Binary Linear Programming as a Tool of Cost Optimization for a Water Supply Operator

Abstract

The problem of scheduling pumps is widely discussed in the literature in the context of improving energy efficiency, production costs, emissions, and reliability. In some studies, the authors analyze the available case studies and compare the results; others present their own computational methods. In the paper, a problem of pump scheduling in regular everyday operations of a water supply operator is considered. The issues of water production optimization and energy savings are part of the topic of sustainable development. The objective of the article is the minimization of the cost of electric power used by the pumps supplying water. It is achieved thanks to the variability of both the demand for water and the price of electric power during the day combined with the possibility of storing water. The formulation of an existing electric power cost optimization problem as a binary linear programming problem was improved. An essential extension of the above mathematical model, which enables more flexible management of the pump system, was also proposed. An example containing real-world input data was successfully solved using Microsoft Excel with a free OpenSolver add-in.

Simulation of the Progress of the Decarbonization Process in Poland’s Road Transport Sector

“…The optimization models that are built are implemented in Microsoft Excel's module "Solver" in order to process the calculations [28][29][30]. The task of optimizing non-linear programming is the basis for developing correct conclusions that provide many practical implications in the decision-making process [31,32].…”

Multi-Objective Optimization of the Organization’s Performance for Sustainable Development

“…In the economic and quality field, binary linear-programming optimization by minimization of the cost, while optimizing environmental pollution and the quality of products, was proposed by [22,23]. Moreover, in the electrical field, integer linear programming was used to maintain energy storage and prolong the battery life cycle, while minimizing load shedding [24].…”

“…From the analysis of recent works, it is observed that the emphasis is on the product [17][18][19][20][21][22][23][24][25] and not on the organization. Thus, to eliminate all the shortcomings mentioned above, a multi-criterial optimization was conceived, focusing on economic, environmental, and social development.…”

“…A substantial improvement is observed both in the maximization and minimization functions, which shows the fact that the optimal final function allows an increase in both the unitary performances (sales, costs, and productivity) and the global performance of the organization. Cost optimization is often targeted by researchers [22,29], profit optimization is focus of specialists [12], and multi-objective optimization of the two indicators is also geted [6,11,18,24]; however, a multi-objective vision that involves the optimization sales, as well as costs and productivity, is the novelty brought by the current work. A lyzing the results obtained, it can be stated that the final multi-objective function allow for the global optimization of the sustainable development of the organization.…”

“…The input data include the objectives planned by the compa regarding the turnover to be achieved, the production and delivery costs, and the prod tivity achieved by employees. Customer requirements for orders, production capac delivery costs, and resource consumption are also taken into account for optimization Starting from the multi-objective model, several mono-objective optimization pr lems are formulated: the problem of maximizing turnover, the problem of minimiz Cost optimization is often targeted by researchers [22,29], profit optimization is the focus of specialists [12], and multi-objective optimization of the two indicators is also targeted [6,11,18,24]; however, a multi-objective vision that involves the optimization of sales, as well as costs and productivity, is the novelty brought by the current work. Analyzing the results obtained, it can be stated that the final multi-objective function allowed for the global optimization of the sustainable development of the organization.…”