mathematical programming

This paper discusses a special situation in project management in which an analyst wants to prioritize several independent activities to handle all them one after another, in such a way that there are no precedence relationships over the activities. As a novel idea, in this research, the notion is that the structure of prioritized activities is a linear arrangement, and therefore it could be taken into account as a combinatorial optimization problem. The paper formulates a mathematical model, develops a row-generation solving procedure, and reports the computational results for the problem instances of size up to 300 activities. The results demonstrate the applicability and efficiency of the proposed methodology.

In this research the master surgical scheduling (MSS) problem at the tactical level of hospital planning and scheduling is studied. Before constructing the MSS, a strategic level problem, i.e. case mix planning problem (CMPP), shall be solved to allocate the capacity of operating room (OR) to each surgical specialty. In order to make an effective coordination between CMPP and MSS, the results obtained from solving the CMPP is used as an input for the respective MSS. In the MSS, frequently performed elective surgeries are planned in a cyclic manner for a pre-defined planning period. As a part of the planning process, it is required to level downstream limited resources such as intensive care unit (ICU) and ward beds with patient flow. In this study, a mathematical model is developed to construct an MSS. The proposed model is based on a lexicographic goal programming approach which is aimed at minimizing the OR spare time while considering the results of the CMPP. In this paper, data required to solve MSS, is collected from a medium-sized Iranian hospital. Hence, a robust estimation method is applied to reduce the effect of outliers in the decision making process. The results testify the performance of the proposed method against the solution put in practice in the hospital.

Train scheduling is one of the significant issues in the railway industry in recent years since it has an important role in efficacy of railway infrastructure. In this paper, the timetabling problem of a multiple tracked railway network is discussed. More specifically, a general model is presented here in which a set of operational and safety requirements is considered. The model handles the trains overtaking in stations and considers the stations capacity. The objective function is to minimize the total travel time. Unfortunately, the problem is NP-hard and real size problems cannot be solved in an acceptable amount of time. In order to reduce the processing time, we presented some heuristic rules, which reduce the number of binary variables. These rules are based on problem's parameters such as travel time, dwell time and safety time of stations and try to remove the impracticable areas of the solution space. Furthermore, a Lagrangian Relaxation algorithm model is presented in order to find a lower-bound. Finally, comprehensive numerical experiments on the Tehran Metro case are reported. Results show the efficiency of the heuristic rules and also the Lagrangian Relaxation method in a way that for all analyzed problems the optimum value are obtained.

The rectangular two-dimensional Single Knapsack Problem (SKP) consists of packing a fixed rectangular space (so-called pallet) with a subset of smaller rectangular shapes (so-called pieces) of different dimensions, and without rotation. Pieces have different values. The objective is to maximize the sum of the values of the pieces packed. This paper proposes a new method for solving rectangular two-dimensional SKP based on the column generation approach. Mathematical formulation of the proposed model is simplest than the present mathematical formulations in the state-of-the art. The computational performance indicates that it is an effective method in the view of quality of solution.