dynamic programming

The development and complexity of new markets, on the one hand, and economic constraints, on the other hand, have made it an inevitable necessity to pay attention to the two principles of providing a desirable and reliable level of service to customers and reducing supply and maintenance costs. Therefore, the need to study the methods that enable the production system to deal with these issues is felt more than ever. Just-In-Time production strategy has been mentioned as one of the appropriate approaches to balance between the two principles. On the other hand, the issue of sequencing and scheduling of operations in batch processing systems has been widely considered in the last two decades. A batch processing machine can process a batch of jobs simultaneously, which reduces the machine's set-up time and facilitates material flow management. This study aims to minimize the total weighted earliness and tardiness penalties of jobs with non-identical sizes on the batch processing machine, considering that the due date is tight.

Design/methodology/approach:

 Mathematical programming has been used to model the problem. A mixed integer linear programming model has been proposed for the research problem. Since the problem is shown to be NP-hard, heuristic and meta-heuristic methods have been developed to find near-optimal solutions for industrial-sized instances. Also, a dynamic programming approach has been proposed to find the optimal scheduling of a predetermined batch of jobs.

The dynamic programming algorithm requires a high computational effort, and the solution time by this algorithm increases significantly when the number of jobs increases. However, the obtained results indicated that the proposed heuristic algorithms lead to good performance with less time and in practice, such algorithms can be used for real applications and large-size instances. The average relative deviation of the proposed particle swarm algorithm is less than 1%, and the value of this index for the proposed heuristic algorithm is 1.78%.

Research implications:

 Examining the two investigated methods for batching the jobs, one based on a heuristic algorithm and the other with the help of solving a mathematical model, indicated no significant difference between these two methods. Therefore, if necessary, the heuristic algorithm with less computational effort can be used without losing the quality of the solution.Practical implications: According to the findings, developing efficient heuristic and meta-heuristic algorithms for batch processing machine scheduling in just-in-time production systems can reduce production costs.

Originality/value:

 For the first  the heuristic and meta-heuristic algorithms were proposed for the problem of scheduling a batch processing machine considering a tight due date in a just-in-time production system. A dynamic programming approach was also proposed for the first time to find the optimal scheduling of a predetermined batch of jobs.

Companies must be able to preserve their customers and change them to the faithful ones. The automotive industry is one of the leading industries in the field of customer satisfaction. In this paper, based on a hierarchical analysis approach, customer satisfaction is formulated based on indicators after sale services, sale process, initial quality study, initial quality study, automotive performance execution and layout of the automobile industry. Also, by presenting an optimization model, the optimum customer satisfaction path from 1395 to 1404 is presented as a perspective for Iran Khodro, Saipa and Pars Khodro companies using an optimized control methodology, which is used to solve the MATLAB software. Finally, the cost of upgrading the customer satisfaction of the products of these companies for two consecutive years is 1396-1395. The results of the research show that the number of initial quality study has the most impact on customer satisfaction, which should be given more importance in the future planning of automobile companies as the most important control variable in order to improve the optimum route of customer satisfaction over the years to come.

Portfolio selection has always been one of the important issues in the field of investment management, which discusses how to allocate an investor's capital to different assets and form an efficient portfolio. If the modeling assumptions for portfolio optimization is closer to the real world, the results will be more reliable. Considering single horizon for investment is not real and more investors are investing for more than one period to be able to revise their positions over time. Moreover, in the real world, data and parameters are always uncertain. Therefore, the development of multi-period portfolio optimization models is a basic requirement. In this paper, based on the portfolio theory, a new multi-period portfolio selection model is proposed, which contains transaction costs, liquidity constraints, threshold constraints, cardinality constraints and class constraints. Moreover, mean absolute deviation is used as a measure of risk and uncertainty of data is modeled with scenario tree. Also, in order to solve the proposed model, the dynamic programming method has been used and finally, the model efficiency was tested using data for 5 stocks from Tehran Stock Exchange in a period of 1390 to 1394. In the proposed model, the effect of some factors such as boundary of decision variables and the number of assets in the portfolio is examined. The results indicate that the proposed model has a suitable performance and completely consistent with the theory.

