Parallel-Machine Scheduling to Minimize Flowtime, Holding, and Batch Delivery Costs

2014 ◽  
Vol 31 (06) ◽  
pp. 1450044 ◽  
Author(s):  
Yunqiang Yin ◽  
Shuenn-Ren Cheng ◽  
Chin-Chia Wu
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Optimal Number ◽  
Batch Size ◽  
Batch Delivery ◽  
Delivery Costs ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Delivery Scheduling

This paper considers a batch delivery scheduling problem in which n independent and simultaneously available jobs are to be processed on m unrelated or uniform parallel machines. The jobs scheduled on the same machine are delivered in batches to customers and the delivery date of a batch equals the completion time of the last job in the batch. The number of jobs in each delivery batch is constrained by the batch size, and the cost of delivering a batch depends not only on the number of jobs in the batch but also on the machine on which the batch is processed. The objective is to find jointly the optimal number of batches on each machine, the optimal assignment of jobs to the batches, and the optimal job processing sequence to minimize the sum of total flowtime, total holding time, and delivery costs. When the number of batches has a fixed upper bound, we present polynomial-time algorithms to solve the problems with unrelated and uniform parallel machines. If the bound constraint on the number of batches is relaxed, we provide polynomial-time algorithms to solve two special cases of the problem with uniform parallel machines.

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.

scholarly journals Preemptive Scheduling with Controllable Processing Times on Parallel Machines

2015 ◽  
Vol 3 (1) ◽  
pp. 68-76
Author(s):  
Guiqing Liu ◽  
Kai Li ◽  
Bayi Cheng
Keyword(s):  
Polynomial Time ◽  
Resource Use ◽  
Parallel Machines ◽  
Optimal Algorithm ◽  
Parallel Machine Scheduling ◽  
Controllable Processing Times ◽  
Scheduling Problems ◽  
Processing Times ◽  
Online Problems ◽  
Machine Scheduling Problems

AbstractThis paper considers several parallel machine scheduling problems with controllable processing times, in which the goal is to minimize the makespan. Preemption is allowed. The processing times of the jobs can be compressed by some extra resources. Three resource use models are considered. If the jobs are released at the same time, the problems under all the three models can be solved in a polynomial time. The authors give the polynomial algorithm. When the jobs are not released at the same time, if all the resources are given at time zero, or the remaining resources in the front stages can be used to the next stages, the offline problems can be solved in a polynomial time, but the online problems have no optimal algorithm. If the jobs have different release dates, and the remaining resources in the front stages can not be used in the next stages, both the offline and online problems can be solved in a polynomial time.

scholarly journals Internet shopping optimization problem

2010 ◽  
Vol 20 (2) ◽  
pp. 385-390 ◽  
Author(s):  
JACEK B£A ZÿEWICZ ◽  
Mikhail Kovalyov ◽  
Jędrzej Musiał ◽  
Andrzej Urbanski ◽  
Adam Wojciechowski
Keyword(s):  
Polynomial Time ◽  
Optimization Problem ◽  
Partial Solution ◽  
The Internet ◽  
Internet Shopping ◽  
Single Product ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Multiple Item ◽  
Np Hardness

Internet shopping optimization problemA high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.

BIPARTITIONING INTO OVERLAPPING SETS

1995 ◽  
Vol 06 (01) ◽  
pp. 67-88
Author(s):  
JAMES HARALAMBIDES ◽  
SPYROS TRAGOUDAS
Keyword(s):  
Parallel Machines ◽  
Np Hard ◽  
Vlsi Layout ◽  
Grid Graphs ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Partitioning Problem ◽  
Overlapping Sets ◽  
Min Cut ◽  
Flow Techniques

We consider a generalization of the min-cut partitioning problem where we partition a graph G=(V,E) into two sets V1 and V2 such that |V1∩V2|≤d, d<|V|, and such that |{(u, v)|u∈V1−V2, v∈V2−V1}| is minimized. The problem is trivially solvable using flow techniques for any fixed d, but we show that it is NP-hard for integer values of d. It remains NP-hard if we impose restrictions on the size of V1, i.e., |V1|=k, k∈Z+. The latter problem variation may apply in VLSI layout and hypertext partitioning. We present polynomial time algorithms for the special cases of solid grids and series-parallel graphs. Series-parallel graphs find applications in hypertext partitioning whereas grid graphs model the mapping of a class of Partial Differential Equation computations into parallel machines.

scholarly journals The Complexity of Pattern Matching for $321$-Avoiding and Skew-Merged Permutations

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Michael H. Albert ◽  
Marie-Louise Lackner ◽  
Martin Lackner ◽  
Vincent Vatter
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Matching Problem ◽  
Polynomial Time Algorithms ◽  
Permutation Pattern ◽  
Special Cases ◽  
Np Complete

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first algorithm is applicable if both $\pi$ and $\tau$ are $321$-avoiding; the second is applicable if $\pi$ and $\tau$ are skew-merged. Both algorithms have a runtime of $O(kn)$, where $k$ is the length of $\pi$ and $n$ the length of $\tau$.

scholarly journals Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

2019 ◽  
Author(s):  
Yongjie Yang
Keyword(s):  
Polynomial Time ◽  
Control Problems ◽  
Fixed Parameter Tractability ◽  
Voting Rules ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Fixed Parameter ◽  
And Control ◽  
Manipulation And Control

We study the complexity of several manipulation and control problems for six prevalent approval based multiwinner voting rules. We show that these rules generally resist the proposed strategic types. In addition, we also give fixed-parameter tractability results for these problems with respect to several natural parameters and derive polynomial-time algorithms for certain special cases.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

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