scholarly journals Graph Coloring based Heuristic for Crew Rostering

2020 ◽  
Author(s):  
László Hajdu ◽  
Attila Tóth ◽  
Miklós Krész

In the last years personnel cost became a huge factor in the financial management of many companies and institutions.The firms are obligated to employ their workers in accordance with the law prescribing labour rules. The companies can save costs with minimizing the differences between the real and the expected worktimes. Crew rostering is assigning the workers to the previously determined shifts, which has been widely studied in the literature. In this paper, a mathematical model of the problem is presented and a two-phase graph coloring method for the crew rostering problem is introduced. Our method has been tested on artificially generated and real life input data. The results of the new algorithm have been compared to the solutions of the integer programming model for moderate-sized problems instances.

2013 ◽  
Vol 361-363 ◽  
pp. 2070-2074
Author(s):  
Ji Hui Ma ◽  
Tao Liu ◽  
Wei Guan

This paper addresses the balanced bus crew rostering problem (BBCRP). In this problem, the duty assignment to bus crews in a given time horizon should satisfy that the total workload should be evenly distributed. We firstly formulate the problem as a multi-level balanced assignment problem. Then, a genetic algorithm-based approach is designed to solve the proposed model. Finally, a simple numerical example is given to illustrate the application of the approach. Implementation results show that the proposed approach can obtain good quality solutions in a reasonable time and can be applied to real-life BBCRPs.


Author(s):  
Simona Filipova-Petrakieva ◽  
Ivan Stankov

Transport problem is a basic problem arising in transportation the products from several distributors to several clients. The solution of this problem consists of determining optimal transportation according to needed allocations the products. In fact, this problem describes with linear programming model which in general solves with simplex method. The algorithm of this method is a build-in tool for Excel – SOLVER. Unfortunately when it has the large amount of input data the filling of the Excel’s tables is a very difficult process. Thus, in this paper is suggested an add-in which visualize and make easier inputting the initial data. It is based on the Visual Studio tools for development the add-ins for MS Office. The main advantage of this solution consists of a user-friendly interface of the mathematical model of the problem which significantly makes easily and good visualization the input data and final solution in tables. As an illustrative example, the proposed add-in is applied for solving the real problem connected with transportation the products of pharmacy company.


Author(s):  
Gilberto Pérez Lechuga ◽  
Otilio A. Acevedo Sandoval ◽  
Karla N. Madrid Fernández ◽  
Raúl Román Aguilar

In this chapter, the authors present a mathematical model to calculate the exact quantities of animals that must compose a herd given the water, food, and land conditions available for their breeding. In the same model, the optimal calculation of vegetables that can be cultivated in the available land spaces is incorporated considering the same restrictions of water, nutrients, and area available for planting. Both models focus primarily from a deterministic perspective. Subsequently, the randomness of the same is uncovered through the uncertainty in the availability of water. Therefore, the first part of the proposal is made through a simple model of linear mathematical programming. The stochastic model is constructed from a two-phase mathematical programming model. The novelty of the proposal and its contribution consists of illustrating, step by step, the construction and solution of the scenarios of the stochastic model for a problem related to agriculture and animal husbandry.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhiqiang Tian

This paper studies the crew rostering problem with the consideration of multilicense of crewmembers. A 0-1 integer programming model is established to minimize the number of crewmembers used and to maintain the working time balance and the income balance of crewmembers. The method for calculating the reasonable cycle schemes is designed by considering the parameters of monthly working time standard and the number and the average working time of crew routes. The order for selecting the optimal cycle scheme is then determined with consideration of the connection relationships between crew routes. According to the characteristics of the problem and the requirements in application, this paper presents the design of an improved ant colony algorithm for solving the optimization model. The reasonableness of the model and the effectiveness of the algorithm are verified by a numerical example with 43 generated crew routes.


2021 ◽  
Vol 43 (1) ◽  
pp. 1-73
Author(s):  
David J. Pearce

Rust is a relatively new programming language that has gained significant traction since its v1.0 release in 2015. Rust aims to be a systems language that competes with C/C++. A claimed advantage of Rust is a strong focus on memory safety without garbage collection. This is primarily achieved through two concepts, namely, reference lifetimes and borrowing . Both of these are well-known ideas stemming from the literature on region-based memory management and linearity / uniqueness . Rust brings both of these ideas together to form a coherent programming model. Furthermore, Rust has a strong focus on stack-allocated data and, like C/C++ but unlike Java, permits references to local variables. Type checking in Rust can be viewed as a two-phase process: First, a traditional type checker operates in a flow-insensitive fashion; second, a borrow checker enforces an ownership invariant using a flow-sensitive analysis. In this article, we present a lightweight formalism that captures these two phases using a flow-sensitive type system that enforces “ type and borrow safety .” In particular, programs that are type and borrow safe will not attempt to dereference dangling pointers. Our calculus core captures many aspects of Rust, including copy- and move-semantics, mutable borrowing, reborrowing, partial moves, and lifetimes. In particular, it remains sufficiently lightweight to be easily digested and understood and, we argue, still captures the salient aspects of reference lifetimes and borrowing. Furthermore, extensions to the core can easily add more complex features (e.g., control-flow, tuples, method invocation). We provide a soundness proof to verify our key claims of the calculus. We also provide a reference implementation in Java with which we have model checked our calculus using over 500B input programs. We have also fuzz tested the Rust compiler using our calculus against 2B programs and, to date, found one confirmed compiler bug and several other possible issues.


2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hongyan Li ◽  
Xianfeng Ding ◽  
Jiang Lin ◽  
Jingyu Zhou

Abstract With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ w = ( 0.112 , 0.097 , 0.496 , 0.395 ) of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ α = 0.32 and $\beta =0.40$ β = 0.40 , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.


2021 ◽  
Vol 375 ◽  
pp. 111062
Author(s):  
Shambhavi Nandan ◽  
Florian Fichot ◽  
Fabien Duval

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 177
Author(s):  
Suzana Uran ◽  
Matjaž Malok ◽  
Božidar Bratina ◽  
Riko Šafarič

Constructing a micro-sized microfluidic motor always involves the problem of how to transfer the mechanical energy out of the motor. The paper presents several experiments with pot-like microfluidic rotational motor structures driven by two perpendicular sine and cosine vibrations with amplitudes around 10 μm in the frequency region from 200 Hz to 500 Hz. The extensive theoretical research based on the mathematical model of the liquid streaming in a pot-like structure was the base for the successful real-life laboratory application of a microfluidic rotational motor. The final microfluidic motor structure allowed transferring the rotational mechanical energy out of the motor with a central axis. The main practical challenge of the research was to find the proper balance between the torque, due to friction in the bearings and the motor’s maximal torque. The presented motor, with sizes 1 mm by 0.6 mm, reached the maximal rotational speed in both directions between −15 rad/s to +14 rad/s, with the estimated maximal torque of 0.1 pNm. The measured frequency characteristics of vibration amplitudes and phase angle between the directions of both vibrational amplitudes and rotational speed of the motor rotor against frequency of vibrations, allowed us to understand how to build the pot-like microfluidic rotational motor.


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