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.

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

2021 ◽  
pp. 928-946
Author(s):  
Shubin Xu ◽  
John Wang
Keyword(s):  
Genetic Algorithm ◽  
Medical Devices ◽  
Programming Model ◽  
Flow Time ◽  
Nonlinear Integer Programming ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Work In Process ◽  
Completion Times ◽  
Sum Of Completion Times

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

Applying Constraint Programming and Integer Programming to Solve the Crew Scheduling Problem for Railroad Systems: Model Formulation and a Case Study

2021 ◽  
pp. 036119812110363
Author(s):  
Guei-Hao Chen ◽  
Jyh-Cherng Jong ◽  
Anthony Fu-Wha Han
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Hybrid Approach ◽  
Crew Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Systems Model ◽  
Crew Scheduling Problem

Crew scheduling is one of the crucial processes in railroad operation planning. Based on current regulations and working and break time requirements, as well as the operational rules, this process aims to find a duty arrangement with minimal cost that covers all trips. Most past studies considered this subject for railroad systems as an optimization problem and solved it with mathematical programming-based methods or heuristic algorithms, despite numerous logical constraints embedded in this problem. Few studies have applied constraint programming (CP) approaches to tackle the railroad crew scheduling problem. This paper proposes a hybrid approach to solve the problem with a CP model for duty generation, and an integer programming model for duty optimization. These models have been applied to the Kaohsiung depot of Taiwan Railways Administration, the largest railroad operator in Taiwan. The encouraging results show that the proposed approach is more efficient than the manual process and can achieve 30% savings of driver cost. Moreover, the approach is robust and provides flexibility to easily accommodate related operational concerns such as minimizing the number of overnight duties. Thus, this hybrid two-phase approach seems to have the potential for applications to the railroad crew scheduling problems outside Taiwan.

scholarly journals Fitness Distance Correlation Strategy for Solving the RGV Dynamic Scheduling Problem

2020 ◽  
Vol 14 (3) ◽  
pp. 20-40
Author(s):  
Wei Li ◽  
Furong Tian ◽  
Ke Li
Keyword(s):  
Dynamic Scheduling ◽  
Programming Model ◽  
Operating Efficiency ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Distance Correlation ◽  
Fast Running ◽  
Stable Performance ◽  
Fitness Distance Correlation ◽  
Working Efficiency

Rail guide vehicle (RGV) problems have the characteristics of fast running, stable performance, and high automation. RGV dynamic scheduling has a great impact on the working efficiency of an entire automated warehouse. However, the relative intelligent optimization research of different workshop components for RGV dynamic scheduling problems are insufficient scheduling in the previous works. They appear idle when waiting, resulting in reduced operating efficiency during operation. This article proposes a new distance landscape strategy for the RGV dynamic scheduling problems. In order to solve the RGV dynamic scheduling problem more effectively, experiments are conducted based on the type of computer numerical controller (CNC) with two different procedures programming model in solving the RGV dynamic scheduling problems. The experiment results reveal that this new distance landscape strategy can provide promising results and solves the considered RGV dynamic scheduling problem effectively.

scholarly journals Analysis of usage of genetic and tabu search algorithms in shop scheduling

2008 ◽  
Vol 48 ◽  
Author(s):  
Edgaras Šakurovas ◽  
Narimantas Listopadskis
Keyword(s):  
Genetic Algorithms ◽  
Tabu Search ◽  
Real World ◽  
Job Shop ◽  
Flow Shop ◽  
Proper Time ◽  
Search Algorithms ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Shop Scheduling

A wide area of scheduling problem is industrial so-called shop scheduling (Job Shop, Flow Shop and Open Shop) which has important applications in real world industrial problems. Metaheuristic algorithms(Genetic and Tabu search algorithms in this case) seem to be one of the best candidates for finding nearbyoptima in proper time. In this work we implemented several genetic algorithms (separated by values oftheir parameters) and several Tabu search algorithms (separated by neighborhood of solution). Finally, implemented eight algorithms are examined for random shop scheduling problems in terms of variouscriteria.

