Allowable cut effects without even flow constraints

1984 ◽  
Vol 14 (3) ◽  
pp. 317-320 ◽  
Author(s):  
Clark S. Binkley
Keyword(s):  
Forest Management ◽  
Economic Analysis ◽  
General Situation ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
General Part ◽  
Flow Constraints

The allowable cut effect in harvest scheduling problems stems from the constraints which link harvests between periods. Historically, allowable cut effects have been associated with even flow constraints, but this is only one example of a more general situation. This paper describes two generic problems where allowable cut effects arise without any flow constraint. Allowable cut effects are a general part of the harvest scheduling problem. Valid economic analysis of forest management programs requires the inclusion of the positive or negative incomes associated with them.

scholarly journals A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Martin B. Bagaram ◽  
Sándor F. Tóth ◽  
Weikko S. Jaross ◽  
Andrés Weintraub
Keyword(s):  
Forest Management ◽  
Probability Space ◽  
Forest Growth ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
Progressive Hedging ◽  
Climate Uncertainty

Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

Systematische Navigation für die Reihenfolgeplanung/Systematic solution space navigation for job shop scheduling problems

2020 ◽  
Vol 110 (07-08) ◽  
pp. 563-571
Author(s):  
Edzard Weber ◽  
Eduard Schenke ◽  
Luka Dorotic ◽  
Norbert Gronau
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Solution Space ◽  
Comparative Test ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Job Shop Scheduling Problem ◽  
Shop Scheduling ◽  
Space Navigation ◽  
Systematic Solution

Dieser Beitrag stellt einen Algorithmus für das Job-shop-Scheduling-Problem vor, welcher den Lösungsraum indexiert und eine systematische Navigation zur Lösungssuche durchführt. Durch diese problemadäquate Aufbereitung wird der Lösungsraum nach bestimmten Kriterien vorzustrukturiert. Diese Problemrepräsentation wird formal beschrieben, sodass ihre Anwendung als Grundlage für ein navigationsorientiertes Suchverfahren dienen kann. Ein vergleichender Test mit anderen Optimierungsansätzen zeigt die Effizienz dieser Lösungsraumnavigation.   This paper presents an algorithm for the job-shop scheduling problem indexing the solution space and performing systematic navigation to find good solutions. By this problem-adequate preparation of the solution space, the solution space is pre-structured according to certain criteria. This problem representation is formally described so that its application can serve as a basis for a navigation-oriented search procedure. A comparative test with other optimization approaches shows the efficiency of this solution space navigation.

scholarly journals Realtime production scheduling and control systems in smart industry

Impact ◽  
2020 ◽  
Vol 2020 (8) ◽  
pp. 60-61
Author(s):  
Wei Weng
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Production Scheduling ◽  
Production Control ◽  
Optimal Solution ◽  
Scheduling Problem ◽  
Optimal Solutions ◽  
Scheduling Problems ◽  
Smart Industry ◽  
And Control

For a production system, 'scheduling' aims to find out which machine/worker processes which job at what time to produce the best result for user-set objectives, such as minimising the total cost. Finding the optimal solution to a large scheduling problem, however, is extremely time consuming due to the high complexity. To reduce this time to one instance, Dr Wei Weng, from the Institute of Liberal Arts and Science, Kanazawa University in Japan, is leading research projects on developing online scheduling and control systems that provide near-optimal solutions in real time, even for large production systems. In her system, a large scheduling problem will be solved as distributed small problems and information of jobs and machines is collected online to provide results instantly. This will bring two big changes: 1. Large scheduling problems, for which it tends to take days to reach the optimal solution, will be solved instantly by reaching near-optimal solutions; 2. Rescheduling, which is still difficult to be made in real time by optimization algorithms, will be completed instantly in case some urgent jobs arrive or some scheduled jobs need to be changed or cancelled during production. The projects have great potential in raising efficiency of scheduling and production control in future smart industry and enabling achieving lower costs, higher productivity and better customer service.

scholarly journals Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 246
Author(s):  
Yuri N. Sotskov ◽  
Еvangelina I. Mihova
Keyword(s):  
Graph Coloring ◽  
Precedence Constraints ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Mixed Graph ◽  
Coloring Problem ◽  
Release Times ◽  
Schedule Length ◽  
Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness for integer due dates to the scheduling problem, where along with precedence constraints given on the set of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set . We prove that the extended scheduling problem with integer release times of the jobs to minimize schedule length may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) to the vertices of the mixed graph such that, if two vertices and are joined by the edge , their colors have to be different. Further, if two vertices and are joined by the arc , the color of vertex has to be no greater than the color of vertex . We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs , have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.

