The Average Sum Method for the Unbalanced Assignment Problems

Dubey, Sarvesh; Kumar, Ashok; Upadhyay, Virendra

doi:10.14445/22315373/ijmtt-v55p512

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…The company will experience losses when it comes to financing and time, and the company will benefit if the available sources get profits and wins. Existing sources affect the maximum and minimal analysis data (Dubey et al, 2018). Güneri et al, (2019), it is explained that to apply the Hungarian Method, the number of assigned resources must be equal to the number of tasks to be completed.…”

Section: Hungarian Methodsmentioning

confidence: 99%

Division of Tasks Using the Hungarian Method

Zain

Akbar

2022

JBMR

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Optimization is the process of optimizing existing resources in order to obtain effective and efficient results. The maximum division of tasks is when each employee does one job at a time. The division of work needs to be seriously handled so that every employee gets the maximum wage according to the working hours determined by the company. This research was conducted in the Rumah Jahit Nia, Sewing House industry in Pekanbaru City, Riau Province, Indonesia. The purpose of this study is that the company can divide each worker’s tasks to minimize the budget expenditure for paying overtime salaries so that the sources of financing and time used to complete the work are minimized. The research design uses quantitative data with applied research. The analysis method uses an assignment model with the Hungarian method. The completion of the Hungarian method is that the number of employees employed must be equal to the number of jobs that must be completed. In this study, the data source is seven employees with seven jobs to produce the minimum total financing. The study results obtained minimal financing with one employee doing one job. The minimization optimization results are Operator A, assignment IV financing Rp.13,333,-; Operator B, assignment VII with the financing of IDR 20,000; Operator C, assignment VI, financing Rp. 30,000, -; Operator D, assignment III with the financing of Rp. 25,333,-; Operator E, assignment I financing Rp. 25,000, - ; Operator F, assignment V financing Rp. 42,000, - ; Operator G, assignment II financing Rp.33,750,- Total minimum financing Rp.189,416,-.

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Section: Hungarian Methodsmentioning

confidence: 99%

Division of Tasks Using the Hungarian Method

Zain

Akbar

2022

JBMR

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“…"A Lexi-search algorithm" is employed by ( Yadaiah & Haragopal2, 2016) to allocate all tasks to resources effectively. (Dubey, et al, 2018) suggests an economical methodology of reaching the best assignments and the answer obtained is the same as results from Hungarian procedure but with fewer steps to reach the optimal solution.…”

Section: Artículomentioning

confidence: 99%

New Systematic Heuristic Based Approach to Cope With Unbalanced Assignment Problem Efficiently

2019

JAUS

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The assignment subject is always an old renewed problem that attracts the researchers for its fundamental relationship with productivity, efficiency, cost reduction and optimal utilization of resources in an age of competition and globalization. Assignment problem arises in diverse situations, where one needs to determine an optimal way to assign subjects to subjects in the best possible way. The assignment signifies the underlying combinatorial structure, while the objective function reflects the desires to be optimized as much as possible. In fact, this is a well-studied topic in combinatorial optimization problems under optimization or industrial engineering branches. A new heuristic innovative method is proposed to tackle the assignment problem in a clear systematic stepwise procedure, easy to follow without needing to initiate dummy activities in case of an unbalanced problem. The main aim of the developed procedure is to raise the efficiency of resource usage based on optimizing the objectives as loads are distributed to machines to the least possible variation to carry out all the work with the least possible time and almost to reach overall equilibrium loading. The procedure is enforced by illustration examples with complex relation between n and m. Keywords: Assignment Problem, Unbalance problem, Hungarian Method, Combinatorial Optimization, Efficiency RESUMEN/ El tema de la tarea es siempre un viejo problema renovado que atrae a los investigadores por su relación fundamental con la productividad, la eficiencia, la reducción de costos y la utilización óptima de los recursos en una era de competencia y globalización. El problema de asignación surge en diversas situaciones, donde uno necesita determinar una manera óptima de asignar sujetos a sujetos de la mejor manera posible. La asignación significa la estructura combinatoria subyacente, mientras que la función objetivo refleja los deseos de ser optimizados tanto como sea posible. De hecho, este es un tema bien estudiado en problemas de optimización combinatoria en las ramas de optimización o ingeniería industrial. Se propone un nuevo método innovador heurístico para abordar el problema de asignación en un procedimiento paso a paso claro y sistemático, fácil de seguir sin necesidad de iniciar actividades ficticias en caso de un problema desequilibrado. El objetivo principal del procedimiento desarrollado es aumentar la eficiencia del uso de los recursos basado en la optimización de los objetivos, ya que las cargas se distribuyen a las máquinas con la menor variación posible para llevar a cabo todo el trabajo con el menor tiempo posible y casi para alcanzar la carga de equilibrio general. El procedimiento se aplica mediante ejemplos de ilustración con una relación compleja entre n y m. Palabras clave: problema de asignación, problema de desequilibrio, método húngaro, optimización combinatoria, eficiencia Nuevo enfoque sistemático basado en la heurística para hacer frente al problema de asignación desequilibrada de manera eficiente  Publicación /28-08-2019...

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“…Clearly, the GAP considered in this paper can be transformed into a classical AP when some dummy jobs or agents are introduced. And the Hungarian method and its variants [24][25][26] are presented for optimizing GAP recently. However, the transformation will result in a larger-scale problem and worse space complexity.…”

Section: Introductionmentioning

confidence: 99%

A Network Flow Algorithm for Solving Generalized Assignment Problem

Liu

2021

Mathematical Problems in Engineering

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The generalized assignment problem (GAP) is an open problem in which an integer k is given and one wants to assign k ′ agents to k k ′ ≤ k jobs such that the sum of the corresponding cost is minimal. Unlike the traditional K -cardinality assignment problem, a job can be assigned to many, but different, agents and an agent may undertake several, but different, jobs in our problem. A network model with a special structure of GAP is given and an algorithm for GAP is proposed. Meanwhile, some important properties of the GAP are given. Numerical experiments are implemented, and the results indicate that the proposed algorithm can globally and efficiently optimize the GAP with a large range cost.

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The Average Sum Method for the Unbalanced Assignment Problems

Cited by 4 publications

References 3 publications

Division of Tasks Using the Hungarian Method

Division of Tasks Using the Hungarian Method

New Systematic Heuristic Based Approach to Cope With Unbalanced Assignment Problem Efficiently

A Network Flow Algorithm for Solving Generalized Assignment Problem

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