## OPSEARCH

OPSEARCH is the official journal of the Operational Research Society of India (ORSI) publishing the research papers in the field of operations research and related fields. It is a quarterly publication (March, June, September and December).

• a) official publication of the prestigious Operational Research Society of India
• b) premier Indian journal in the field of Operational Research

The journal OPSEARCH published by the Operational Research Society of India (ORSI) is a national forum set up with the objective of promoting the education and applications of Operational Research (OR) in day-to-day environment in business, industry and other organizations.

Related subjects » Business & Management - Mathematics - Operations Research & Decision Theory

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1. ### Abstract

A new intelligent computing based approach for solving multi-objective unit commitment problem (MOUCP) and its fuzzy model is presented in this paper. The proposed intelligent approach combines binary-real-coded genetic algorithm (BRCGA) and K-means clustering technique to find the optimal schedule of the generation units in MOUCP. BRCGA is used in order to tackle both the unit scheduling and load dispatch problems. While, K-means clustering technique is used to divide the population into a specific number of subpopulation with-dynamic-sizes. In this way, different genetic algorithm (GA) operators can apply to each sub-population, instead of using the same GA operators for all population. The proposed intelligent algorithm has been tested on standard systems of MOUCPs. The results showed the efficiency of the proposed approach to solve (MOUCP) and its fuzzy model.

2. ### Abstract

This paper deals with multi-model assembly line balancing problem (MuMALBP). In multi-model assembly lines several products are produced in separate batches on a single assembly line. Despite their popular applications, these kinds of lines have been rarely studied in the literature. In this paper, a multi-objective mixed-integer linear programing model is proposed for balancing multi-model assembly lines. Three objectives are simultaneously considered in the proposed model. These are: (1) minimizing cycle time for each model (2) maximizing number of common tasks assigned to the same workstations, and (3) maximizing level of workload distribution smoothness between workstations. Performance of the proposed model is empirically investigated in a real world engine assembly line. After applying the proposed model, possible minimum cycle time is attained for each model. All common tasks are assigned to the same workstations and a highest possible level of workload distribution smoothness is achieved. It is shown that the best compromise solution has led to the best value of the first and second objective functions with a slight distance from the best value of third one.

3. ### Abstract

In this work, we propose a hybrid regression model to solve a specific problem faced by a modern paper manufacturing company. Boiler inlet water quality is a major concern for the paper machine. If water treatment plant can not produce water of desired quality, then it results in poor health of the boiler water tube and consequently affects the quality of the paper. This variation is due to several crucial process parameters. We build a hybrid regression model based on regression tree and support vector regression for boiler water quality prediction and show its excellent performance as compared to other state-of-the-art.

4. ### Abstract

In this paper, we consider a network of switches in which some of the switches may malfunction. Our aim is to find out efficiently (a) if any of the switches in a network of switches are defective, and (b) if there are defective switches, to identify those switches. We find an optimal solution for the first problem and a heuristic solution to the second, and demonstrate the feasibility of our approach through computational experiments.

5. ### Abstract

In this paper, we concentrate on solving the zero-sum two-person continuous differential games using rough programming approach. A new class defined as rough continuous differential games is resulted from the combination of rough programming and continuous differential games. An effective and simple technique is given for solving such problem. In addition, the trust measure and the expected value operator of rough interval are used to find the $$\upalpha$$ -trust and expected equilibrium strategies for the rough zero-sum two-person continuous differential games. Moreover, sufficient and necessary conditions for an open loop saddle point solution of rough continuous differential games are also derived. Finally, a numerical example is given to confirm the theoretical results.

6. In the original published article the “Conclusion and future scope” paragraph has been incorrectly published.

7. ### Abstract

Given a weighted directed graph without positive cycles, we construct a framework to detect all longest paths for pairs of nodes in a network. The interest is to identify all routes with the highest cumulative cost for each source–destination pair. The significance and need for this arises in several scheduling contexts, an example of which is called critical chain project management. All longest routes are enumerated and compared for each output to determine a bottleneck path referred to as critical chain. Besides finding longest paths, minimizing duration needs to be considered. This indicates that multiple types of optimization problems coexist in one methodology. We thus aim to contain the longest-paths problem through constraints, for which an optimal solution that minimizes duration can be detected by solving a single optimization problem. The framework is reduced to a constraint satisfaction problem in a mixed-integer linear-programming context, and the solution can be derived using a general purpose solver. Optimality for the longest-paths problem is proven using the small-m method. Since the developed framework does not require an objective function specification, the methodology can also be incorporated within other optimization based problem contexts.

8. ### Abstract

As businesses operating in the production sector often need to deal with defective products and machine breakdowns, they may experience challenges in their production planning and control processes. This study addresses random machine breakdown to derive an optimal production time for defective products under an abort/resume inventory control policy. Machine time-to-breakdown involves two scenarios: namely, the occurrence of machine breakdown during production and its occurrence after production. Total expected cost functions are derived for each scenario. The average cost is then assessed in terms of expense over time. This study explores assumptions such as the performance of the inspection both during and after production, defective products being discarded, and others being sold at discount prices, and the time-to-breakdown being exponentially distributed. Numerical examples are given to explain the model which has been developed, and the convex formation of the expected function of total cost is illustrated in a graph. Optimal values are investigated for production time and total cost based on two different values of the number of machine breakdowns per unit time. Sensitivity analyses are used to show how a number of system parameters affect the optimal solution. These analyses demonstrate that the demand rate and the number of machine breakdowns have a significant effect on the optimal solutions.

