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Energy-aware lot sizing problem: Complexity analysis and exact algorithms

INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 203卷 254-263页

作者： Rapine, Christophe Goisque, Guillaume Akbalik, Ayse Univ Lorraine LCOMS Technopole Metz Metz France Univ Lorraine Metz France

The single-item lot sizing problem under a periodic energy limitation is considered in this paper. Identical and parallel capacitated machines constitute the production system, each one consuming a certain amount of energy when being switched on, when reserved, and when producing. We consider a cost for starting-up the machines, a reservation cost to keep the machines ready for production, in addition to classical lot sizing costs, such as, joint setup cost, unit production cost and unit holding cost, all being time-dependent. Besides the classical lot sizing decisions of how much and in which periods to produce, we have to decide the number of machines to switch on and to switch off in each period. We show that this problem is NP-hard even under restricted conditions. In contrast, assuming stationary energy parameters, we propose two polynomial time dynamic programming algorithms to solve the problem to optimality. The first algorithm is proposed for the case with null setup cost, null reservation cost and null reservation energy consumption, and runs in O ((MT4)-T-5) time, with M being the number of machines and T the number of periods. We show that we can extend this algorithm to solve the generalized version of the problem in time complexity O ((MT6)-T-6).

关键词： Lot sizing problem Energy Capacitated parallel machines polynomial time algorithm Complexity

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polynomial time algorithmS FOR VARIANTS OF GRAPH MATCHING ON PARTIAL k-TREES

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FOUNDATIONS OF COMPUTING AND DECISION SCIENCES 2016年第3期41卷 163-181页

作者： Nagoya, Takayuki Tottori Univ Environm Studies 1-1-1 Wakabadai Kita Tottori Tottori 6891111 Japan

In this paper, we deal with two variants of graph matching, the graph isomorphism with restriction and the prefix set of graph isomorphism. The former problem is known to be NP-complete, whereas the latter problem is ... 详细信息

关键词： graph isomorphism with restriction partial k-trees polynomial time algorithm

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Inventory replenishment planning with a full truckload cost and a full return policy

Inventory replenishment planning with a full truckload cost ...

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16th IFAC Symposium on Information Control Problems in Manufacturing (INCOM)

作者： Farhat, Mlouka Akbalik, Ayse Sauer, Nathalie Hadj-Alouane, Atidel B. Univ Lorraine LGIPM Technopole F-57073 Metz France Univ Lorraine LCOMS Technopole F-57073 Metz France Univ Tunis El Manar OASIS Ecole Natl Ingenieurs Tunis BP 37 Le Belvedere Tunis 1002 Tunisia

This paper addresses the single-item uncapacitated lot sizing problem with batch ordering under the buyback contract between a retailer and a supplier. The form of this type of contract consists in returning all the unused products at the end of every w periods (with w >= 1) to the supplier. This problem is studied with only full batches (OFB), which means that the procurement in each period is restricted to a multiple of a constant batch size, where each demand is satisfied without backlogging and all cost parameters are time-dependent. In this extension, we consider a stepwise discontinuous procurement cost structure due to the fixed cost per batch replenished, incurred by the retailer, in addition to the classical lot sizing costs. Several properties of the optimal solution are proposed to develop an efficient dynamic programming algorithm performed in time complexity O(Tw). (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Lot sizing replenishment planning buyback contract stepwise cost polynomial time algorithm

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A new efficient algorithm for weighted vertex cover in bipartite graphs based on a dual problem 9

A new efficient algorithm for weighted vertex cover in bipar...

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9th International Conference on Information Technology in Medicine and Education (ITME)

作者： Zhang Yujiao Duan Xia Yue Xuerong Chen Zhibin Kunming Univ Sci & Technol Dept Math Fac Sci Kunming Yunnan Peoples R China

ISBN: (纸本)9781538677438

The (un-weighted) vertex cover problem in general graphs is a classical NP-hard problem, but it is polynomial time solvable in bipartite graphs. This paper considers two combinatorial optimization problems. One is the weighted vertex cover problem and the other is the so-called maximum edge packing problem. We proved that in bipartite graphs, maximum edge packing problem can be viewed as the dual of the weighted vertex cover problem, and hence these two problems are polynomial time solvable. We explored the relationships between these two problems in bipartite graphs and some structural results are obtained accordingly. Furthermore, a new efficient algorithm for the weighted vertex cover problem in bipartite graphs is also derived. Our method generalized some previous algorithms for un-weighted vertex cover in bipartite graphs.

关键词： matching vertex cover edge packing polynomial time algorithm dual problem

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Transmitting Particles in a Polygonal Domain by Repulsion 12th

Transmitting Particles in a Polygonal Domain by Repulsion

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12th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Mozafari, Amirhossein Shermer, Thomas C. Simon Fraser Univ Sch Comp Sci Burnaby BC Canada

ISBN: (纸本)9783030046514;9783030046507

In this paper, we introduce the problem of transmitting particles to a target point by the effect of a repulsion actuator (RA). In this problem, we are given a polygonal domain P and a target point t inside it. Also, there is a particle at each point of P. The question is which particles can get to the target point t by activating a RA in P. We present the first polynomial time algorithm to solve this problem.

