportional linear deterioration effects and common due window assignment simultaneously are considered. Two different objective functions are studied, the first is to minimize the sum of the number of early jobs, number of tardy jobs and due window location and due window size, the second is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Optimality properties for all problems are provided and polynomial time algorithms for solving these problems are given.

A Memetic Algorithm for Multiskill Resource-Constrained Project Scheduling Problem under Linear Deterioration

This paper proposes a general variable neighborhood search-based memetic algorithm (GVNS-MA) for solving the multiskill resource-constrained project scheduling problem under linear deterioration. Integrating a solution recombination operator and a local optimization procedure, the proposed GVNS-MA is assessed on two sets of instances and achieves highly competitive results. One set of benchmark instances is commonly used in the literature where the capability of the proposed algorithm to find high quality solutions is demonstrated, compared with the state-of-the-art algorithms in the literature. The other set revises the former through incorporating the linear deterioration effect. Two key components of the proposed algorithm are investigated to confirm their critical role to the success of the proposed method.

Batch Scheduling with Proportional-Linear Deterioration and Outsourcing

We consider the bounded parallel-batch scheduling with proportional-linear deterioration and outsourcing, in which the actual processing time is pj=αj(A+Dt) or pj=αjt. A job is either accepted and processed in batches on a single machine by manufactures themselves or outsourced to the third party with a certain penalty having to be paid. The objective is to minimize the maximum completion time of the accepted jobs and the total penalty of the outsourced jobs. For the pj=αj(A+Dt) model, when all the jobs are released at time zero, we show that the problem is NP-hard and present a pseudo-polynomial time algorithm, respectively. For the pj=αjt model, when the jobs have distinct m (<n) release dates, we provide a dynamic programming algorithm, where n is the number of jobs.