9. ### Abstract

So far, many methods have been proposed to classify items based on ABC analysis, but the results of these methods have had relatively low compliance with the principles of ABC. More precisely, collective value and sometimes the number of items belonging to each category in the methods provided do not meet the basic requirements of ABC called Pareto’s principle. In this study, a number of hybrid methodologies including Shannon’s entropy, TOPSIS (the technique for order preference by similarity to ideal solution) and goal programming are respectively used for determining the weight of criteria which are effective in the inventory items classification, calculations of each item value and its classification based on Pareto’s principle. To this end, the value of each item as well as classification of inventory items is calculated based on Pareto’s principle. The performance of the proposed method is evaluated through (1) statistical analysis, (2) checking the percentage of similarity with other methods and (3) comparison with another method in terms of the number and value allocated to each class. The results confirm the capability of the listed method.

10. ### Abstract

Public distribution system (PDS) is the lifeline of food security in India which involves provisioning of foodgrains. To manage this supply chain more efficiently, an effective performance management system is a pre-requisite. This paper utilises the performance objectives-productivity approach to formalise a performance measurement methodology for the PDS supply chain of foodgrains at state level. Here, the actual values of the performance measures are compared with the objectivated values to arrive at the productivity index which indicates the degree of performance of PDS and its various components. In this model the optimal values of the “objectivated output” can be obtained either by solving a goal programming model or through benchmarking in the multi attribute utility theory framework. As fast movement of foodgrains is vital to reduce the degree of perishability due to losses during transit and storage, this multi-dimensional performance measurement system also rates the losses of foodgrains during various stages of freight transportation with a view to minimise the same. The primary aim in applying this method is to arrive at a benchmarking technique to assess if such supply chain is working effectively and efficiently which is akin to auditing the system. By using the given approach some standardisation could be brought into arrive at the authentic performance level of the PDS.

11. ### Abstract

This article presents a continuous review perishable inventory system in which the perished items will be replaced by the supplier at a later time. Demands occur according to a Markov arrival process. The items in the inventory have exponential life times and these perished items are stored in a place, called pool for replacement. The (sS) ordering policy is adopted. At the time of placing an order, the ordering quantity is adjusted with number of items in the pool. The lead time is assumed to have phase type distribution. The joint probability distribution of the inventory level and the number of pooled items is obtained in the steady state case using the matrix-geometric methods. Various system performance measures in the steady state are derived and the total expected cost rate is calculated under a prefixed cost structure. The results derived in this work are numerically illustrated.

12. ### Abstract

Fully fuzzy quadratic programming became emerge naturally in numerous real-world applications. Therefore, an effective model based on the bound and decomposition method and the separable programming method is proposed in this paper for solving Fully Fuzzy Multi-Level Quadratically Constrained Quadratic Programming (FFMLQCQP) problem, where the objective function and the constraints are quadratic, also all the coefficients and variables of both objective functions and constraints are described fuzzily as fuzzy numbers. The bound and decomposition method is recommended to decompose the given (FFMLQCQP) problem into series of crisp Quadratically Constrained Quadratic Programming (QCQP) problems with bounded variable constraints for each level. Each (QCQP) problem is then solved independently by utilizing the separable programming method, which replaces the quadratic separable functions with linear functions. At last, the fuzzy optimal solution to the given (FFMLQCQP) problem is obtained. The effectiveness of the proposed model is illustrated through an illustrative numerical example.

13. ### Abstract

To transport the commodities in minimum time with maximum safety, the difficulties arise due to mutiny, territory slide, bad road and crashed communication systems, etc. and to overcome these kind of problems, the stochastic solid transportation models with safety and time objective functions under essential constraints are formulated. Taking expected value criterion, Chance-constrained programming technique, uniform distribution $${\mathfrak{U}}\left( {a,b} \right)$$ , exponential distribution $${\mathcal{E}\mathcal{X}\mathcal{P}}\left( \beta \right)$$ and normal distribution $${\mathcal{N}}\left( {\mu ,\sigma^{2} } \right)$$ , four new de-randomization processes are proposed to handle the stochastic programming problem. Finally, the deterministic form of the model is solved using generalized reduced gradient techniques (LINGO.13.0 optimization software). Finally, an enlarge comparison of the proposed concept with the earlier concept are presented and the nature of the solutions is discussed.

14. ### Abstract

The purpose of the present paper is to study the global convergence of a practical Augmented Lagrangian model algorithm that considers non-quadratic Penalty–Lagrangian functions. We analyze the convergence of the model algorithm to points that satisfy the Karush–Kuhn–Tucker conditions and also the weak second-order necessary optimality condition. The generation scheme of the Penalty–Lagrangian functions includes the exponential penalty function and the logarithmic-barrier without using convex information.

