Optimization of the Distribution and Localization of Wireless Sensor Networks Based on Differential Evolution Approach

Location information for wireless sensor nodes is needed in most of the routing protocols for distributed sensor networks to determine the distance between two particular nodes in order to estimate the energy consumption. Differential evolution obtains a suboptimal solution based on three features included in the objective function: area, energy, and redundancy. The use of obstacles is considered to check how these barriers affect the behavior of the whole solution. The obstacles are considered like new restrictions aside of the typical restrictions of area boundaries and the overlap minimization. At each generation, the best element is tested to check whether the node distribution is able to create a minimum spanning tree and then to arrange the nodes using the smallest distance from the initial position to the suboptimal end position based on the Hungarian algorithm. This work presents results for different scenarios delimited by walls and testing whether it is possible to obtain a suboptimal solution with inner obstacles. Also, a case with an area delimited by a star shape is presented showing that the algorithm is able to fill the whole area, even if such area is delimited for the peaks of the star

Multiobjective Optimization for a Wireless Ad Hoc Sensor Distribution on Shaped-Bounded Areas

Resource efficiency in wireless ad hoc networks has become a widely studied NP-problem. This problem may be suboptimally solved by heuristic strategies, focusing on several features like the channel capacity, coverage area, and more. In this work, maximizing coverage area and minimizing energy consumption are suboptimally adjusted with the implementation of two of Storn/Price’s Multiobjective Differential Evolution (DE) algorithm versions. Additionally, their extended representations with the use of random-M parameter into the mutation operator were also evaluated. These versions optimize the initial random distribution of the nodes in different shaped areas, by keeping the connectivity of all the network nodes by using the Prim–Dijkstra algorithm. Moreover, the Hungarian algorithm is applied to find the minimum path distance between the initial and final node positions in order to arrange them at the end of the DE algorithm. A case base is analyzed theoretically to check how DE is able to find suboptimal solutions with certain accuracy. The results here computed show that the inclusion of random-M and completion of the algorithm, where the area is pondered with 60% and the energy is pondered with 40%, lead to energy optimization and a total coverage area higher than 90%, by considering the best results on each scenario. Thus, this work shows that the aforementioned strategies are feasible to be applied on this problem with successful results. Finally, these results are compared against two typical bioinspired multiobjective algorithms, where the DE algorithm shows the best tradeoff

Two Level Trade Credit Policy Approach in Inventory Model with Expiration Rate and Stock Dependent Demand under Nonzero Inventory and Partial Backlogged Shortages

In present real life situations, the stock and expiration date directly impact on the demand of an item. In this context, this research work develops an inventory model for stock and expiration rate-dependent demand under a two-level trade credit policy. Specifically, the following three situations are studied: (i) trade credit policy without zero ending inventory; (ii) trade credit policy with zero ending inventory; (iii) trade credit policy with partial backlogged shortages. The proposed inventory model is formulated as a non-linear constrained optimization problem. Some theoretical results are derived, and an algorithm is stated in order to solve the proposed inventory model. The main objective of the inventory model is to determine the optimal cycle length, the optimal ending inventory level, and the optimal number of units displayed which maximize the total profit. Some numerical examples are solved. Finally, a sensitivity analysis is done with the aim to see the impacts of a variation of the input parameters on the decision variables and the total profit

An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters

An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters

Effects of variable prepayment installments on pricing and inventory decisions with power demand pattern and non-linear holding cost under carbon cap-and-price regulation

Regulators’ increasingly stringent carbon rules to protect the environment are encouraging practitioners to modify their operational activities that are accountable for releasing emissions into the atmosphere. Thereby, practitioners dealing with product inventory planning are seeking proper management strategies not only to increase profits but also to reduce released carbons from operations. In addition, increasing uncertainty in supply operations has motivated suppliers to impose prepayment mechanisms in recent decades. This study examines the best prepayment installment policy for a practitioner for the first time, where the consumption behavior of consumers changes as a result of the combined effects of unit selling price and storage time. Moreover, to make the present inventory planning more realistic, the unit holding cost function is adopted as a power function of the inventory unit's storage period. The goal of this study is to provide the best combined installment for advance payment, price, and replenishment strategies for a practitioner under cap-and-price, cap-and-trade, and carbon tax environmental guidelines by ensuring maximum profit. For this purpose, an algorithm is created by combining all derived theoretical results from the analytical study, whereas the efficacy of the algorithm is assessed through the examination of five illustrative numerical instances. A plethora of noteworthy management insights for the practitioner are obtained by investigating the dynamic shifts in optimal strategies resulting from fluctuations in system parameters. The results reveal that if the demand is low in the nascent phases of the business cycle, then the prudent approach for the practitioner entails procuring a comparatively smaller lot-size using a modest number of payment frequencies and then setting a relatively small unit selling price to increase profits

A Fuzzy Imperfect Production Inventory Model Based on Fuzzy Differential and Fuzzy Integral Method

In the inventory theory, to treat the uncertainty, the fuzzy set concept is used in order to provide a feasible approach to deal with the uncertainty problem. In this research work, a fuzzy economic production quantity model with interactive fuzzy demands is proposed. In a production process, in the beginning, the system is assumed to be in a controlled state in which only perfect items are manufactured. Later, the manufacturing production process shifts to be an out-of-control-state system; producing both perfect and imperfect items simultaneously, this is considered as a fuzzy state. The defective production rate is also taken into account as a fuzzy state. Here, the selection process of produced items is realized during the production period. With the aim of studying the practical feasibility of the fuzzy economic production inventory model along with a sensitivity analysis of some parameters, different numerical examples are illustrated

Sustainability Economic Production Quantity with Warm-Up Function for a Defective Production System

Inventory management seeks to improve manufacturing by contracting inventory costs in a similar fashion to raise efficiency and profit. One approach is to develop inventory management models according to actual production systems. Furthermore, governmental policies in many countries impose many regulations on firms to fulfill the growing demand for a reduction in carbon emissions. Warm-up is a familiar concept in industrial applications. It allows the manufacturing system to work at a higher level of productivity and efficiency, as well as decreasing the number of defective items and maintenance costs. Along with fewer poor-quality items, the system has less waste as scrap items entering the environment and also requires less energy and workload to focus on reworking. The economic production quantity (EPQ) problems with a warm-up as an input parameter have been studied in a few works recently. This paper proposes a production-inventory model which considers the warm-up period as a decision variable and investigates its impact on the total cost. Furthermore, the defective rate is a decreasing linear function related to the warm-up period’s length. The production-inventory model takes into account the carbon emission tax policy. The main aim of this research is to jointly optimize both the length of the warm-up period and the production cycle in order to minimize the total cost of the production-inventory system and, therefore, reduce emitted carbon emissions. The comparison of tax prices and the effect of the proper warm-up period on the amount of carbon emissions are discussed in the sensitivity analysis

A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility

The mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work, the concept of the mixing problem is studied in the branch of production inventory. Here, a production model of mixed liquids with price-dependent demand and a stock-dependent production rate is formulated under preservation technology. In the formulation, first of all, the mixing process is presented mathematically with the help of simultaneous differential equations. Then, the mixed liquid produced in the mixing process is taken as a raw material of a manufacturing system. Then, all the cost components and average profit of the system are calculated. Now, the objective is to maximize the corresponding profit maximization problem along with the highly nonlinear objective function. Because of this, the mentioned maximization problem is solved numerically using MATHEMATICA software. In order to justify the validity of the model, two numerical examples are worked out. Finally, to show the impact of inventory parameters on the optimal policy, sensitivity analyses are performed and the obtained results are presented graphically