Leasing currently plays an important role for the global economy. The equipment leasing earning acquired through leasing rather than cash or credit, has reached a dominant level. With this regards, this paper represents a basic mixed-integer non-linear programming model. The study deliberates a firm that leases new products and remanufactured leased merchandises. The proposed study considers the end of lease contract, which contains several options: Return the leased product, return the used product and purchase other remanufactured product and buying the leased product. The primary objective is to maximize the discrepancy between the revenue and the costs of a firm, which leases new products as well as selling remanufactured ones. The product deteriorates with time and the difference between a new and used good is obvious. The product must undergo a remanufacturing procedure before being sold as a remanufactured product.

The purpose of the current study is to investigate a special case of art gallery problem, namely a sculpture garden problem. In this problem, for a given polygon P, the ultimate goal is to place the minimum number of guards (landmarks) to define the interior polygon P by applying a monotone Boolean formula composed of the guards. Using this problem, it can replace the operation-based method with time-consuming, pixel-based algorithms. So, the processing time of some problems in the fields of machine vision, image processing and gamification can be strongly reduced. The problem has also many applications in mobile device localization in the Internet of Things (IoT). An open problem in this regard is the proof of Eppstein’s conjecture, which has remained an open problem since 2007. According to his conjecture, in the worst case, n−2 vertex guards are required to describe any n-gon. In this paper, a lower bound is introduced for the special case of this problem (natural vertex guard), which shows that if a polygon can be defined with natural vertex guards, then n−2 is a lower bound.

In the field of enterprise architecture (EA), qualitative scenarios are used to understand the qualitative characteristics better. In order to reduce the implementation cost, scenarios are prioritized to be able to focus on the higher priority and more important scenarios. There are different methods to evaluate enterprise architecture including architecture Trade-off Analysis Method (ATAM).Prioritizing qualitative scenarios is one of the main phases of this method. Since none of the recent studies meet the prioritizing qualitative scenarios requirements, considering proper prioritizing criteria and reaching an appropriate speed priority, non-dominated sorting genetic algorithms is used in this study (NSGA-II). In addition to previous research standards more criteria were considered in the proposed algorithm, these sets of structures together as gene and in the form of cell array constitute chromosome. The proposed algorithm is evaluated in two case studies in the field of enterprise architecture and architecture software. The results showed the accuracy and the more appropriate speed comparing to the previous works including genetic algorithms.

Guarding of an environment by cameras or guards is a longstanding problem in computational geometry. In this paper, we introduce a new type of guarding problems called Γ-guarding using staircase visibility. A point inside an orthogonal environment is said to be staircase visible for a given camera if there exists a staircase path from camera to the point so that it is completely contained in the environment. In this model, we place a small number of guards inside an orthogonal polygon so that each point of polygon is staircase visible through at least four directions. We present an algorithm for Γ-guarding an arbitrary orthogonal polygon that yields an upper bound for the number of guards that protect an orthogonal polygon through four directions.