scholarly journals Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Cuixia Miao
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Parallel Machine ◽  
Batch Scheduling ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Identical Parallel Machine ◽  
Parallel Machine Problem ◽  
Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

scholarly journals Scheduling on a Single Machine and Parallel Machines with Batch Deliveries and Potential Disruption

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hua Gong ◽  
Yuyan Zhang ◽  
Puyu Yuan
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Manufacturing Industry ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Approximation Schemes ◽  
Scheduling Problems ◽  
Delivery Scheduling ◽  
Production Part

In this paper, we study several coordinated production-delivery scheduling problems with potential disruption motivated by a supply chain in the manufacturing industry. Both single-machine environment and identical parallel-machine environment are considered in the production part. The jobs finished on the machines are delivered to the same customer in batches. Each delivery batch has a capacity and incurs a delivery cost. There is a situation that a possible disruption in the production part may occur at some particular time and will last for a period of time with a probability. We consider both resumable case and nonresumable case where a job does not need (needs) to restart if it is disrupted for a resumable (nonresumable) case. The objective is to find a coordinated schedule of production and delivery that minimizes the expected total flow times plus the delivery costs. We first present some properties and analyze the NP-hard complexity for four various problems. For the corresponding single-machine and parallel-machine scheduling problems, pseudo-polynomial-time algorithms and fully polynomial-time approximation schemes (FPTASs) are presented in this paper, respectively.

POLYNOMIAL APPROXIMATION SCHEMES FOR THE MAX-MIN ALLOCATION PROBLEM UNDER A GRADE OF SERVICE PROVISION

2009 ◽  
Vol 01 (03) ◽  
pp. 355-368 ◽  
Author(s):  
JIANPING LI ◽  
WEIDONG LI ◽  
JIANBO LI
Keyword(s):  
Polynomial Time ◽  
Service Provision ◽  
Processing Time ◽  
Approximation Scheme ◽  
Allocation Problem ◽  
Approximation Schemes ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Running Time ◽  
Grade Of Service

The max-min allocation problem under a grade of service provision is defined in the following model: given a set [Formula: see text] of m parallel machines and a set [Formula: see text] of n jobs, where machines and jobs are all entitled to different levels of grade of service (GoS), each job [Formula: see text] has its processing time pj and it can only be allocated to a machine Mi whose GoS level is no more than the GoS level the job Jj has. The goal is to allocate all jobs to m machines to maximize the minimum machine load among these m machines, where the machine load of Mi is the sum of the processing time of jobs executed on Mi. The best known approximation algorithm [4] to solve this problem produces an allocation in which the minimum machine completion time is at least Ω ( log log log m/ log log m) of the optimal value. In this paper, we respectively present four approximation schemes to solve this problem and its two special versions: (1) a polynomial time approximation scheme (PTAS) with a running time [Formula: see text] for the general version, where ϵ > 0; (2) a PTAS and a fully polynomial time approximation scheme (FPTAS) with the running time O(n) for the version where the number m of machines is fixed; (3) a PTAS with the running time O(n) for the version where the number of GoS levels is bounded by k.

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