scholarly journals 3/2-approximation algorithm for a single machine scheduling problem

2021 ◽  
Vol 17 (3) ◽  
pp. 240-253
Author(s):  
Natalia S. Grigoreva ◽  
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Scheduling Problem ◽  
Delivery Time ◽  
Scheduling Problems ◽  
Delivery Times ◽  
Jobshop Scheduling ◽  
Single Processor

The problem of minimizing the maximum delivery times while scheduling tasks on a single processor is a classical combinatorial optimization problem. Each task ui must be processed without interruption for t(ui) time units on the machine, which can process at most one task at time. Each task uw; has a release time r(ui), when the task is ready for processing, and a delivery time g(ui). Its delivery begins immediately after processing has been completed. The objective is to minimize the time, by which all jobs are delivered. In the Graham notation this problem is denoted by 1|rj,qi|Cmax, it has many applications and it is NP-hard in a strong sense. The problem is useful in solving owshop and jobshop scheduling problems. The goal of this article is to propose a new 3/2-approximation algorithm, which runs in O(n log n) times for scheduling problem 1|rj.qi|Cmax. An example is provided which shows that the bound of 3/2 is accurate. To compare the effectiveness of proposed algorithms, random generated problems of up to 5000 tasks were tested.

scholarly journals Mathematical models for a batch scheduling problem to minimize earliness and tardiness

2018 ◽  
Vol 11 (3) ◽  
pp. 390 ◽  
Author(s):  
Basar Ogun ◽  
Çigdem Alabas-Uslu
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Lean Manufacturing ◽  
Programming Model ◽  
Computational Study ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Earliness And Tardiness ◽  
Customer Orders

Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem is addressed to provide on-time completion of customer orders in the environment of lean manufacturing. The problem is to optimize partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components.Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid from inventory of final products. The first model is a non-linear integer programming model while the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented.Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times comparing to the other two models. It was also showed that the alternative model can solve moderate sized real-world problems.Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature since it includes new circumstances which may arise in real-world applications. This research, also, contributes the literature of batch scheduling problem by presenting new optimization models.

scholarly journals Harvest scheduling with spatial aggregation for two and three strip cut system under shelterwood management

2011 ◽  
Vol 57 (No. 6) ◽  
pp. 271-277 ◽  
Author(s):  
M. Konoshima ◽  
R. Marušák ◽  
A. Yoshimoto
Keyword(s):  
Spatial Aggregation ◽  
Decision Variable ◽  
Scheduling Problem ◽  
Harvest Scheduling ◽  
Aggregation Method ◽  
Management Units ◽  
Decision Variables ◽  
Optimal Harvest ◽  
Cutting System ◽  
Sequential Cuts

We propose a spatial aggregation method to solve an optimal harvest scheduling problem for strip shelterwood management. Strip shelterwood management involves either a two-cut system with a preparatory-removal cut cycle, or a three-cut system with a preparatory-establishment-removal cut cycle. In this study we consider these connected sequential cuts as one decision variable, then employ conventional adjacency constraints to seek the best combination of sequential cuts over space and time. Conventional adjacency constraints exclude any spatially-overlapped strips in the decision variables. Our results show the proposed approach can be used to analyze a strip shelterwood cutting system that requires "connectivity" of management units.

The Simulation Optimization for Job-Shop Scheduling Based on Plant Simulation Using Genetic Algorithm

2012 ◽  
Vol 217-219 ◽  
pp. 1444-1448
Author(s):  
Xiang Ke Tian ◽  
Jian Wang
Keyword(s):  
Genetic Algorithm ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Problems ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Job Shop Scheduling Problem ◽  
Shop Scheduling ◽  
Combinatorial Optimization Problems ◽  
Plant Simulation

The job-shop scheduling problem (JSP), which is one of the best-known machine scheduling problems, is among the hardest combinatorial optimization problems. In this paper, the key technology of building simulation model in Plant Simulation is researched and also the build-in genetic algorithm of optimizing module is used to optimize job-shop scheduling, which can assure the scientific decision. At last, an example is used to illustrate the optimization process of the Job-Shop scheduling problem with Plant Simulation genetic algorithm modules.

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