constraint method

In this paper, we introduce a two stages model for allocation of injuries and medical supplies to medical centers. In the first stage a multi objective mathematical model allocates injured people from the affected neighborhood to medical centers. In the second stage a single objective linear model allocates medical supplies from the supply points to medical centers. The first stage’s objective is simultaneously minimizing the total relief time and costs and maximizing the level of matching the type of injury with the specialized field of the medical centers those injuries are sent. The second stage’s objective is to minimize the costs of allocating medical supplies to medical centers. An integrated model that combines the two previous models is presented and comparing the results with the two stages model. Proposed models are applied to one of the districts of Tehran to demonstrate their effectiveness. The case study includes two affected neighborhood and four medical centers and three supply points. ϵ-constraint method is used to produce the Pareto optimal solutions in a MOMP.

This paper focused on scheduling problems arising in a two-machine, identical parts robotic cell configured in a flow shop. Through current research, a mathematical programming model on minimizing cycle time as well operational cost, considering availability of robotic cell as a constraint, is proposed to search for the optimum allocation and schedule of operations to these two machines. Two solution procedures, including weighted sum method and ∊-constraint method are provided. Based on the weighted sum method, like some previous studies, sensitivity analysis on model parameters were done and the optimum solutions were compared with previous results, while the ∊-constraint method can find the Pareto optimal solutions for problems with up to 18 operations in a reasonable time.

Surgical theater is one of the most expensive hospital sources that a high percentage of hospital admissions are related to it. Therefore, efficient planning and scheduling of the operating rooms (ORs) is necessary to improve the efficiency of any healthcare system. Therefore, in this paper, the weekly OR planning and scheduling problem is addressed to minimize the waiting time of elective patients, overutilization and underutilization costs of ORs and the total completion time of surgeries. We take into account the available hours of ORs and the surgeons, legal constraints and job qualification of surgeons, and priority of patients in the model. A real-life example is provided to demonstrate the effectiveness and applicability of the model and is solved using ε-constraint method in GAMS software. Then, data envelopment analysis (DEA) is employed to obtain the best solution among the Pareto solutions obtained by ε-constraint method. Finally, the best Pareto solution is compared to the schedule used in the hospitals. The results indicate the best Pareto solution outperforms the schedule offered by the OR director.

In this article, we propose a special case of two-echelon location-routing problem (2E-LRP) in cash-in-transit (CIT) sector. To tackle this realistic problem and to make the model applicable, a rich LRP considering several existing real-life variants and characteristics named BO-2E-PCLRPSD-TW including different objective functions, multiple echelons, multiple periods, capacitated vehicles, distribution centers and automated teller machines (ATMs), different type of vehicles in each echelon, single-depot with different time windows is presented. Since, routing plans in the CIT sector ought to be safe and efficient, we consider the minimization of total transportation risk and cost simultaneously as objective functions. Then, we formulate such complex problem in mathematical mixed integer linear programming (MMILP). To validate the presented model and the formulation and to solve the problem, the latest version of ε-constraint method namely AUGMECON2 is applied. This method is especially efficient for solving multi objective integer programing (MOIP) problems and provides the exact Pareto fronts. Results substantiate the suitability of the model and the formulation.

This paper considers a two-stage assembly flow shop problem (TAFSP) where m machines are in the first stage and an assembly machine is in the second stage. The objective is to minimize a weighted sum of earliness and tardiness time for n available jobs. JIT seeks to identify and eliminate waste components including over production, waiting time, transportation, inventory, movement and defective products.Two-stage assembly flow shop is a combinational production system in which different parts are manufactured on parallel machines independently. This system can be used as a method to produce a variety of products through assembling and combining different set of parts. We apply e-constraint method as an exact approach to validate the proposed model and to obtain fronts of the solutions in the solution spaceThe goal of the proposed problem is trade off between two objectives, minimization makespan and total weighted tardiness and earliness. To analyze effects of n and m factors on the efficiency and performance of the proposed algorithm, we calculate the complexity of sub problems based on factors n and m and the computational results demonstrate that the computational time increases with increasing in n and m, in other words, complexity of the problem increases.