Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

Exploiting the Chain Convenience Store Supplier Selection Based on ANP-MOP Model

The purchase cost of chain convenience stores accounts for a large proportion of the total cost. Enterprises are facing the problem of how to reasonably reduce the purchase cost while ensuring the quality of service. This paper first considers the uniqueness of chain convenience stores, draws on existing research results, and establishes an evaluation index system for chain convenience store suppliers through field research. Then, we use the principal component analysis method of selection to determine the weight of each index and make a preliminary ranking of the importance of chain convenience store suppliers. Secondly, according to the relevant weights determined by the network hierarchy method, the collected data are substituted into the multiobjective mathematical programming model to analyze the distribution of supplier procurement and calculate the procurement cost. The level of procurement expenditures accounted for by suppliers confirms the importance of suppliers. The results show that through the evaluation and ranking of suppliers and the effective management of suppliers according to the ranking results, not only the goal of cost minimization is achieved but also the reasonable service level is guaranteed, which is scientific.

Best-compromise nutritional menus for childhood obesity

Childhood obesity is an undeniable reality and has shown a rapid growth in many countries. Obesity at an early age not only increases the risks of chronic diseases but also produces a problem for the whole healthcare system. One way to alleviate this problem is to provide each patient with an appropriate menu that can be defined with a mathematical model. Existing mathematical models only partially address the objective and constraints of childhood obesity; therefore, the solutions provided are insufficient for health specialists to prepare nutritional menus for individual patients. This manuscript proposes a multiobjective mathematical programming model to aid healthy nutritional menu planning to prevent childhood obesity. This model enables a plan for combinations and amounts of food across different schedules and daily meals. This approach minimizes the major risk factors of childhood obesity (i.e., glycemic load and cholesterol intake). In addition, it considers the minimization of nutritional mismatch and total cost. The model is solved using a deterministic method and two metaheuristic methods. To complete this numerical study, test instances associated with children aged 4-18 years old were created. The quality of the solutions generated using the three methods was similar, but the metaheuristic methods provided solutions in less computational time. The numerical results indicate proper guidelines for personalized plans for individual children.

Multiobjective Mathematical Programming Model for the Optimization of End-of-Life Buildings’ Deconstruction and Demolition Processes

Nowadays, construction and demolition waste management has become a critical process for the construction industry, as the specific waste stream poses important environmental issues and challenges. In the case of dismantling end-of-life buildings, the selection of the appropriate technique between deconstruction and conventional demolition is a critical decision affecting the total volume and type of produced waste. Toward this effect, in this paper, a novel decision-making model for the optimization of end-of-life buildings’ deconstruction and demolition processes is proposed. The objective of the proposed model is the simultaneous and weighted optimization of the total cost and time for the completion of the deconstruction and demolition processes, taking into consideration economic, legislative, and environmental criteria. Finally, a demonstration of the application of the proposed model is presented via two specific case studies and by discussing a few interesting managerial insights.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

Optimization Model and Algorithm Design for Airline Fleet Planning in a Multiairline Competitive Environment

This paper presents a multiobjective mathematical programming model to optimize airline fleet size and structure with consideration of several critical factors severely affecting the fleet planning process. The main purpose of this paper is to reveal how multiairline competitive behaviors impact airline fleet size and structure by enhancing the existing route-based fleet planning model with consideration of the interaction between market share and flight frequency and also by applying the concept of equilibrium optimum to design heuristic algorithm for solving the model. Through case study and comparison, the heuristic algorithm is proved to be effective. By using the algorithm presented in this paper, the fleet operational profit is significantly increased compared with the use of the existing route-based model. Sensitivity analysis suggests that the fleet size and structure are more sensitive to the increase of fare price than to the increase of passenger demand.