Abstract
A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan. Different jobs call for dissimilar sizes of storing space in the process of transportation. A range of jobs of one customer in the problem have priority to be processed on two identical parallel machines without preemption and then delivered to the customer by two vehicles in batches. For this NP-hard problem, we first prove that it is impossible to have a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P = NP. Thereafter, we develop a polynomial heuristic for this problem, the worst-case ratio of which is bounded by 2.
Highlights
Production and distribution operations are two key operational functions in a supply chain; it is critical to integrate these two functions and schedule them jointly in a coordinated manner so as to achieve optimal operational performance [1]
The problem of interest is regarded as an integrated production and outbound distribution scheduling (IPODS) model of jobs with general size and a finite quantity of vehicles. erefore, in the following, we just review a few closely related research works
Some works on IPODS models with parallel machines and equal-size jobs were done, in which all the jobs have the same size
Summary
Production and distribution operations are two key operational functions in a supply chain; it is critical to integrate these two functions and schedule them jointly in a coordinated manner so as to achieve optimal operational performance [1]. Wang and Cheng [6] ever studied a model with two identical parallel machines and a single vehicle to minimize the makespan. Jiang and Tan [14] designed a polynomial-time heuristic with a worst-case ratio of 2 for the model with a single machine and two vehicles. Makespan of a schedule is defined as Cmax It is duration from one of the vehicles accomplishing delivery of the last batch to customers to the moment it goes back to the manufacturing system. Jobs in Jj | j ∈ S∗ and Jj | j ∉ S∗ are separately processed by machines M1 and M2 followed by assignment to two different batches, each of which is delivered by one vehicle, with the makespan of. Erefore, for the problem, there is no possibility for obtaining a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P NP
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