关键词： Geometric algorithm Polygonal domain Repulsion actuator polynomial time algorithm

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Parallel Machine Scheduling with Rejection under Special Conditions 2018

Parallel Machine Scheduling with Rejection under Special Con...

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8th International Conference on Communication and Network Security (ICCNS)

作者： Zheng, Shengshi Yue, Xuerong Chen, Zhibin Kunming Univ Sci & Technol Dept Math Fac Sci Kunming Yunnan Peoples R China

ISBN: (纸本)9781450365673

We consider a version of parallel machine scheduling with rejection. There are m machines and n jobs, and each job is either accepted and then processed by one of the machines, or rejected and then a rejected fee is paid. The goal is to find a way of partitioning the set of jobs into two subsets, the subset of accepted and the subset of rejected jobs, the subset of accepted and the subset of rejected jobs, and to schedule all the accepted jobs to m machines such that the sum of the makespan and the total rejection fees of the rejected jobs is minimized. In this paper, we focus on a special case of this NP-hard problem where the processing time of each job is a power of 2. We show that if one more condition is satisfied, namely, if the ratio of rejection fee and processing time of each job can be indexed in the same way as the order of processing time, then the problem is polynomial time solvable. We therefore present an efficient algorithm for this case. Our result is also applicable to the case in which the processing times are the powers of q, where q is a positive integer.

关键词： Scheduling with rejection powers of 2 optimal solution polynomial time algorithm

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The stochastic lot-sizing problem with quantity discounts

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COMPUTERS & OPERATIONS RESEARCH 2017年 80卷 1-10页

作者： Jiao, Wen Zhang, Ju-Liang Yan, Hong Hong Kong Polytech Univ Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China Beijing Jiaotong Univ Sch Econ & Management Dept Logist Management Beijing 100044 Peoples R China

This paper addresses the stochastic lot-sizing problem with quantity discounts. In particular, we examine the uncapacitated finite-period economic lot-sizing problem in which the parameters in each period are random and discrete. When an order is placed, a fixed cost is incurred and an all-unit quantity discount is awarded based on the quantity ordered. The lead time is zero and the order is delivered immediately. First we study the case with overstocks by which the excess inventory incurs a holding cost. The objective in this case is to minimize the expected total cost including ordering and holding costs. The stochastic dynamics is modeled with a scenario tree. We characterize properties Of the optimal policy and propose a polynomial time algorithm with complexity O(n(3)) for single discount level, where n is the number of nodes in the scenario tree. We extend the results to cases allowing stockout and multi-discount levels. Numerical experiments are conducted to evaluate the performance of the algorithm and to gain the management insights. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Inventory Stochastic lot-sizing problem All-unit quantity discounts polynomial time algorithm

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Single machine scheduling with slack due dates assignment

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ENGINEERING OPTIMIZATION 2017年第4期49卷 709-717页

作者： Liu, Weiguo Hu, Xiangpei Wang, Xuyin Dalian Univ Technol Inst Syst Engn Dalian 116024 Peoples R China Northwest Normal Univ Sch Business Lanzhou Peoples R China

This paper considers a single machine scheduling problem in which each job is assigned an individual due date based on a common flow allowance (i.e. all jobs have slack due date). The goal is to find a sequence for jobs, together with a due date assignment, that minimizes a non-regular criterion comprising the total weighted absolute lateness value and common flow allowance cost, where the weight is a position-dependent weight. In order to solve this problem, an O (n log n) time algorithm is proposed. Some extensions of the problem are also shown.

关键词： Scheduling single machine polynomial time algorithm due date assignment

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NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期257卷 483-493页

作者： Akbalik, Ayse Hadj-Alouane, Atidel B. Sauer, Nathalie Ghribi, Houcem Univ Lorraine Lab LGIPM F-57012 Metz France Univ Tunis El Manar Ecole Natl Ingn Tunis OASIS BP 37 Le Belvedere Tunis 1002 Tunisia

In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred;and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomial time dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Inventory Lot sizing Capacity reservation contract Complexity polynomial time algorithm

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Clique coloring B₁-EPG graphs

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DISCRETE MATHEMATICS 2017年第5期340卷 1008-1011页

作者： Bonomo, Flavia Pia Mazzoleni, Maria Stein, Maya Univ Buenos Aires Fac Ciencias Exactas & Nat Dept Computac Buenos Aires DF Argentina Univ Buenos Aires CONICET Inst Invest Ciencias Computac ICC Buenos Aires DF Argentina Consejo Nacl Invest Cient & Tecn La Plata Argentina FCE UNLP Dept Matemat La Plata Argentina Univ Chile Dept Ingn Matemat Santiago Chile

We consider the problem of clique coloring, that is, coloring the vertices of a given graph such that no (maximal) clique of size at least two is monocolored. It is known that interval graphs are 2-clique colorable. In this paper we prove that B-1-EPG graphs (edge intersection graphs of paths on a grid, where each path has at most one bend) are 4-clique colorable. Moreover, given a B1-EPG representation of a graph, we provide a linear time algorithm that constructs a 4-clique coloring of it. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Clique coloring Edge intersection graphs Paths on grids polynomial time algorithm

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