Geometric Programming Approach Research Articles

Profit maximization inventory model with uncertain demand and costs: A geometric programming approach

Profit maximization inventory model with uncertain demand and costs: A geometric programming approach

Geometric Programming Approach to Glitch Minimization via Gate Sizing

Geometric Programming Approach to Glitch Minimization via Gate Sizing

A stochastic geometric programming approach for power allocation in wireless networks

A stochastic geometric programming approach for power allocation in wireless networks

A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level

A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level

A GEOMETRIC PROGRAMMING APPROACH TO CONVEX MULTI-OBJECTIVE PROGRAMMING PROBLEMS

Over the past few years, convex optimization has played a vital role in the study of complex engineering problems in different fields. Geometric programming is one of the available techniques particularly used for solving nonconvex programming problems. But in this article, a suitable attempt has been made to solve a real-life model on convex multi-objective using geometric programming technique with help of the E-constraint method and result is compared with the solutions obtained by fuzzy technique. Finally, a conclusion is presented by analyzing the solutions to a numerical problem.

On the Maximum Energy Efficiency of Random Access-Based OMA and NOMA in Multirate Environment

The paradigm of the upcoming 5G and beyond is the machine type communications (MTC), where a large number of devices automatically operate wireless communications. Due to their automatic and energy-intensive operations, energy efficiency (EE) becomes very important, but there is a lack of investigation for EE of random access networks, which is the underlying platform for MTC. In this paper, we focus on the EE of random access orthogonal and non-orthogonal multiple access (OMA and NOMA) networks. We first construct mathematical models of their EE performances. Information-theoretic theories are employed to transform probabilistic decodability into deterministic form for OMA, and along with the unique features of NOMA decoding process, by pivoting around the decodability of a specific packet, we realize the modeling for NOMA. Then, based on the established models, exploiting the nature of random access networks, a complementary geometric programming approach is used for performance optimization. From our investigation, the following results are discovered: (1) NOMA has significant advantage over OMA in EE performance due to its strong data recovery; (2) to maximize the EE performance, devices with higher data rate should transmit more frequently, but with lower transmission power; (3) lower data rates have beneficial effects on EE.

On a Geometric Programming Approach to Profit Maximization: The Case of CES Technology

The profit maximization problem takes a central place in the theory of the firm, especially when conditions for perfect competition hold. In this paper, we solve the profit maximization problem of a perfectly competitive firm when the constant elasticity of substitution (CES) production function with n≥2 inputs describes its technology. Commonly, this problem is solved by using multivariable differential calculus. However, to avoid tedious algebraic manipulations and bypass checking nontrivial necessary and sufficient conditions, we employ geometric programming (GP), and the power mean inequality (PMI) as an elegant complementary tool to multivariable calculus. Since the GP and the PMI are simple optimization techniques without derivatives, they can provide new insights into the given problem to managers, students, and other audiences who may be unfamiliar with multivariable differential calculus. Additionally, by using the properties of limits, we show that the solution to the profit maximization problem with Cobb-Douglas technology is a limiting case of our result.

EOQ model with price, marketing, service and green dependent neutrosophic demand under uncertain resource constraint: A geometric programming approach

EOQ model with price, marketing, service and green dependent neutrosophic demand under uncertain resource constraint: A geometric programming approach

Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach

The geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimization problems efficiently. The work’s motivation is to introduce a bounded solution approach for the GPP while considering the variation among the right-hand-side parameters. The bounded solution method uses the two-level mathematical programming problems and obtains the solution of the objective function in a specified interval. The benefit of the bounded solution approach can be realized in that there is no need for sensitivity analyses of the results output. The demonstration of the proposed approach is shown by applying it to the system reliability optimization problem. The specific interval is determined for the objective values and found to be lying in the optimal range. Based on the findings, the concluding remarks are presented.

Geometric programming solution of second degree difficulty for carbon ejection controlled reliable smart production system

Smart manufacturing systems should always aim to be fully sustainable while simultaneously being as reliable as possible which is difficult to reach. Furthermore, climate change especially by carbon emission in the industry is a significant topic and carbon emission should be controlled and reduced to save the environment. Contributing towards a greener environment in a positive manner is done by reducing the number of insufficient items that are produced in a smart production system which also can be reached with higher reliability in the system. Therefore, this study models a smart reliable production system with controlled carbon ejection. To solve the proposed smart production system in this study, a geometric programming approach with a degree of difficulty level two is used which results in optimum results that are quasi-closed. Furthermore, numerical experiments are conducted to validate the proposed model and prove that by using a higher degree geometric programming approach, an optimal solution is found. The numerical results do not only show optimal solutions but also that the smart production system with controlled carbon ejection is reliable.

Signomial Geometric Programming Approach to Solve Non-Linear Fractional Programming Problems

Signomial Geometric Programming Approach to Solve Non-Linear Fractional Programming Problems

Achievable Rate Analysis and Max-Min SINR Optimization in Intelligent Reflecting Surface Assisted Cell-Free MIMO Uplink

In this paper, we study the uplink transmission in an intelligent reflecting surface (IRS) assisted cell-free multiple-input multiple-output (MIMO) system where the central processing unit (CPU) only has statistical channel state information (CSI) to detect symbols, and to design the receiver filter coefficients, the power allocations, and the IRS phase shifts. The access points (APs) estimate only their local end-to-end channels with the users using minimum mean squared error (MMSE) estimation to implement matched filtering, thereby avoiding the large overhead associated with estimating individual IRS-assisted channels. Under this framework, we derive a closed-form expression for the achievable uplink net rate that only depends on the channel statistics. Using this expression, we formulate the problem of maximizing the minimum (max-min) signal-to-interference plus noise ratio (SINR) to design the receiver filter coefficients at the CPU, the power allocations at the users, and the phase shifts at the IRS, subject to per user power constraints as well as IRS phase shift resolution constraints. The resulting problem is jointly non-convex in the three design variables and is solved using an alternating optimization algorithm. In particular, the receiver filter design is formulated as a generalized eigenvalue problem leading to a closed-form solution, the power allocation problem is solved using a geometric programming (GP) approach, and the IRS phase shifts are designed using an alternating maximization algorithm. For comparison, we also formulate and solve the max-min SINR problem for the scenario where the instantaneous imperfect CSI of all individual direct and IRS-assisted channels is available at the CPU. Numerical results show that the scheme designed using statistical CSI has the potential to outperform the scheme based on instantaneous CSI for moderate to large number of IRS elements, due to savings in the channel estimation overhead.

