Computational Methods in Engineering

---

This paper presents a summary of the results from the simulation of a given two-stages production system which uses JIT. The system consists of an assembly line with two automated assembly cells and two assembly stock points and one manufacturing cell with three manufacturing stock points for storing reserved parts and one receiving stock. Carts with fixed capacity are used for handling the parts. A kanban is attached to each cart. The minimum number of kandbans required to operate the system without shortage in stock are estimated. The effects of changing the demands mean and its variation on the number of carts are also investigated. Finally, a different simulation model is developed for the same production system using conventional job shop decipline and some main characteristics have been compared to the results, from the first model.

---

Flow shop sequencing problem is included in NP-hard problems and a number of heuristic methods have been developed to solve it. Most of these methods are offered for the crisp processing time. However fuzzy algorithm is appropriate for the problems with fuzzy processing time. This paper presents a method in which an algorithm is used to minimize make span of flow shop with fuzzy processing time by taking advantage of fuzzy mathematics. This method is based on the behavior of the decision maker who can make either pessimistic or the most likely decisions. The algorithm includes proper relations and corresponding results.

---

The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for neighboring jobs have been developed and the dominant set for the optimal solution is determined. Branch and Bound (BB) method is also used for this problem. The strong upper and lower limits are introduced in BB, resulting in optimal solutions to a lot of problems in short time periods. To show the effectiveness of the suggested solution methods, as many as 720 problems in different sizes, with 5 to 100 jobs, have been randomly generated and solved.

---

In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually considered. The cutting problems belong to the category of Np-hard problems. So finding a desirable solution in a suitable time is practically impossible and heuristic methods must be used. A meta-heuristic algorithm using SA approach is presented.Then attempt will be made to regulate the SAs parameters. Initial solutions are produced with a rule based algorithm and two internal and main SAs are used that lead to better performance of the algorithm. Due to lack of benchmark or test problems, two procedures for generating random problems is presented and are used to study efficiency of the algorithm. For this purpose, problems about 10 to 50 types of pieces with maximum demands of 2400 are generated and solved using the proposed algorithm. The results indicate that the algorithm capable of finding a solution with less than 6% of waste for problems with 30 types of pieces and total demands of 500.

---

Introducing distributed generation into a power system can lead to numerous benefits including technical, economic, environmental, etc. To attain these benefits, distributed generators with proper rating should be installed at suitable locations. Given the similar effects of distributed generators and capacitor banks on operation indices of a distribution system, simultaneous assignment of best locations and sizes to both will not only lead to greatest benefits from distributed generators but also to lower reactive power capacity requirements. In this paper, a new combined planning problem involving distributed generation and Volt/VAr control means planning is formulated and solved in which the quantity of distributed generators and reactive power sources are simultaneously assigned to buses in a distribution system. Also tap positions of voltage regulators are computed such that with a given distributed generation under peak load conditions, power losses and the reactive power capacity required are minimized. Like many other problems in power network planning, the problem formulated here is a nonlinear combinatorial one. Hence, we employ the tabu search algorithm to solve the optimization problem. The results from applying the algorithm to distribution networks with 6, 19, and 33 buses are presented and compared with those obtained from employing the second order method.

---

This paper deals with resource unconstrained project scheduling problems with the objective of maximizing the net present value (NPV) of project cash flows. Here we present a heuristic algorithm named as differential procedure (Dif_AOA). In order to evaluate the efficiency of this algorithm, networks with node numbers between 10-1000 and network complexity coefficients between 1.3-6.6 have been generated. We have compared both the total time for solving the problem and NPV of the Dif_AOA with those of the recursive search procedure. Computational results show that the Dif_AOA performs very effectively. Extensive analysis have been performed to evaluate the node number, complexity network coefficients(CNC), and deadline.

---

While a great portion of the scheduling literature focuses on time-based criteria, the most important goal of management is maximizing the profitability of the firm. In this paper, the net preset value criterion is studied taking account of linear time-dependent cash flows in single machine and flow shop scheduling problems. First, a heuristic method is presented for the single machine scheduling problem with NPV criterion. Second, the permutation flow shop scheduling problem is studied with NPV criterion. An efficient Branch & Bound algorithm is accordingly presented using strong lower and upper bounds and dominace rules which are expanded for this problem. Finally, three heuristic methods are presented and compared to find appropriate solutions over short periods. By generating random problems of different sizes, it has been shown that the Branch & Bound method is efficient in solving small and medium sized problems, and also that the presented heuristic algorithm is efficient in tackling problems of any size.

---

Nowadays, outpatient providers are struggling to reduce the current costs and improve the service quality. A part of the outpatient service provider is a hemodialysis department with expensive supplies and equipment. Therefore, in the present paper, the scheduling of hemodialysis patients with their preferences has been studied. The aim of scheduling hemodialysis patients in this study is to minimize the normalized weighted sum of deviations from the  patients' preferences and the  total completion time. It should be noted that the patient's preferences include beds, treatment combination of days and their turn. To solve the problem, two mathematical models have been presented. Performence of the models in solving the real data of the hemodyalisis department of Imam Khomeini Hospital, in Kermanshah, was investigated. The results showed the efficiency of the proposed models in considering the preferences of patients;  however, these preferences in the hospital schedule were considered in few cases, as far as it was possible.  So, these preferences has no priority in the hospital schedule. In addition to considering the patients’ preferences, the solution of models reduced the total completion time of the pationts treatment. Also, one of the proposed models in this papercould  optimally solve the instances three times larger than the hospital cases

---

Scheduling in production environments is used as a competitive tool to improve efficiency and respond to customer requests. In this paper, a scheduling problem is investigated in a three-stage flexible flowshop environment with the consideration of blocking and batch processing. This problem has been inspired by the charging and packaging line of a large battery manufacturer. In this environment, the first and third stages involve a single processor machine, and the second one consists of m identical parallel batch processing machines. The objective is to minimize the total weighted tardiness of the received orders.Given the lack of consideration of this problem in the literature, first, a mathematical programming model is presented for the problem. Also, due to the NP-hardness of the problem, a variable neighborhood search algorithm and a memetic algorithm are developed to solve it. The computational results show that the variable neighborhood search algorithm can solve instances up to 1200 orders and 15 machines with an average deviation of about 1.9%, relative to the best solution of the two algorithms, and the memetic algorithm can solve instances up to 1200 orders and 15 machines with an average deviation of about 7.8%, as compared e to the best solution of the two algorithms. In general, computational results show the better performance of the variable neighborhood search algorithm in comparison to the memetic algorithm.