15. ### Abstract

In this paper, we propose a model to study the queueing characteristics of nodes in a wireless network in which the channel access is governed by the well known binary exponential back off rule. By offering the general phase type (PH) distributional assumptions to channel idle and busy periods and assuming Poisson packet arrival processes at nodes, we represent the model as a quasi birth death process and analyse it by using matrix analytic methods. Stability of the system is examined. Several important queueing characteristics that help in efficient design of such systems are derived. Extensive simulation analysis is performed to establish the validity of our theoretical results.. It is shown that both the simulated and theoretical results agree on some important performance measures. Some real life data has been used to get approximate PH representations for channel idle and busy period variates, which in turn are used for numerical illustrations.

16. ### Abstract

This investigation presents a Markov model for the performance analysis of the fault tolerant machining system with failure-prone server and supported by warm standbys. To utilize the server’s idle time, provision of server’s working vacation has been done which make the system cost effective. The online and warm standby machines may fail and can be repaired by a single skilled repairman. Due to capacity constraint, when the system reaches its full capacity, no more jobs for repairing of failed machines are allowed until the workload of repair jobs reduces to a threshold level ‘F’. Before initiating the repair of the failed machines in case of coming back from the vacation state, the server requires the setup time. To make system fault tolerable, apart from standby provisioning and repairing of failed machines, the concepts of reboot and recovery are included for the formulation of Markov model. The various performance measures including the reliability indices are derived by using the transient probabilities which are computed using Runge–Kutta method. By taking a suitable numerical illustration, various system indices are examined with respect to different parameters. The computational tractability and sensitivity analysis carried out for the established metrics will provides valuable insights for the maintainability and up-gradation of the existing machining systems.

17. ### Abstract

In the present competitive world, it is often said that “Time is Money” in almost every aspect of life. Time is a factor which affects the various real-life problems directly or indirectly. So, in order to incorporate the “time” as a factor in transportation problems (TPs), we have considered the probabilistic cost/profit function termed as “survival cost/profit” which is again a time-dependent function. In this study, we have assumed that the supply and demand quantities are varying between some specified intervals. Due to the variation in the supply and demand quantities, the value of the objective function is also obtained between interval which is bounded by lower and upper values. Based on the above-stated assumptions, we have developed a couple of mathematical optimization models for the TPs. The solution procedure has also been discussed to solve the proposed mathematical models. At last, a numerical illustration has been presented to show the validity of the model and solution procedure which is helpful in the decision-making process.

18. ### Abstract

Keeping track of employees’ time and attendance is difficult and time-consuming task for the companies. Today many companies are performing the digital time and attendance systems that automatically track and process the data to improve their operations and save money. There are many alternatives for the time and attendance systems in the market and appropriate selection among them is not easy in the presence of multiple, usually conflicting, criteria. So this selection may be considered as a Multi Criteria Decision Making (MCDM) problem. In this paper, the new combined decision making approach based on Criteria Importance Through Inter criteria Correlation (CRITIC) and Weighted Aggregated Sum Product Assessment (WASPAS) methods is used for the time and attendance software selection problem of the private hospital. The weights of the criteria are determined by CRITIC method and the alternatives are ranked by WASPAS method for finding the most suitable alternative. The novelty of this paper to the literature is to combine CRITIC and WASPAS methods for the first time.

19. ### Abstract

Cellular manufacturing is a vital part of lean manufacturing. It is an application of group technology. Three problems in cellular manufacturing are cell formation, machine layout and cell layout problems. However, these problems are NP-hard optimisation problems and cannot be solved using exact methods. A difficult part is to form the machine groups or cells, also called Cell Formation Problem and several techniques have been proposed to solve the same. In this paper, the Cell Formation Problem is solved using an integrated approach of heuristics along with Genetic Algorithm and Membership Index. Heuristics technique is used for domain selection which is used in Genetic Algorithm as the initial population. Genetic Algorithm is useful for optimising the results of machine assignment to cells, and Membership Index is used to assign parts to the cells. The performance is analysed using performance measures such as group technology efficiency and some exceptional elements. The proposed computational methodology is tested on standard problems of diverse size from literature papers using the hybrid approach. Results from test problems show that the proposed method is effective and efficient. The paper is useful from the practicality aspect and also relevant from current research and industry trends.

20. ### Abstract

This paper studies a new algorithm to solve the uncertain generalized assignment problem. The presented technique is based on the concept of branch and bound rather than the usual simplex based techniques. At first, the problem is relaxed to the transportation model which is easy to handle and work with. The model, so obtained is solved by the conventional transportation technique. The obtained solution serves as starting solution for further sub problems. The ambiguity in parameters is represented by triangular fuzzy numbers. We propose a linear ranking function, called the grade function which is based on the centroid method. The grade function is used to rank the triangular fuzzy numbers. The proposed approach is justified numerically by showing its application in generalized machine allocation problem.