A sphere packing approach to break even and profitability analysis

Enkhbat, Rentsen; Tungalag, N.

doi:10.3934/jimo.2022237

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…To fulfill this gap, we propose a new mathematical methodology based on optimization methods. On the other hand, we continue a recent research done in Rentsen & Natsagdorj (2023) on profitability analysis of business. In this paper, we define constrained break even points with respect to price.…”

Section: Introductionmentioning

confidence: 64%

Optimization Approach to Constrained Break Even Points with Respect to Price

Rentsen,

Chuluundorj,

Natsagdorj

2023

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Break even and profitability analysis is a classical and widely used topic in business analysis. Break-Even Point or point of equilibrium is the point of sales volume making neither a profit nor a loss. It is a valuable number to know. Traditional break-even analysis is used to determine how much sales volume your business needs to start making a profit. In this paper, we extend the classical break-even point concept by introducing a new notion of constrained break-even points with respect to prices. In this case, a traditional method of calculating break even point may fail. For this purpose, for finding constrained break-even points, we propose an optimization approach based on solving convex and nonconvex optimization problems. Convex minimization and convex maximization algorithms are used. We show that global minimum, local maximum, and stationary points of both problems are the constrained break-even points with respect to price. The proposed approaches illustrated on some fictitious business examples providing numerical results.

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Section: Introductionmentioning

confidence: 64%

Optimization Approach to Constrained Break Even Points with Respect to Price

Rentsen,

Chuluundorj,

Natsagdorj

2023

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“…This problem has important applications in science and technology. Recently, new applications of sphere packing theory have appeared in finance (Badam et al, 2021), business (Enkhbat & Tungalag, 2023) and the mining industry (Enkhbat, 2022). There are other studies that focus on optimizing government revenue and expenditure independently.…”

Section: Introductionmentioning

confidence: 99%

Application of Sphere Packing Theory in Government Budget

Ganlkhagva,

Chuluunbaatar,

Natsagdorj

et al. 2023

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The sphere packing problem involves packing non-overlapping spheres with maximum volume into a convex set. The purpose of this work is to propose a novel application of the sphere packing problem to the government budget issue and to formulate a mathematical model for reducing the government budget deficit. In the numerical experiment, we used statistical data on the Mongolian economy from 2013 to 2022. We considered 19 types of revenues and 28 types of expenditures. The numerical experiment shows that with specific adjustments to current government revenue and expenditure, the government can decrease the budget deficit.

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A sphere packing approach to break even and profitability analysis

Cited by 2 publications

References 18 publications

Optimization Approach to Constrained Break Even Points with Respect to Price

Optimization Approach to Constrained Break Even Points with Respect to Price

Application of Sphere Packing Theory in Government Budget

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