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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 develops a methodology to assist critical facility operators in designing physical protection systems to defend against a single adversary (thief, saboteur, terrorist, etc.) attack. The developed methodology utilizes a multicriteria decision-making approach that balances the competing goals of minimal security system cost and maximum system performance. The methodology utilizes a network-based approach to facility security system design and analysis, which locates physical protection (detection, delay, and response) elements throughout a facility. These elements enable the facility owner to prevent attacks through deterrence and to defeat the adversary if he or she chooses to attack. The developed approach results in the ability for the facility operator to assess relative facility and/or infrastructure safety, and make decisions regarding how to optimally allocate resources for physical protection elements to balance cost and performance. A hypothetical example is discussed which demonstrates the usefulness of the developed methodology.

In this chapter, four bi-objective vehicle routing problems are considered. Weighted-sum approach optimization models are formulated with the use of mixed-integer programming. In presented optimization models, maximization of capacity of truck versus minimization of utilization of fuel, carbon emission, and production of noise are taken into account. The problems deal with real data for green logistics for routes crossing the Western Pyrenees in Navarre, Basque Country, and La Rioja, Spain.

Heterogeneous fleet of trucks is considered. Different types of trucks have not only different capacities, but also require different amounts of fuel for operations. Consequently, the amount of carbon emission and noise vary as well. Modern logistic companies planning delivery routes must consider the trade-off between the financial and environmental aspects of transportation. Efficiency of delivery routes is impacted by truck size and the possibility of dividing long delivery routes into smaller ones. The results of computational experiments modeled after real data from a Spanish food distribution company are reported. Computational results based on formulated optimization models show some balance between fleet size, truck types, and utilization of fuel, carbon emission, and production of noise. As a result, the company could consider a mixture of trucks sizes and divided routes for smaller trucks. Analyses of obtained results could help logistics managers lead the initiative in environmental conservation by saving fuel and consequently minimizing pollution. The computational experiments were performed using the AMPL programming language and the CPLEX solver.

Historically, public and private sector enterprises have been viewed as existing on opposing ends of the performance measurement spectrum, due to seemingly incompatible worldviews. Private sector enterprises are traditionally viewed as profit-driven and focused on a return on investment paradigm, while public sector enterprises are seen as mission-oriented and answerable to a paradigm less focused on investment and more on improving enterprise capability. The authors propose that, in fact, these worldviews are not mutually exclusive, as private and public sector enterprises must both account for investment and mission concerns. In order to leverage real synergy to be gained from distinct but complementary viewpoints, a systemic approach to evaluating organization performance through the novel fusion of operational test and evaluation and multi-criteria decision analysis is developed. Use of this framework is demonstrated within an enterprise that involves consideration of public and private sector concerns. The authors hope that the approach proposed in this chapter will enable public and private sector enterprises to comprehensively address performance.

This chapter presents two optimization multicriteria models (bi and triple objective) using a lexicographic approach. Solved models are formulated as assignment of workers to different jobs or services of a real hospital, taking into account the available budget and requirements of each job. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method for mixed integer mathematical programming.

The purpose of this chapter is to solve multi-objective formulation for traveling salesman and transportation problems. Computations are based on real data for the road freight transportation of a Spanish company. The company was selected because of its importance in Spanish economy and market. This company is important in the whole country; however, it has its higher importance in the northern part of Spain. The requirements for these models are the minimization of total distance and the CO₂ emissions. To achieve this, it is required to know and carry out the minimization of the total distance traveled by the trucks during the deliveries. The deliveries are going to be executed between the different locations, nodes, in the region, and Elorrio, where the depot is situated. The data have been used to decide the best route in order to obtain a minimization of cost for the company. As it was mentioned earlier, the problems are focused on the reduction of the amount of CO₂ emissions and minimization of total distance; by studying different parameters, the best solutions of route transportation have been obtained. The software used to solve these models is CPLEX solver with AMPL programming language.

The purpose of this chapter is to optimize multi-criteria formulation for green vehicle routing problems by mixed integer programming. This research is about the road freight transportation of a Spanish company of groceries. This company has more power in the north of Spain and hence it was founded there. The data used for the computational experiments are focused in the northern region of Spain. The data have been used to decide the best route in order to obtain a minimization of costs for the company. The problem focused on the distance traveled and the altitude difference; by studying these parameters, the best solution of route transportation has been made. The software used to solve this model is CPLEX solver with AMPL programming language. This has been helpful to obtain the results for the research and some conclusions have been obtained from them.