scholarly journals Linear Programming Model and Online Algorithm for Customer-Centric Train Calendar Generation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Tommaso Bosi ◽  
Andrea D’Ariano
Keyword(s):  
Linear Programming ◽  
Online Algorithm ◽  
Programming Model ◽  
Strong Dependence ◽  
Computation Time ◽  
Linear Programming Model ◽  
Divide And Conquer ◽  
Problem Complexity ◽  
Ict System ◽  
Important Objective

An important objective for train operating companies is to let users, especially commuters, directly query the ICT system about trains’ availability calendar, based on an online approach, and give them clear and brief information, expressed through “intelligent” phrases instead of bit maps. This paper provides a linear programming model of this problem and a fast and flexible heuristic algorithm to create descriptive sentences from train calendars. The algorithmic method, based on the “Divide and Conquer” approach, takes the calendar period queried in its whole and divides it into subsets, which are successively processed one by one. The dominant limitation of previous methods is their strong dependence on the size and complexity of instances. On the contrary, our computational findings show that the proposed online algorithm has a very limited and constant computation time, even when increasing the problem complexity, keeping its processing time between 0 and 16 ms, while producing good quality solutions that differ by an average surplus of 0.13 subsentences compared to benchmark state-of-art solutions.

scholarly journals Minimal Total Weighted Tardiness in Tight-Tardy Single Machine Preemptive Idling-Free Scheduling

2019 ◽  
Vol 24 (2) ◽  
pp. 150-160 ◽  
Author(s):  
Vadim Romanuke
Keyword(s):  
Linear Programming ◽  
Single Machine ◽  
Programming Model ◽  
Computation Time ◽  
Linear Programming Model ◽  
Total Weighted Tardiness ◽  
Weighted Tardiness ◽  
Exact Model

Abstract Two possibilities of obtaining the minimal total weighted tardiness in tight-tardy single machine preemptive idling-free scheduling are studied. The Boolean linear programming model, which allows obtaining the exactly minimal tardiness, becomes too time-consuming as either the number of jobs or numbers of job parts increase. Therefore, a heuristic based on remaining available and processing periods is used instead. The heuristic schedules 2 jobs always with the minimal tardiness. In scheduling 3 to 7 jobs, the risk of missing the minimal tardiness is just 1.5 % to 3.2 %. It is expected that scheduling 12 and more jobs has at the most the same risk or even lower. In scheduling 10 jobs without a timeout, the heuristic is almost 1 million times faster than the exact model. The exact model is still applicable for scheduling 3 to 5 jobs, where the averaged computation time varies from 0.1 s to 1.02 s. However, the maximal computation time for 6 jobs is close to 1 minute. Further increment of jobs may delay obtaining the minimal tardiness at least for a few minutes, but 7 jobs still can be scheduled at worst for 7 minutes. When scheduling 8 jobs and more, the exact model should be substituted with the heuristic.

A Linear Programming Model for Product Mix Profit Maximization in A Small Medium Enterprise Company

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
S Mohd Baki ◽  
Jack Kie Cheng
Keyword(s):  
Linear Programming ◽  
Production Planning ◽  
Business Performance ◽  
Programming Model ◽  
Profit Maximization ◽  
Optimal Level ◽  
Linear Programming Model ◽  
Product Mix ◽  
Small Medium Enterprises ◽  
Medium Enterprises

Production planning is often challenging for small medium enterprises (SMEs) company. Most of the SMEs are having difficulty in determining the optimal level of the production output which can affect their business performance. Product mix optimization is one of the main key for production planning. Many company have used linear programming model in determining the optimal combination of various products that need to be produced in order to maximize profit. Thus, this study aims for profit maximization of a SME company in Malaysia by using linear programming model. The purposes of this study are to identify the current process in the production line and to formulate a linear programming model that would suggest a viable product mix to ensure optimum profitability for the company. ABC Sdn Bhd is selected as a case study company for product mix profit maximization study. Some conclusive observations have been drawn and recommendations have been suggested. This study will provide the company and other companies, particularly in Malaysia, an exposure of linear programming method in making decisions to determine the maximum profit for different product mix.

A Linear Programming Model to Evaluate Gas Availability for Vital Industries in Saudi Arabia

1992 ◽  
Vol 43 (11) ◽  
pp. 1035-1045
Author(s):  
S O Duffuaa ◽  
J A Al-Zayer ◽  
M A Al-Marhoun ◽  
M A Al-Saleh
Keyword(s):  
Saudi Arabia ◽  
Linear Programming ◽  
Programming Model ◽  
Linear Programming Model

Living costs and welfare ratios in Western Europe: new estimates using a linear programming model

2021 ◽  
Author(s):  
Luis Felipe Zegarra
Keyword(s):  
Linear Programming ◽  
Western Europe ◽  
Programming Model ◽  
Living Standards ◽  
Linear Programming Model ◽  
Nutrient Requirements ◽  
European Cities

Abstract This study provides new estimates on welfare ratios for London, Amsterdam, Paris, Strasbourg, Munich, and Leipzig for 1600–1850. I use a linear programming model to compute the basket that minimizes the food cost subject to nutrient requirements. For a balanced nutrition, I take into consideration that people should ingest not only calories and proteins, but also fat, iron, and some basic vitamins. The results suggest that living standards in Western Europe were lower than previously thought. However, like previous studies, this article suggests that welfare ratios in London were higher than in other European cities.

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