chance constrained programming

Portfolio optimization is a widely studied problem in financial engineering literature. Its objective is to effectively distribute capital among different assets to maximize returns and minimize the risk of losing capital. Although portfolio optimization has been extensively investigated, there has been limited focus on optimizing portfolios consisting of cryptocurrencies, which are rapidly growing and emerging markets. The cryptocurrency market has demonstrated significant growth over the past two decades, offering potential profits but also presenting heightened risks compared to traditional financial markets. This situation creates challenges in constructing portfolios, necessitating the development of new and improved risk management models for cryptocurrency funds. This paper utilizes a new risk measurement approach called Conditional Drawdown at Risk (CDaR) in constructing portfolios within high-risk financial markets. Traditionally, portfolio optimization has been approached under certain conditions, considering risk and profit as decision criteria. However, recent approaches have addressed uncertainty in the decision-making process. To contribute to the advancement of scientific knowledge in this field, this paper proposes a new mathematical formulation of CDaR based on a chance-constrained programming (CCP) approach for portfolio optimization. To demonstrate the effectiveness of the proposed model, a practical empirical case study is conducted using real-world market data from 10 months focused on cryptocurrencies. The results obtained from this model can provide valuable guidance in making investment decisions in high-risk financial markets.

The process of designing and redesigning supply chain networks is subject to multiple uncertainties. Given the growing environmental pollution and global warming caused by societies' industrialization, this process can be completed when environmental considerations are also taken into account in the decisions. In this study, an integrated four-level closed-loop supply chain network, including factories, warehouses, customers, and disassembly centers (DCs) is designed to fulfill environmental objectives in addition to economic ones. The reverse flow, including recycling and reprocessing the waste products, is considered to increase production efficiency. Also, the different transportation modes between facilities, proportional to their cost and greenhouse gas emissions, are taken into account in the decisions. A random cost function and chance constraints are presented firstly to handle the uncertainties in different parameters. After defining the random constraints using the chance-constraint programming approach, a deterministic three-objective model is presented. The developed model is solved using the GAMS software and the goal attainment (GA) method. Also, the effect of the priority of the goal, uncertain parameters, and confidence level of chance constraints on objective function values has been carefully evaluated using different numerical examples.

A fresh look at the system analysis helped us in finding a new way of calculating the risks associated with the system. The author found that, due to the shortcomings of RPN, more researches needed to be done in this area to use RPNs as a new source of information for system risk analysis. It is the purpose of this article to investigate the fundamental concepts of failure modes and effects analysis to propose a conceptual hierarchically based model for calculating the risk associated with a system in general. To do so, the author developed a chance constrained goal programming model for solving the problem.
A sample problem is provided to show the calculation process of risk evaluation. The findings of this article can be used for calculating the level of risk associated with the entire system provided that the RPN of each unit of subsystems is known beforehand. This model helps the managers to calculate the system risk from the perspective of management, because it is a computer aided decision making (CADM) tool

A chance-constraint multi-objective model under uncertainty in the availability of subassemblies is proposed for scheduling in ATO systems. The on-time delivery of customer orders as well as reducing the company's cost is crucial; therefore, a three-objective model is proposed including the minimization of1) overtime, idletime, change-over, and setup costs, 2) total dispersion of items’ delivery times in customers’ orders, and 3) tardiness and earliness costs.In order to reduce the involved risk,the uncertainty in the subassembly availabilities is addressed via a chance-constrained programming. The lexicographic method is employed to solve the model. The performance and validity is then evaluated using the real data from an electrical company. Notably, the decision maker can draw the appropriate results by a priority establishment between the costs and delivery time objectives. Moreover, formulating the existing uncertainty in the subassembly availabilities helps avoiding delay in the orders’ completion dates. Finally, applying joint lot size policy leads to a more proper scheduling of assembly sequence.

It is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (CC) problem. For this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. A sample problem is presented for clarification purposes.

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software for large scaled complex nonlinear programming problem with 0-1 type decision variables for stochastic vehicle routing problem (SVRP) is not easily available merely then the value of an approximation technique becomes imperative. In this article, theorems which build a foundation for moving toward the development of an approximate methodology for solving SVRP are stated and proved. Key Words: Vehicle Routing Problem, Chance Constrained Programming, Linear approximation, Optimization.