Annual increases in power use need improved energy management. Several universities and research organizations have focused on pursuing energy efficiency and renewable energy to satisfy this stipulation. This study provides a thorough and organized systematic review of over 2000 operational research studies conducted between 2019 and 2023. In summary, this study explores potential innovations to enhance existing literature utilizing mathematical tools in energy management. Our systematic literature review indicates that geometric planning is a novel mathematical technique in energy management. Based on the specific problems, this paper discusses geometric planning and proposes its integration with other mathematical techniques.

The article presents solution procedure of geometric programming to solve the structural model with imprecise coefficients. We have considered a single objective structural optimization model with weight as an objective function. Geometric programming provides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number. In this paper, we transform this interval number to a parametric interval-valued functional form and then solve the parametric problem by geometric programming technique. The advantage of this technique is that we can find directly optimal solution of the objective function without solving two-level mathematical programs. Numerical example is given to illustrate the model through this approximation method.

In this paper, we establish an economic production quantity (EPQ) based inventory model by
considering various types of non-perfect products. We classify products in four groups of
perfect, imperfect, defective but reworkable and non-reworkable defective items. The demand
is a power function of price and marketing expenditure and production unit cost is considered to
be a function of lot size. The objective of this paper is to determine lot size, marketing
expenditure, selling price, set up cost and inventory holding cost, simultaneously. The problem
is modeled as a nonlinear posynomial geometric programming and an optimal solution is
derived. The implementation of the proposed method is demonstrated using a numerical
example and the sensitivity analysis is also performed to study the behavior of the model.

Nowadays electronic commerce plays an important role in many business activities, operations, and transaction processing. The recent advances on e-businesses have created tremendous opportunities to increase profitability. This paper presents a multi-objective marketing planning model which simultaneously determines efficient marketing expenditure, service cost and product & apos; s selling price in two competitive markets. To solve the proposed model, we discuss a multi-objective geometric programming (GP) approach based on compromise programming method. Since our proposed model is a signomial GP and global optimality is not guaranteed for the problem, we transform the model to posynomial form. Finally, the solution procedure is illustrated via a numerical example and a sensitivity analysis is presented.

Vendor Managed Inventory (VMI) is one of the effective techniques for managing the inventory in supply chain. VMI models have been proven to reduce the cost of inventory compared with traditional ones under some conditions such as constant demand and production expenditure. However, the modeling of the VMI problem has never been studied under some realistic assumptions such as price dependent demand. In this paper, three problem formulations are proposed. In the first problem formulation, we study a VMI problem with one buyer and one supplier when demand is considered to be a function of price and price elasticity to demand, and production cost is also a function of demand. The proposed model is formulated and solved in a form of geometric programming. For the second and the third models, we consider VMI problem with two buyers and two suppliers assuming that each buyer centre is relatively close to the other buyer centre. Each supplier has only one product which is different from the product of the other supplier. Two suppliers cooperate in customer relationship management and two buyers cooperate in supplier relationship management as well, so the suppliers send the orders of two buyers by one vehicle, simultaneously. For the third model, an additional assumption which is practically applicable and reasonable is considered. For all the proposed models, the optimal solution is compared with the traditional one. We demonstrate the implementation of our proposed models using some numerical examples.