scholarly journals Model and Algorithm for Human Resource-Constrained R&D Program Scheduling Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Junjie Chen ◽  
Shurong Tong ◽  
Hongmei Xie ◽  
Yafei Nie ◽  
Jingwen Zhang
Keyword(s):  
Project Scheduling ◽  
Optimization Problems ◽  
Programming Model ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Resource Constrained ◽  
Enumeration Algorithm ◽  
Resource Constrained Project Scheduling ◽  
Project Scheduling Problem

In resource-constrained project scheduling problems, renewable resources can be expanded into human resources with competency differences. A flexible resource-constrained project scheduling problem with competency differences is proposed, which is a practical extension close to Research and Development (R&D) program management, from the traditional multimode resource-constrained project scheduling problem. A parameter and estimation formula to measure staff competency is presented, and a mixed-integer programming model is established for the problem. The single-objective optimization problems of optimal duration and optimal cost are solved sequentially according to the biobjective importance. To solve the model, according to the assumptions and constraints of the model, the initial network diagram of multiple projects is determined, the enumeration algorithm satisfying constraint conditions provides the feasible solution sets, and the algorithm based on dynamic programming is designed for phased optimization. Experimental results show that the proposed optimization model considering competence differences can solve the problem effectively.

scholarly journals A SORTING IMPROVEMENT IN THE HEURISTIC BASED ON REMAINING AVAILABLE AND PROCESSING PERIODS TO MINIMIZE TOTAL TARDINESS IN PROGRESSIVE IDLING-FREE 1-MACHINE PREEMPTIVE SCHEDULING

2021 ◽  
Author(s):  
Vadim V. Romanuke
Keyword(s):  
Negative Impact ◽  
Computational Study ◽  
Total Tardiness ◽  
Release Dates ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Worst Case ◽  
Priority Weights

Background. In preemptive job scheduling, which is a part of the flow-shop sequencing tasks, one of the most crucial goals is to obtain a schedule whose total tardiness would be minimal. Total tardiness minimization is commonly reduced to solving a combinatorial problem which becomes practically intractable as the number of jobs and the numbers of their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in which the decisive ratio is the reciprocal of the maximum of a pair of the remaining processing period and remaining available period, is closely the best one. However, the heuristic may produce schedules of a few jobs whose total tardiness is 25 % greater than the minimum or even worse. Therefore, this heuristic needs a corrective branch which would further try to minimize total tardiness under certain conditions. Objective. The goal is to ascertain what is to be corrected in the heuristic so that the total tardiness value could be obtained lesser. The heuristic will be applied to tight-tardy progressive idling-free 1-machine preemptive scheduling, where the release dates are given in ascending order starting from 1 to the number of jobs, and the due dates are tightly set after the release dates. In this scheduling problem, the inaccuracy of finding the minimal total tardiness has the strongest negative impact, so this is almost the worst case, which defines the accuracy limit of the heuristic and positively serves just as the principle of minimax guaranteeing decreasing losses in the worst conditions. Methods. The heuristic sorts maximal decisive ratios by release dates, where the scheduling preference is given to the earliest job. To achieve the said goal, three other sorting approaches are presented and a computational study is carried out with applying each of the four heuristic approaches to minimize total tardiness. For this, two series of 266000 and 1064000 scheduling problems are generated. Results. The earliest-job sorting ensures a heuristically minimal total tardiness value in more than 97.6 % of scheduling problems, but it fails to minimize total tardiness in no less than 2.2 % of the cases. Nevertheless, a sorting approach with minimizing remaining processing periods produces a heuristically minimal total tardiness for almost any scheduling problem. If an exception occurs, this sorting approach “loses” to the other sorting approaches very little. Moreover, the exceptions are quite rare as it has been registered just a one scheduling problem (out of 31914 cases followed by a sole “win” of a heuristic version) whose minimal total tardiness is achieved by the earliest-job sorting. Conclusions. The best heuristic version is that one which uses the sorting approach with minimizing remaining processing periods. This, however, is confirmed only for the case where jobs do not have any priorities. The case when jobs have their priority weights is to be yet analyzed.

