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

    This paper discusses a priority based unbalanced time minimization assignment problem which deals with the allocation of n jobs to \(m~(<n)\) persons such that the project is executed in two stages, viz. Stage-I and Stage-II. Stage-I is composed of \(n_1(<m)\) primary jobs and Stage-II is composed of the remaining \((n-n_1)\) secondary jobs which are commenced only after Stage-I jobs are completed. Each person has to do at least one job whereas each job is to be assigned to exactly one person. It is assumed that the nature of primary jobs is such that one person can perform exactly one job whereas a person is free to perform more than one job in Stage-II. Also, persons assigned to primary jobs cannot perform secondary jobs. In a particular stage, all persons start performing the jobs simultaneously. However, if a person is performing more than one job, he does them one after the other. The objective of the proposed study is to find the feasible assignment that minimizes the overall completion time (i.e., the sum of Stage-I and Stage-II time) for the two stage implementation of the project. In this paper, an iterative algorithm is proposed that solves a constrained unbalanced time minimization assignment problem at each iteration and generates a pair of Stage-I and Stage-II times. In order to solve this constrained problem, a solution strategy is developed in the current paper. An alternative combinations based method to solve the priority based unbalanced problem is also analysed and a comparative study is carried out. Numerical demonstrations are provided in support of the theory.

  2. Abstract

    The Karush–Kuhn–Tucker (KKT) optimality conditions are necessary and sufficient for a convex programming problem under suitable constraint qualification. Recently, several papers (Dutta and Lalitha in Optim Lett 7(2):221–229, 2013; Lasserre in Optim Lett 4(1):1–5, 2010; Suneja et al. Am J Oper Res 3(6):536–541, 2013) have appeared wherein the convexity of constraint function has been replaced by convexity of the feasible set. Further, Ho (Optim Lett 11(1):41–46, 2017) studied nonlinear programming problem with non-convex feasible set. We have used this modified approach in the present paper to study vector optimization problem over cones. The KKT optimality conditions are proved by replacing the convexity of the objective function with convexity of strict level set, convexity of feasible set is replaced by a weaker condition and no condition is assumed on the constraint function. We have also formulated a Mond–Weir type dual and proved duality results in the modified setting. Our results directly extend the work of Ho (2017) Suneja et al. (2013) and Lasserre (2010).

  3. Abstract

    The zero weights in data envelopment analysis evaluation causes some problems such as ignoring the some inputs and/or outputs of DMUs under evaluation. Moreover, some authors claimed that the great differences in weights might be a problem. The aim of this paper is to extend the multiplier bound approach to avoid zero weights and great differences in the values of multipliers more. We show that our proposed model is equivalent to the type I assurance region model that will be used in the evaluation efficiency.

  4. Abstract

    Portfolio optimization is defined as the most appropriate allocation of assets so as to maximize returns subject to minimum risk. This constrained nonlinear optimization problem is highly complex due to the presence of a number of local optimas. The objective of this paper is to illustrate the effectiveness of a well-tested and effective Laplacian biogeography based optimization and another variant called blended biogeography based optimization. As an illustration the model and solution methodology is implemented on data taken from Indian National Stock Exchange, Mumbai from 1st April, 2015 to 31st March, 2016. From the analysis of results, it is concluded that as compared to blended BBO, the recently proposed LX-BBO algorithm is an effective tool to solve this complex problem of portfolio optimization with better accuracy and reliability.

  5. Abstract

    Cactus graph is a graph in which any two simple cycles has at most one vertex in common. In this paper we address the ordered 1-median location problem on cactus graphs, a generalization of some popular location models such as 1-median, 1-center, and 1-centdian problems. For the case with non-decreasing multipliers, we show that there exists a cycle or an edge that contains an ordered 1-median. Based on this property, we develop a combinatorial algorithm that finds an ordered 1-median on a cactus in \(O(n^2\log n)\) time, where n is the number of vertices in the underlying cactus.

  6. Abstract

    We present a notion of Henig proper subdifferential and characterize it in terms of Henig efficiency. We also present existence and some calculus rules for Henig proper subdifferentials. Using this subdifferential, we derive optimality criteria for a constrained set-valued optimization problem.

  7. Abstract

    The electric vehicle (EV) technology has been getting momentum due to rapid depletion of fossil fuels and also in taking care of environment. Many manufacturers are investing a lot in electric vehicles for a particular outcome coming from it which can show a sign for replacement of conventional I.C engines. They are taking interest about the customer findings in a car. There are various factors which affect the performance of an electric vehicle such as battery capacity, charging time, price, driving range etc. As we know there are many electric vehicle models that are present in market with different combinations and this study is based on the performance evaluation of electric vehicles using multiple criteria decision making tool from customer point of view. This study highlights the best electric vehicle model in Asian market so that findings of an EV buyer can be fulfilled. Fuzzy analytic hierarchy process has been used to determine criteria weight whereas evaluation of mixed data has been used for performance evaluation and ranking. According to the study BYD E6 becomes the best electric vehicle model in Asian market.

  8. Abstract

    This paper presents a multi-objective dual-resource constrained flexible job-shop scheduling problem (MODRCFJSP) with the objectives of minimizing the makespan, critical machine workload and total workload of machines simultaneously. Two types of multi-objective evolutionary algorithms including fast elitist non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are proposed for solving MODRCFJSP. Some efficient mutation and crossover operators are adapted to the special chromosome structure of the problem for producing new solutions in the algorithm’s generations. Besides, we provide controlled elitism based version of NSGA-II and NRGA, namely controlled elitist NSGA-II (CENSGA-II) and controlled elitist NRGA (CENRGA), to optimize MODRCFJSP. To show the performance of the four proposed algorithms, numerical experiments with randomly generated test problems are used. Moreover, different convergence and diversity performance metrics are employed to illustrate the relative performance of the presented algorithms.