The cell formation problem and the group layout problem, both are two important problems in designing a cellular manufacturing system. The cell formation problem is consist of grouping parts into part families and machines into production cells. In addition, the group layout problem is to find the arrangement of machines within the cells as well as the layout of cells.
In this paper, an integrated approach is presented to solve the cell formation, group layout and routing problems. By Considering the dimension of machines, the width of the aisles, and the maximum permissible length of the plant site, a new framework, called spiral layout, is suggested for the layout of cellular manufacturing systems. To extend the applicability of the problem, parameters such as part demands, operation sequences, processing times and machine capacities are considered in the problem formulation. The problem is formulated as a bi-objective integer programming model, in which the first objective is to minimize the total material handling cost and the second one is to maximize the total similarity between machines. As the problem is NP-hard, three metaheuristic algorithms, based on Genetic Algorithm and Simulated Annealing are proposed to solve it. To enhance the performance of the algorithms, a Dynamic Programming algorithm is embedded within them. The performance of the algorithms is evaluated by solving numerical examples from the related literature. Finally, a comparison is carried out between the proposed spiral layout and the linear multi-row layout which has recently presented in the literature.

The amount of gas lift from the common field of South Pars highly depends on the pattern field development the by each party. This paper models the optimum production of gas from a reservoir block of the South Pars field and analyzes the effects of the economic parameters on the optimum path. Dynamic programming has been used to solve the optimization problem. To solve the problem numerically, state variables have been considered as discrete variables. According to the results, economic parameters including projected path of natural gas prices and the government discount factor play important role in determining the optimum path of gas production from the field. Therefore, for the gas field under investigation, despite being a common field between Iran and Qatar, the maximum potential production by the field is not necessarily the optimum production for the field. In this way, maximizing the return of the reservoir is not necessarily equivalent to maximizing the recovery factor of the field. Accordingly, maximizing the economic return should be considered in the development of hydrocarbon fields.

In competitive markets, attracting potential customers and keeping current customers is a survival condition for each company. So, paying attention to the requests of customers is important and vital. In this paper, the problem of order acceptance and scheduling has been studied, in which two types of customers or agents compete in a single machine environment. The objective is maximizing sum of the total profit of first agent's accepted orders and the total revenue of second agent. Therefore, only the first agent has penalty and its penalty function is lateness and the second agent's orders have a common due date and this agent does not accept any tardy order. To solve the problem, a mathematical programming, a heuristic algorithm and a pseudo-polynomial dynamic programming algorithm are proposed. Computational results confirm the ability of solving all problem instances up to 70 orders size optimally and also 93.12% of problem instances up to 150 orders size by dynamic programming.

In recent decades، information technology systems and tools play an essential role in improving the method for responding the requests from managers. Decision support system as an important tool has the fundamental role in organizations. In the team of Software project allocating people to tasks has a noticeable effect on profits. A decision support system can help managers in making appropriate decisions. In this research the DSS was designed by integrating Dynamic Programming and Goal Programming method. Usually there are different goals and even contradictory ones in Software project. Such goals would complicate the decision making process. Decision support system proposed in this study defines the goal for each criterion. The deviation from the goal is for evaluating the answers. The advantage of decision support systems is combining goals that are different in nature. The proposed algorithm compared with other methods requires less computation.

Considering its application, stochastic lot sizing is a significant subject in production planning. Also the concept of service level is more applicable than shortage cost from manager's viewpoint. In this paper, the stochastic multi period multi item capacitated lot sizing problem has been investigated considering service level constraint. First, the single item model has been developed considering service level and with no capacity constraint and then, it has been solved using dynamic programming algorithm and the optimal solution has been derived. Then the model has been generalized to multi item problem with capacity constraint. The stochastic multi period multi item capacitated lot sizing problem is NP-Hard, hence the model could not be solved by exact optimization approaches. Therefore, simulated annealing method has been applied for solving the problem. Finally, in order to evaluate the efficiency of the model, low level criterion has been used.

Since at the present time, one of the major revenues of the government are from taxes, realizing the amount of tax revenues and making decisions of policies likely to enhance earnings in proper times with considering the tax current value is very important. According to the Markov chain method capabilities in understanding the possible random processes and dynamic programming methods, in this article, combination of these two methods with using information from income tax firms in the country in 1384-88 were used to represent a suitable pattern for discount in tax policy. Results showed that according to the prior data periods, the amount of non-received tax revenue was 3926 billion Rials. With 2% discount to customers and the tax received current value, it proceeded to 4511 billion Rials. In this way, the discount- index was determined for each year. As the process of tax revenues is also a transition period, paying taxes during the 12- month- period and the discount based on the tax current value were taking into consideration. The current value of future tax -cash flows during this period was equivalent to 16,034 billion Rials. Finally, using dynamic programming, the break event point of tax discount index was determined. Accordingly, in this manner, if the value of discount was less than 22%, the optimal policy for the government to increase the value of the received tax would be not to give discount to the customers and if the discount factor was over 22%, the favorable government policy would be providing discount to customers.