Annals of Optimization Theory and Practice
Volume:1 Issue: 1, Winter 2018

During the recent years, demand for healthcare services has dramatically increased. As the demand for healthcare services increases, so does the necessity of constructing new healthcare buildings and redesigning and renovating existing ones. Increasing demands necessitate the use of optimization techniques to improve the overall service efficiency in healthcare settings. However, high complexity of care processes remains the major challenge to accomplish this goal. This study proposes a method based on process mining results to address the high complexity of care processes and to find the optimal layout of the various medical centers in an emergency department. ProM framework is used to discover clinical pathway patterns and relationship between activities. Sequence clustering plug-in is used to remove infrequent events and to derive the process model in the form of Markov chain. The process mining results served as an input for the next phase which consists of the development of the optimization model. Comparison of the current ED design with the one obtained from the proposed method indicated that a carefully designed layout can significantly decrease the distances that patients must travel.

This paper focuses on formulating a typical U-type assembly line balancing problem. A cost based objective function including equipment cost, worker time related cost, and station opening cost is introduced to be minimized in existence of a constant cycle time. Finally, efficiency of the proposed formulation of the introduced problem is studied and tested over some benchmarks.

Agricultural production can be described by discrete time as there is harvest in every year only once. The agricultural production is uncertain because of the weather and the ever changing technology. At the same time, the sector prefers stability which is reflected in the small changes in the prices. The uncertainty of the price may be modeled by a set-valued function in a single product market. The independent variable is the price expectation of the producer which is the future value of the price estimated by the producer. It can be assumed that the set-valued function is decreasing because in the case of higher price expectation, greater quantity appears on the market and thus the real market price becomes the lower. The stability of the market may require some control. In this paper the existence of an appropriate control to reach a target interval and to keep the trajectory in the interval is investigated from mathematical point of view. Necessary and sufficient conditions are given for the existence of the viable solution. The “striped structure” of the dynamical system is explored as well.

In this paper, the problem of determining the most general Lie point approximate symmetries group for the nonlinear filtration equation with a small parameter is analyzed. By applying the basic Lie approximate symmetry method for the nonlinear filtration equation with a small parameter, the classical Lie point approximate symmetry operators are obtained. Also, the algebraic structure of the Lie algebra of approximate symmetries is discussed and an optimal system of one-dimensional subalgebras of the nonlinear filtration equation with a small parameter, symmetry algebra which creates the preliminary classification of group invariant solutions is constructed. Particularly, the Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries and group invariant solutions associated to the symmetries are obtained.

In real life, many events may have severe effects on human being lives. These events can happen casually such as accident, heart attack or another severe disease, and deliberately like fights among people. From the engineering point of view, it does not matter what the reason of happening such events is, but the important thing is to rescue the affected people as much as possible in a short time and based on a scheduling point of view. In this study, we consider a real-life medical emergency service problem for a city with its known hospitals or medical care center locations. A limited number of ground and aerial vehicles, like ambulance and helicopter, are given to be assigned to these sites in which at most one vehicle from each type can be assigned. The aim is minimizing the total travel distances which are a function of the response time to the patients. To solve the problem, a mathematical formulation is proposed, and a metaheuristic solution method based on the genetic algorithm is developed, since the problem belongs to the NP-hard family of problems.

In this paper, we restrict our attention to the efficient frontier of the BCC model, where the BCC model is a well-known basic model in Data Envelopment Analysis (DEA). We here assume that each Decision Making Unit (DMU) has one input and one output. In order to obtain BCC efficient frontier, the paper proposes a polynomial-time algorithm of complexity bonded by  to produce well-behaved affine functions. The produced functions are then used to determine a point-wise minimum of a finite number of affine functions. It will be shown that by finding this function, we in fact also determine the efficient frontier of the BCC model. The main advantage of this approach is ability to achieve the efficient frontier, without solving a mathematical programming problem. Also, all of the Pareto efficient DMUs, as BCC-efficient DMUs, can be easily obtained using the proposed algorithm. A numerical example is presented to explain the use and effectiveness of the proposed algorithm.

A closed-loop supply chain network (CLSCN) is consisted of both forward and reverse supply chains. In this paper, a CLSCN is including multiple plants, collection centers, demand markets, products and disposal centers. The plants manufacture the new products, then the new products are distributed to the demand market locations and the returned products are collected for sending to the collection centers. Collection centers have important role in recognizing the returned products conditions and the next action of supply chain as follows: inspection and/or separation of the collected products to check whether they are recoverable for sending to remanufacturing plants or unrecoverable ones to be sent to the disposal centers. A mixed-integer linear programming model is proposed to minimize the total cost. Since the uncertain parameters including cost, capacity, demand and the returned products influence the proposed CLSCN, a trapezoidal fuzzy model has been proposed to cope with the vagueness. The expected value is applied to the objective function and the chance constrained programming approach is used to model the uncertain constraint with fuzzy parameters. The numerical examples are coded and solved by GAMZ software. The computational results demonstrate the applicability of the proposed model and solution approach.