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

    The core competency of the healthcare system is to provide treatment and care to the patient. The prime focus has always been towards appointing specialized physicians, well-trained nurses and medical staffs, well-established infrastructure with advanced medical equipment, and good quality pharmacy items. But, of late, the focus is driven towards management side of healthcare systems which include proper capacity planning, optimal resource allocation, and utilization, effective and efficient inventory management, accurate demand forecasting, proper scheduling, etc. and may be dealt with a number of operations research tools and techniques. In this paper, a Markov decision process inventory model is developed for a hospital pharmacy considering the information of bed occupancy in the hospital. One of the major findings of this research is the significant reduction in the inventory level and total inventory cost of pharmacy items when the demand for the items is considered to be correlated with the number of beds of each type occupied by the patients in the healthcare system. It is observed that around 53.8% of inventory cost is reduced when the bed occupancy state is acute care, 63.9% when it is rehabilitative care, and 55.4% when long-term care. This may help and support the healthcare managers in better functioning of the overall healthcare system.

  2. Abstract

    To achieve safer machining environment, and minimize emission of harmful and toxic substances during electrical discharge machining (EDM) process along with improvement in its performance, this paper emphasizes on identifying the best parametric combination of a green EDM process using superiority and inferiority ranking (SIR) method. Decision making trial and evaluation laboratory method is also employed to visualize the interrelationships between the responses of the said process while splitting them into cause and effect groups. In this process, peak current, pulse duration, dielectric level and flushing pressure are the input parameters, while process time, relative tool wear ratio, process energy, concentration of aerosol and dielectric consumption are considered as the responses. The optimal parametric combination as derived employing the SIR method is validated with the help of developed regression equations for each of the responses, which show that the adopted approach outperforms the other popular optimization techniques in obtaining the best mix of the green EDM process parameters for having improved machining performance and less hazardous effects on the environment.

  3. Abstract

    Queueing systems experienced in real-life situations are very often influenced by negative arrivals which are independent of service process and cause the elimination of jobs from the system. Such a scenario occurs in computer network and telecommunication systems where an attack by a malicious virus results in the removal of some or all data files from the system. Along this direction many authors have proposed various killing processes in the past. This paper unifies different killing mechanisms into the classical single server queue having infinite capacity, where arrival occurs as renewal process with exponential service time distribution. The system is assumed to be affected by negative customers as well as disasters. The model is investigated in steady-state in a very simple and elegant way by means of supplementary variable and difference equation technique. The distribution of system-content for the positive customers is derived in an explicit form at pre-arrival and random epochs. The influence of different parameters on the system performance are also examined.

  4. Abstract

    This paper examines a continuous review inventory model for perishable items with two demand classes. Demands for both classes occur according to Poisson process. The items in inventory are perishable products and have exponential lifetimes. The time after placing an order is an exponential random variable. When the on-hand inventory drops to pre-specified level s, only the priority customer demands are met whereas the demands from ordinary customers are lost. And also, the demand occurring stock-out periods are lost. The inventory system is characterized by continuous-time Markov process and steady-state probabilities are derived. The expected cost function is formulated and a numerical study is provided for optimization.

  5. Abstract

    In today’s technology-driven world, despite of efficient planning of manufacturing system and development of refined production technologies and control systems; the items produced in a manufacturing system may have some fraction of defectives. Thus inspection of a lot of the items is essential to differentiate perfect and imperfect products. Every business sector has some hidden costs involved in additional managerial cost which are also imperative to calculate for smooth running of the business sector. This work considers an entropic order quantity model with selling price dependent demand and screening to separate imperfect quality products. We find an important observation about effect of entropy cost on the maximization of profit which states that the entropy cost has similar behavior as the selling price of the product. Our findings enlighten the insights of the entropic order inventory model and enrich the advancement of the literature of inventory model. Finally, a hypothetical numerical example is set to validate the model and sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

  6. Abstract

    In this paper we present a simple heuristic algorithm to find high-quality, feasible solutions, for the traveling salesman problem (TSP). We hypothesize, that the quality of the initial solution provided by the proposed heuristic will improve the performance of the subsequent algorithm in terms of number of iterations required to reach a certain level TSP solution. The proposed heuristic does not attempt to compete against known TSP algorithms and heuristics, but instead, should be considered to serve as a “pre-processor”. The method provides a simple framework for testing new node selection and neighborhood rules. The cost matrix of origin and destination pairs is processed in a systematic way starting from a principal diagonal matrix element to find a feasible TSP tour. The matrix reduction, systematic moves in rows and columns, systematic elimination of rows and columns from further consideration, and the “reserved” column declaration, assure that the resulting sequence of nodes and edges forms a complete TSP tour. The process can be repeated from each principal diagonal element. The best TSP tour found can then be used, for example, as an input to another algorithm (e.g. the TABU search, simulated annealing, ant colony optimization, nearest neighbor, or another heuristic) to attempt to improve the tour further. It should be noted, that the proposed technique can also be used for testing of presence of cycles of a proposed solution provided by another algorithm. While the goal of the heuristic algorithm is to attempt to find the optimum tour, optimality cannot be guaranteed.

  7. Abstract

    Many methods have being used for finding optimal ordering policy for the fixed lifetime inventory system. The dynamic programming approach is one of such methods. Hitherto, the claim is that the approach is not applicable to systems with lifetime greater than two periods. In this work, we used a total cost function in the literature to derive the equations for the ordered quantity in each period, for a products with lifetime greater than two periods. MATHEMATICA 8 was used to solve the equations.

  8. Abstract

    In this paper, we develop a model to assign airplane seats to ordinary passengers to minimize their boarding time while some seats have been reserved earlier by high priority passengers. Our proposed mixed integer programming model assigns ordinary passengers to seats based on the amount of their carry-on bags and results in the minimum time to complete boarding of the airplane. The proposed model can result in 5% to 20% reductions in the average boarding time compared to the situation when passengers’ luggage is not considered.

  9. Abstract

    In this paper, an EPQ model for delayed deteriorating items is presented, where the demand before deterioration sets in is assumed to be time dependent quadratic demand and the holding (carrying) cost is assumed to be linearly dependent on time. Three stages are considered as follows: (1) production build up period, (2) period before deterioration starts and, (3) period after deterioration sets in. There is no demand during production build up period and the demand before deterioration begins is assumed to be quadratic time dependent while that after deterioration sets in is assumed to be constant. It is also assumed that shortages are not allowed. The purpose of this paper is to investigate the optimal set of production rates that minimizes the total inventory cost per unit time, the best cycle length and the economic production quantity. A numerical example is given to illustrate the applicability of the model and sensitivity analysis carried out on the example to see the effect of changes on some system parameters.

  10. 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.

  11. 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).

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.