Linear Programming and Resource Allocation Modeling

Panik, Michael J.

doi:10.1002/9781119509479

Cited by 12 publications

(10 citation statements)

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“…Machine cost depends on the site's selected capacity, and construction cost depends on village status, as discussed in the Data section below.

\underset{\sum}{false} ((), 1200 S_{k} + {Ccons}_{k} x_{k}) \leq B

where

x_{k}

is a 0, 1 integer variable, which equals 1 if site k is selected for an MHP project and 0 otherwise. Capacity constraint: Total new capacity in village j

((), \sum_{k \in K_{j}} S_{k})

cannot exceed the capacity shortfall in village j

((), D_{j})

\underset{\sum}{false} S_{k} \leq D_{j} \forall j

Maximum capacity constraint: To enforce the relationship between new generation capacity

((), S_{k})

and the decision as to whether to develop site (

x_{k}

), we include the following constraint in which

N_{k}

is the maximum possible new capacity at the site (kW).

S_{k} \leq N_{k} x_{k} \forall k

Linearity transformation of the second objective: The second objective is a non‐linear function because of the absolute value function. We need to transform it into a linear function by introducing a new variable

f_{i}

and the following constraints (Panik, 2019).

f_{i} \geq \frac{\underset{\sum}{false} S_{k}}{\underset{\sum}{false} D_{j}} - \frac{\underset{\sum}{false} S_{k}}{\underset{\sum}{false} D_{j}} \forall normali

…”

Section: Methodsmentioning

confidence: 99%

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Optimizing an equitable micro‐hydropower deployment: Application of a multi‐objective method for rural Indonesia

Maghfirra

Cohon

Jaramillo

et al. 2021

Multi Criteria Decision Anal

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Much of the developing world is still struggling to provide electricity to rural populations. Extending the grid is frequently not feasible or too expensive in rural and remote areas. In such situations, micro-hydropower (MHP) can be a costeffective source of renewable off-grid electricity and can be easier to implement and more reliable than a number of other generation technologies. This study employs multi-objective mixed-integer-linear programming (MOMILP) to identify nondominated MHP portfolios to meet rural electricity needs across Indonesia. Besides maximizing the new MHP generation capacity within a fixed budget, this study also incorporates equity as an objective. The equity issue becomes crucial to ensure that government resources are deployed in a manner that considers impacts for the entire population. The MOMILP optimizes a weighted objective function that applies different relative weights to the objectives of generation capacity and equity, subject to several constraints on resource availability and capacity shortfall, as well as budget. In this way, we identify solutions on the Pareto frontier for investment in MHP generation in remote Indonesian rural communities. We illustrate the tradeoffs involved in meeting capacity shortfalls with and without considering equity across provinces and identify nondominated MHP portfolios that the Indonesian government could implement to increase rural electrification efficiently.

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“…Machine cost depends on the site's selected capacity, and construction cost depends on village status, as discussed in the Data section below.

\underset{\sum}{false} ((), 1200 S_{k} + {Ccons}_{k} x_{k}) \leq B

where

x_{k}

is a 0, 1 integer variable, which equals 1 if site k is selected for an MHP project and 0 otherwise. Capacity constraint: Total new capacity in village j

((), \sum_{k \in K_{j}} S_{k})

cannot exceed the capacity shortfall in village j

((), D_{j})

\underset{\sum}{false} S_{k} \leq D_{j} \forall j

Maximum capacity constraint: To enforce the relationship between new generation capacity

((), S_{k})

and the decision as to whether to develop site (

x_{k}

), we include the following constraint in which

N_{k}

is the maximum possible new capacity at the site (kW).

S_{k} \leq N_{k} x_{k} \forall k

f_{i}

and the following constraints (Panik, 2019).

f_{i} \geq \frac{\underset{\sum}{false} S_{k}}{\underset{\sum}{false} D_{j}} - \frac{\underset{\sum}{false} S_{k}}{\underset{\sum}{false} D_{j}} \forall normali

…”

Section: Methodsmentioning

confidence: 99%

“…We need to transform it into a linear function by introducing a new variable f i and the following constraints (Panik, 2019).…”

Section: Capacity Constraint: Total New Capacity In Village Jmentioning

confidence: 99%

Optimizing an equitable micro‐hydropower deployment: Application of a multi‐objective method for rural Indonesia

Maghfirra

Cohon

Jaramillo

et al. 2021

Multi Criteria Decision Anal

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“…A full chapter on sensitivity analysis may be found in Eiselt et al [5]. A more up to date version can be found in Panik [6].…”

Section: Ridley Et Al Journal Of Applied Mathematics and Physicsmentioning

confidence: 99%

Randomized Objective Function Linear Programming in Risk Management

Ridley¹,

Llaugel²,

Daniels³

et al. 2021

JAMP

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The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.

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“…The proposed implementation methods turned out to be more effective and flexible than the methods of mathematical programming usually applied to such problems [5,9,18]. This concerned both the hybrid approach (Section 4.1) and the dedicated genetic algorithm (Section 4.2) developed by the authors.…”

Section: Literature Reviewmentioning

confidence: 99%

Proactive and reactive approach to employee competence configuration problem in planning and scheduling processes

Wikarek

Sitek

2021

Appl Intell

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At the time of commonplace automation, robotization and the rapid development of IT, high qualifications of employees have become the critical element of every industry system. This follows from their limited availability, frequently high costs of procurement and possible employee absenteeism. Moreover, the concept of Industry 4.0 will transform current industry employees into knowledge employees. This is due to the fact that hard and routine tasks will be executed by robots and computers. This constitutes change in the required employee competences. Unfortunately, the aspect of management and configuration of employee competences is often overlooked in industrial practice. In response to the existing problem, the article puts forward the original model of employee competence configuration which is a basis for responses to numerous questions of managers of production processes, both general ones, e.g., Do we have a sufficient set of competences to execute a production schedule? as well as detailed ones, e.g., Which and how many competences are missing? etc. An important novelty of the presented model is the possibility of its application with both proactive and reactive questions. Due to the discrete and combinatorial nature of the problem under consideration, the use of mathematical programming methods was limited only to small data instances. Therefore, a proprietary dedicated genetic algorithm was proposed to solve this problem, which turned out to be extremely effective. The use of this genetic algorithm has enabled finding a solution depending on the instance data up to 70 times faster than by use of the mathematical programming.

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Linear Programming and Resource Allocation Modeling

Cited by 12 publications

References 0 publications

Optimizing an equitable micro‐hydropower deployment: Application of a multi‐objective method for rural Indonesia

Optimizing an equitable micro‐hydropower deployment: Application of a multi‐objective method for rural Indonesia

Randomized Objective Function Linear Programming in Risk Management

Proactive and reactive approach to employee competence configuration problem in planning and scheduling processes

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