scholarly journals Scheduling of Anaesthesia Operations in Operating Rooms

Healthcare ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 640
Author(s):  
Pi-Yu Hsu ◽  
Shao-Hua Lo ◽  
Hsin-Gin Hwang ◽  
Bertrand M. T. Lin
Keyword(s):  
Integer Programming ◽  
Completion Time ◽  
Programming Model ◽  
Computational Study ◽  
Computing Time ◽  
Operating Rooms ◽  
Approximation Methods ◽  
Mathematical Form ◽  
Scheduling Problem ◽  
Surgical Operations

This paper considers scheduling of surgical operations across multiple operating rooms subject to the limited availability of anaesthetists. The objective is to construct a feasible operations schedule that has the minimum makespan, i.e., the completion time of all operations. We abstract the problem into a theoretical server scheduling problem and formulate it in a mathematical form by proposing an integer programming model. Due to the intractability of its computing time, we circumvent the exact approaches and develop two approximation methods. Then, the steepest descent search is adopted for improving the solutions. Computational study suggests that the proposed methods can produce quality solutions in a few seconds.

A multi-shop integrated scheduling algorithm with fixed output constraint

2021 ◽  
pp. 1-9
Author(s):  
Yingchun Xia ◽  
Zhiqiang Xie ◽  
Yu Xin ◽  
Xiaowei Zhang
Keyword(s):  
Constraint Programming ◽  
Programming Model ◽  
Scheduling Algorithm ◽  
Processing Parameters ◽  
Scheduling Problem ◽  
Integrated Scheduling ◽  
Scheduling Scheme ◽  
Wide Range ◽  
Constraint Programming Model ◽  
Output Constraint

The customized products such as electromechanical prototype products are a type of product with research and trial manufacturing characteristics. The BOM structures and processing parameters of the products vary greatly, making it difficult for a single shop to meet such a wide range of processing parameters. For the dynamic and fuzzy manufacturing characteristics of the products, not only the coordinated transport time of multiple shops but also the fact that the product has a designated output shop should be considered. In order to solve such Multi-shop Integrated Scheduling Problem with Fixed Output Constraint (MISP-FOC), a constraint programming model is developed to minimize the total tardiness, and then a Multi-shop Integrated Scheduling Algorithm (MISA) based on EGA (Enhanced Genetic Algorithm) and B&B (Branch and Bound) is proposed. MISA is a hybrid optimization method and consists of four parts. Firstly, to deal with the dynamic and fuzzy manufacturing characteristics, the dynamic production process is transformed into a series of time-continuous static scheduling problem according to the proposed dynamic rescheduling mechanism. Secondly, the pre-scheduling scheme is generated by the EGA at each event moment. Thirdly, the jobs in the pre-scheduling scheme are divided into three parts, namely, dispatched jobs, jobs to be dispatched, and jobs available for rescheduling, and at last, the B&B method is used to optimize the jobs available for rescheduling by utilizing the period when the dispatched jobs are in execution. Google OR-Tools is used to verify the proposed constraint programming model, and the experiment results show that the proposed algorithm is effective and feasible.

scholarly journals New Challenges Arising in Engineering Problems with Fractional and Integer Order

2021 ◽  
Vol 5 (2) ◽  
pp. 35
Author(s):  
Haci Mehmet Baskonus ◽  
Luis Manuel Sánchez Ruiz ◽  
Armando Ciancio
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Integer Order ◽  
Engineering Problems ◽  
New Challenges ◽  
Real World Problems

Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

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