scholarly journals Integer Relaxation on Binary Quadratic Programming for Batching and Sequencing in Single Formulation to Minimize Total Actual Flow Times Criteria

2011 ◽  
Vol 2 (2) ◽  
pp. 1083
Author(s):  
Zahedi Zahedi
Keyword(s):  
Batch Scheduling ◽  
Scheduling Problem ◽  
Numerical Experience ◽  
Single Item ◽  
Binary Constraints ◽  
Decision Variables ◽  
Multiple Item ◽  
Batch Sizes ◽  
Actual Flow ◽  
Integer Relaxation

This paper examines batch scheduling problem that has batching and sequencing in single formulation for multiple-item case. The first step is to develop a model for single item single resource discussed in Zahedi (2008). The model determined batch sizes and their schedule simultaneously in single item case. This paper develops the model and algorithm for multiple-item case. The model functions to minimize total actual flow times. An algorithm for the model is developed using a relaxation of the binary constraints. The binary values for the decision variables are obtained from steps provided in algorithm. A numerical experience showing characteristics of this problem is presented. 

scholarly journals A single machine multi-job integer batch scheduling problem with multi due date to minimize total actual flow time

2021 ◽  
Vol 10 (3) ◽  
pp. 231-240
Author(s):  
Rinto Yusriski ◽  
Budi Astuti ◽  
Damawijaya Biksono ◽  
Tika Ayu Wardani
Keyword(s):  
Single Machine ◽  
Flow Time ◽  
Batch Scheduling ◽  
Batch Size ◽  
Simple Problem ◽  
Scheduling Problem ◽  
Due Dates ◽  
Due Date ◽  
Numerical Experience ◽  
Actual Flow

This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.

scholarly journals Multi-items Batch Scheduling Model for a Batch Processor to Minimize Total Actual Flow Time of Parts through the Shop

2018 ◽  
Vol 20 (1) ◽  
pp. 73-88
Author(s):  
Nita P.A Hidayat ◽  
Andi Cakravastia ◽  
T.M.A Ari Samadhi ◽  
Abdul Hakim Halim
Keyword(s):  
Flow Time ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Metal Working ◽  
Due Dates ◽  
Due Date ◽  
Batch Processor ◽  
Scheduling Model ◽  
Actual Flow

This study is inspired by a batch scheduling problem in metal working industry which guarantees to satisfy a due date as a commitment to customers. Actual flowtime adopts the backward scheduling approach and considers the due date. Using the actual flowtime as the objective means that the solution  is oriented to satisfy the due date, and simultaneosly to minimize the length of time of the parts spending in the shop. This research is to address a problem of scheduling batches consisting of multiple items of parts processed on a batch processor where the completed parts must be delivered several time at different due dates. We propose an algorithm to solve the problem.

scholarly journals How to use C-OAR-SE to design optimal standard measures

2016 ◽  
Vol 50 (11) ◽  
pp. 1924-1941 ◽  
Author(s):  
John R. Rossiter
Keyword(s):  
Future Research ◽  
Alternative Measure ◽  
Single Item ◽  
Content Type ◽  
Multiple Item ◽  
Measure Design ◽  
Alternative Measures ◽  
Accepted Practice ◽  
Meta Analyses ◽  
Convergent Validation

Purpose This paper aims to extend Rossiter’s C-OAR-SE method of measure design (IJRM, 2002, p. 19, p. 4, pp. 305-335; EJM, 2011, p. 45, p. 11, p. 12, pp. 1561-1588) by proposing five distinct construct models for designing optimally content-valid multiple-item and single-item measures. Design/methodology/approach The paper begins by dismissing convergent validation, the core procedure in Nunnally’s (1978) and Churchill’s (1979) psychometric method of measure design which allows alternative measures of the same construct. The method of dismissal is the mathematical demonstration that an alternative measure, no matter how highly its scores converge with those from the original measure, will inevitably produce different findings. The only solution to this knowledge-threatening problem is to agree on an optimal measure of each of our major constructs and to use only that measure in all future research, as is standard practice in the physical sciences. The paper concludes by proposing an extension of Rossiter’s C-OAR-SE method to design optimal standard measures of judgment constructs, the most prevalent type of construct in marketing. Findings The findings are, first, the mathematical dismissal of the accepted practice of convergent validation of alternative measures of the same construct, which paves the way for, second, the proposal of five new C-OAR-SE-based construct models for designing optimal standard measures of judgment constructs, three of which require a multiple-item measure and two of which a single-item measure. Practical implications The common practice of accepting alternative measures of the same construct causes major problems for the social sciences: when different measures are used, it becomes impossible, except by remote chance, to replicate findings; meta-analyses become meaningless because the findings are averaged over different measures; and empirical generalizations cannot be trusted when measures are changed. These problems mean that we cannot continue to accept alternative measures of the constructs and that, for each construct, an optimal standard measure must be found. Originality/value The ideas in this paper, which have untold value for the future of marketing as a legitimate science, are unique to Rossiter’s C-OAR-SE method of measure design.

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.

Preemptive scheduling with transportation delays between machines

2020 ◽  
Vol 15 (3) ◽  
pp. 829-847
Author(s):  
Ryma Zineb Badaoui ◽  
Mourad Boudhar ◽  
Mohammed Dahane
Keyword(s):  
Linear Programming ◽  
Neighborhood Search ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Programming Formulation ◽  
Content Type ◽  
Decision Variables ◽  
Linear Programming Formulation ◽  
Local Search Strategy ◽  
Two Stages

Purpose This paper studies the preemptive scheduling problem of independent jobs on identical machines. The purpose of this paper is to minimize the makespan under the imposed constraints, namely, the ones that relate the transportation delays which are required to transport a preempted job from one machine to another. This study considers the case when the transportation delays are variable. Design/methodology/approach The contribution is twofold. First, this study proposes a new linear programming formulation in real and binary decision variables. Then, this study proposes and implements a solution strategy, which consists of two stages. The goal of the first stage is to obtain the best machines order using a local search strategy. For the second stage, the objective is to determine the best possible sequence of jobs. To solve the preemptive scheduling problem with transportation delays, this study proposes a heuristic and two metaheuristics (simulated annealing and variable neighborhood search), each with two modes of evaluation. Findings Computational experiments are presented and discussed on randomly generated instances. Practical implications The study has implications in various industrial environments when the preemption of jobs is allowed. Originality/value This study proposes a new linear programming formulation for the problem with variable transportation delays as well as a corresponding heuristic and metaheuristics.

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.

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