  9. Abstract

    If an exporter or a wholesaler sells goods at a fixed price to be paid in the currency of the seller’s country, then the purchase price of the importer depends upon the prevailing exchange rate of their respective currencies. Ideally, in a floating exchange rate system, the purchase price has to change according to shifts in the exchange rate. In such a scenario the entire exchange rate risk is borne by the importer/buyer. However, in international trade, it is customary for the parties to enter into a risk-sharing agreement, under which the buyer does not pay the seller on the basis of the prevailing exchange rate, but pays a mutually agreed upon price that falls within a range of fluctuating exchange rates. In this manner, the profit or loss due to fluctuations in the exchange rate would be shared by both the parties. These stochastic variations in purchase prices are modeled through a Markov chain. In this article, the resulting purchase and inventory problem is analyzed by identifying a regenerative cycle. An optimal selling price that maximizes the expected profit per unit time is also discussed. Further, optimal ordering policies under no stock-out conditions are derived with an optimal uniform demand corresponding to the optimal selling price. Through sensitivity analyses, differences in profit function with respect to carrying cost fraction, setup costs, and purchase prices are also shown. An investigation into the possible loss if this model solution is not implemented is also made through numerical illustrations. A discussion of a special case of two-purchase price scenario gives additional insight into the problem.

  10. Abstract

    Lean production is a productive philosophy with systematic perspective which takes steps toward eliminating waste materials by applying continual improvement in the sophisticated business processes. Appropriate implementation of this philosophy results in significant changes within a business. Despite the ample efforts devoted to lean production’s evaluation and implementation, this system’s efficient evaluation and implementation are still experiencing countless issues, which seem to be due to absence of a comprehensive model for examining and evaluating lean production within manufacturing companies. Having knowledge of the companies’ performance status, provides us with the possibilities of discovering weakness and strengths, allowing lead strategic managers to have higher performance comparing to their competitors by allocating more volume of market share to themselves. Balanced score card is an important management system which it will be explained using the following four dimensions: management system, exclusive reliance on financial criteria is incomplete and defective. This paper aims at performance evaluation of lean production using balanced score card (BSC), analytic network process (ANP) and inferiority and superiority based ranking (SIR) approaches where, four dimensions have been considered including financial performance, customer, internal business processes and innovation and learning. The expert questionnaire was used to evaluate lean production’s performance based on BSC, DEMATEL survey—for recognizing element’s internal relationships—and TOPSIS survey—for evaluating leanness of production line. To aid us in ranking the production line, data analysis was completed based on Super Decision and Visual PROMETHEE where, the fourth production line with total score of 0.77 stood in the first order, meaning the internal operations with the least level of cost which proves its leanness. The first and sixth line were placed in next ranks with total score of 0.72 and 0.36 which demonstrates leanness level respectively.

  11. Abstract

    In this paper it is discussed that the demand aggregation is an effective approach for reducing inventory levels and the number of facilities under the uncertain supply and demand conditions. Therefore in this paper, an inventory control model is developed incorporating demand aggregation approach for two staged supply chain distribution network under uncertain demand conditions. The two stage of distribution network mainly consists of distributors and retailers. This inventory control model is developed as non-linear programming model with in the different alternatives of distribution networks. The main decision variables of the system are reorder point and the ordering quantity. The prime objective function in this paper is the total cost of system which mainly consists of ordering cost, inventory carrying cost, facility cost, facility operating cost and the cost of shipment. The model is solved for total cost minimization which provides the optimum inventory policy (reorder point and ordering quantity) and the minimum cost. Through this problem best alternative of distribution network is also suggested along with optimum reorder point, ordering quantity and total cost of the system. Some other vital inventory performance parameters besides of ordering quantity and reorder point are also evaluated for the system. These performance parameters are safety stocks, expected shortages per cycle, fill rates, cycle service level, average inventory etc. These performance parameters are evaluated with total cost of the system under different uncertainty levels for a desired service level. This problem also yielded the best network options in given uncertain conditions of demand and supply. This model is formulated for single product and single period. This study mainly focused on the small part of supply chain i.e. distribution network for implementing demand aggregation approach. A case study of a sugar mill distribution network has been performed for validating the industrial applications of the proposed model.

  12. Abstract

    In this paper, a production inventory model is studied considering imperfect production and deterioration of item, simultaneously. Both the serviceable and reworkable items are assumed to deteriorate with time. A cost-minimizing model is developed incorporating both Type I and Type II inspection errors. Shortages are allowed that are completely backlogged. All the screened items are reworked at the end of the production process. To encounter a more practical situation, the deterioration rate is considered to be a type-2 fuzzy number. Such a situation arises when the vendor assigns, with similar priority, a number of experts to determine the rate of deterioration and the decision given by each expert is in linguistic term, which may be replaced by a fuzzy number. The aim of the proposed model is to calculate the maximum back-order quantity allowed and the optimal lot size that must be produced in order to minimize the overall inventory cost. The problem is solved for both the crisp and fuzzy models and a numerical example with practical application is also presented to exemplify the procedure. A novel method for solving a type-2 fuzzy optimization problem is developed which results in a set of Pareto optimal solutions for the proposed problem. It is followed by presenting a sensitivity analysis of various parameters involved on the decision variables and the cost function for a better illustration of the model.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

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

  19. 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.

  20. 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.