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This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

Economic incentives, government regulations, and customer perspective on environmental consciousness (EC) are driving more and more companies into product recovery business, which forms the basis for a reverse supply chain. A reverse supply chain consists a series of activities that involves retrieving used products from consumers and remanufacturing (closed-loop) or recycling (open-loop) them to recover their leftover market value. Much work has been done in the areas of designing forward and reverse supply chains; however, not many models deal with the transshipment of products in multiperiods. Linear physical programming (LPP) is a newly developed method whose most significant advantage is that it allows a decision-maker to express his/her preferences for values of criteria for decision-making in terms of ranges of different degrees of desirability but not in traditional form of weights as in techniques such as analytic hierarchy process, which is criticized for its unbalanced scale of judgment and failure to precisely handle the inherent uncertainty and vagueness in carrying out pair-wise comparisons. In this chapter, two multiperiod models are proposed for a remanufacturing system, which is an element of a Reverse Supply Chain (RSC), and illustrated with numerical examples. The first model is solved using mixed integer linear programming (MILP), while the second model is solved using linear physical programming. The proposed models deliver the optimal transportation quantities of remanufactured products for N-periods within the reverse supply chain.

This study proposes targeted modernization of the Department of Defense (DoD's) Joint Forces Ammunition Logistics information system by implementing the optimized innovative information technology open architecture design and integrating Radio Frequency Identification Device data technologies and real-time optimization and control mechanisms as the critical technology components of the solution. The innovative information technology, which pursues the focused logistics, will be deployed in 36 months at the estimated cost of $568 million in constant dollars. We estimate that the Systems, Applications, Products (SAP)-based enterprise integration solution that the Army currently pursues will cost another $1.5 billion through the year 2014; however, it is unlikely to deliver the intended technical capabilities.

To operate with high efficiency and minimise the risks of power failures, power systems require careful monitoring. The availability of real-time data is crucial for assessing the performance of the grid and assisting operators in gauging the present security of the grid. Traditional supervisory control and data acquisition (SCADA)-based systems actually employed provides steady-state measurement values which are the calculation premise of State Estimation. More often, however, the power grid operates under dynamic state and SCADA measurements can lead to erroneous and inaccurate calculation results. The introduction of the phasor measurement unit (PMU) which provides real-time synchronised voltage and current phasors with very high accuracy is universally recognised as an important aspect of delivering a secure and sustainable power system. PMUs are a relatively new technology and because of their high procurement and installation costs, it is imperative to develop appropriate methodologies to determine the minimum number of PMUs as well as their strategic placements to guarantee full observability of a power system. Thus, the problem of the optimal PMU placement (OPP) is formulated as an optimisation problem subject to various constraints to minimise the number of PMUs while ensuring complete observability of the grid. In this chapter, integer linear programming (ILP), genetic algorithm (GA) and non-linear programming (NLP) constrained models of the OPP problem are presented. A new methodology is proposed to incorporate several constraints using the NLP. The optimisation methods have been written in Matlab software and verified on the standard Institute of Electrical and Electronics Engineers (IEEE) 14-bus test system to authenticate their effectiveness. This chapter targets United Nations Sustainable Development Goal 7.

Supply chain is an important aspect for all the companies and can affect many aspects of companies. Especially the disruption in supply chain is causing huge impacts and consequences that are difficult to deal with. This chapter presents a review of selected multiple criteria problems used in supply chain optimization. Research analyzed the multiple criteria decision-making methods to tackle the problem of supplier evaluation and selection. It also focuses on the problem of supply chain when a disruption happens and presents strategies to deal with the issue of disruptions in supply chain and how to mitigate the impact of disruptions. Prevention, response, protection, and recovery strategies are explained. Practical part is focused in the risk-averse models to minimize expected worst-case scenario by single sourcing. Computational experiments for practical examples have been solved using CPLEX solver.

This chapter presents two multicriteria optimization models with bi and triple objectives solved with weighted-sum approach. Solved problems are allocation of personnel in a health care institution. To deal with these problems, mixed integer programming formulation has been applied. Results have shown the impact of problem parameter change for importance of the different objectives. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method.

This chapter presents a multi-criteria portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a single-objective linear program, as a bi-objective linear program, and as a triple-objective mixed integer program. The problem objective is to allocate the wealth on different securities to optimize the portfolio return. The portfolio approach has allowed the two popular financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied. The decision-maker can assess the value of portfolio return, the risk level, and the number of assets, and can decide how to invest in a real-life situation comparing with ideal (optimal) portfolio solutions. The concave efficient frontiers illustrate the trade-off between the conditional value-at-risk and the expected return of the portfolio. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that both proposed linear and mixed integer programming approaches provide the decision-maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.