Optimal Pricing for Services of Iran’s Internet Exchange Points: A Fuzzy Geometric Programming Approach

Optimal Pricing for Services of Iran’s Internet Exchange Points: A Fuzzy Geometric Programming Approach

On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment

Abstract This article attempts to study cost minimizing multi-objective fractional solid transportation problem with fuzzy cost coefficients c ˜ i j k r {\tilde{c}}_{ijk}^{r} , fuzzy supply quantities a ˜ i {\tilde{a}}_{i} , fuzzy demands b ˜ j {\tilde{b}}_{j} , and/or fuzzy conveyances e ˜ k {\tilde{e}}_{k} . The fuzzy efficient concept is introduced in which the crisp efficient solution is extended. A necessary and sufficient condition for the solution is established. Fuzzy geometric programming approach is applied to solve the crisp problem by defining membership function so as to obtain the optimal compromise solution of a multi-objective two-stage problem. A linear membership function for the objective function is defined. The stability set of the first kind is defined and determined. A numerical example is given for illustration and to check the validity of the proposed approach.

Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach

We propose a multitask learning approach to learn the parameters of a compartmental discrete-time epidemic model from various data sources and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of the model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals’ mobility patterns specific to each region. Using this model, we propose a nonlinear optimal control problem aiming to find the optimal mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. We also show that the solution to this nonlinear optimal control problem can be efficiently found, in polynomial time, using tools from geometric programming. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the COVID-19 pandemic in the Philadelphia metropolitan area.

A geometric programming approach for a vendor managed inventory of a multiretailer multi-item EPQ model

Due to the uncertain situations of the world, considering inventory management in a stochastic environment gains a lot of interest. In this paper, we propose a multi-item economic production quantity (EPQ) model with a shortage for a single-vendor, multi-retailer supply chain under vendor managed inventory (VMI) policy in a stochastic environment. Three stochastic constraints are developed in the model. Geometric programming (GP) approach is employed to find the optimal solution of the nonlinear stochastic programming problem to minimize the mean-variance of the total inventory cost of the system. Since the problem is in the Signomial form, first, an algorithm is used to convert the model into the standard GP form. The performance of the addressed model and the solving method are evaluated based on computational experiments and sensitivity analysis. A case study in an Iranian furniture supply chain is conducted to show the applicability of the proposed model and 17.78% improvement in terms of total cost is gained.

Joint Pilot Allocation and Power Control to Enhance Max-Min Spectral Efficiency in TDD Massive MIMO Systems

In time division duplex (TDD) massive multiple-input multiple-output (MIMO) systems, pilot contamination seriously limits the improvement of spectral efficiency (SE). In order to provide good communication quality for every user, this paper devotes to enhance minimum spectral efficiency of the system. Firstly, a multi-cell multi-user system model is established to derive the objective function of Max-Min spectral efficiency. Through analysis of the mathematical expressions, we found that it is not a convex optimization problem for joint pilot allocation and power control, but a non-deterministic polynomial (NP) problem that is difficult to deal with. In order to solve the problem, a new algorithm is proposed to decompose the problem into two easy-to-handle sub-problems. We employ weight graph coloring (WGC) algorithm to deal with the sub-problem of pilot allocation, where uplink transmission power is fixed. The geometric programming (GP) approach is utilized to solve the sub-problem of power control, in which the large-scale fading factor is fixed. Then the computational complexity of the proposed algorithm is analyzed. Compared with the ideal optimal solution algorithm that requires exhaustive search, our algorithm has much less computational complexity. Finally, the simulation results demonstrate that the proposed algorithm significantly improves the minimum spectral efficiency, which is close to the ideal optimal solution.

An inventory model with credit, price and marketing dependent demand under permitted delayed payments and shortages: A signomial geometric programming approach

An inventory model with credit, price and marketing dependent demand under permitted delayed payments and shortages: A signomial geometric programming approach

A Green Vendor Managed Inventory of a Multi-item Multi-retailer EPQ model under Fuzzy Environment with Stochastic Constraints: A Geometric Programming Approach

The purpose of this paper is to develop a multi-item multi-constraint EPQ model with shortage in the form of backorder for a single-vendor multi-retailer supply chain under vendor managed inventory (VMI) policy. Due to the rising concern in environmental conservation, green supply chain is considered in this paper. To include an extended applicability in real-world situations, three constraints are assumed in stochastic form. In addition, demands are considered imprecise. Since the model is developed in multi-product form, for the vendor's fixed ordering cost different conditions are considered. Geometric programming (GP) approach is employed to find the optimal solution of the model with the objective of minimizing the total cost of the system. Since the model contains signomial terms, an algorithm is utilized to convert the model into the standard form of GP. To evaluate the performance of the model and the solving method, computational experiments are presented.

Optimization of EOQ model with space constraint: An intuitionistic fuzzy geometric programming approach

Optimization of EOQ model with space constraint: An intuitionistic fuzzy geometric programming approach