Arindam Roy

A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment

This paper investigates a production-remanufacturing system for a single product over a known-finite time horizon. Here the production system produces some defective units which are continuously transferred to the remanufacturing unit and the constant demand is satisfied by the perfect items from production and remanufactured units. Remanufacturing unit uses the defective items from production unit and the collected used-products from the customers and later items are remanufactured for reuse as fresh items. Some of the used items in the remanufacturing unit are disposed off which are not repairable. The remanufactured units are treated as perfect items. Normally, rate of defectiveness varies in a production system and may be approximated by a constant or fuzzy parameter. Hence, two models are formulated separately with constant and fuzzy defective productions. When defective rate is imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. Here, it is assumed that remanufacturing system starts from the second production cycle and after that both production and remanufacturing units continue simultaneously. The models are formulated for maximum total profit out of the whole system. Here the decision variables are the total number of cycles in the time horizon, the duration for which the defective items are collected and the cycle length after the first cycle. Genetic Algorithm is developed with Roulette wheel selection, Arithmetic crossover, Random mutation and applied to evaluate the maximum total profit and the corresponding optimum decision variables. The models are illustrated with some numerical data. Results of some particular cases are also presented.

A production inventory model with stock dependent demand incorporating learning and inflationary effect in a random planning horizon: A fuzzy genetic algorithm with varying population size approach

A production inventory model for a newly launched product is developed incorporating inflation and time value of money. It is assumed that demand of the item is displayed stock dependent and lifetime of the product is random in nature and follows exponential distribution with a known mean. Here learning effect on production and setup cost is incorporated. Model is formulated to maximize the expected profit from the whole planning horizon. Following [Last, M. & Eyal, S. (2005). A fuzzy-based lifetime extension of genetic algorithms. Fuzzy Sets and Systems, 149, 131-147], a genetic algorithm (GA) with varying population size is used to solve the model where crossover probability is a function of parents age-type (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. In this GA a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. This GA is named fuzzy genetic algorithm (FGA) and is used to make decision for above production inventory model in different cases. The model is illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Performance of this GA with respect to some other GAs are compared.

Inventory models for breakable items with stock dependent demand and imprecise constraints

This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock dependent demand under imprecise constraints. The units are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function, i.e. rate of breakability per unit time may be linear or non-linear function of current stock level. Here shortages are not allowed. Both the crisp and fuzzy models have been formulated as profit maximization problems with crisp/imprecise space and budget constraints and solved by using a gradient based non-linear programming technique, Generalised Reduced Gradient (GRG) Method. The models are illustrated with a numerical example and some sensitivity analyses have been presented.

A Production-Inventory Model for a Deteriorating Item Incorporating Learning Effect Using Genetic Algorithm

Demand for a seasonal product persists for a fixed period of time. Normally the “finite time horizon inventory control problems” are formulated for this type of demands. In reality, it is difficult to predict the end of a season precisely. It is thus represented as an uncertain variable and known as random planning horizon. In this paper, we present a production-inventory model for deteriorating items in an imprecise environment characterised by inflation and timed value of money and considering a constant demand. It is assumed that the time horizon of the business period is random in nature and follows exponential distribution with a known mean. Here, we considered the resultant effect of inflation and time value of money as both crisp and fuzzy. For crisp inflation effect, the total expected profit from the planning horizon is maximized using genetic algorithm (GA) to derive optimal decisions. This GA is developed using Roulette wheel selection, arithmetic crossover, and random mutation. On the other hand when the inflation effect is fuzzy, we can expect the profit to be fuzzy, too! As for the fuzzy objective, the optimistic or pessimistic return of the expected total profit is obtained using, respectively, a necessity or possibility measure of the fuzzy event. The GA we have developed uses fuzzy simulation to maximize the optimistic/pessimistic return in getting an optimal decision. We have provided some numerical examples and some sensitivity analyses to illustrate the model.

Constrained Solid Travelling Salesman Problem Solving by Rough GA Under Bi-Fuzzy Coefficients

In this paper, a Rough Genetic Algorithm (RGA) is proposed to solve constrained solid travelling salesman problems (CSTSPs) in crisp and bi-fuzzy coefficients. In the proposed RGA, we developed a ‘rough set based selection’ (7-point scale) technique and ‘comparison crossover’ with new generation dependent mutation. A solid travelling salesman problem (STSP) is a tavelling salesman problem (TSP) in which, at each station, there are a number of conveyances available to travel to another station. The costs and risk/discomforts factors are in the form of crisp, bi-fuzzy in nature. In this paper, CSTSPs are illustrated numerically by some standard test data from TSPLIB using RGA. In each environment, some statistical significance studies due to different risk/discomfort factors and other system parameters are presented.

Rough Genetic Algorithm for Constrained Solid TSP with Interval Valued Costs and Times

ABSTRACT This paper presents new rough set based genetic algorithms (RSGAs) to solve constrained solid travelling salesman problems (CSTSPs) with restricted conveyances (CSTSPwR) having uncertain costs and times as interval values. To grow the impreciseness in soft computing (SC), the proposed RSGAs, a rough set based age-dependent selection technique and an age-oriented min-point crossover are used along with three types of probability, p-dependent random mutations. A number of benchmark problems from standard data set, TSPLIB are tested against the proposed algorithms and existing simple GA (SGA). CSTSPwRs are formulated as constrained linear programming problems and solved by both proposed RSGAs and SGA. These are illustrated numerically by some empirical data and the results from the above methods are compared. Statistical significance of the proposed algorithms are demonstrated through statistical analysis using standard deviation. Moreover, the non-parametric test, Friedman test, is performed with the proposed algorithms. In addition, a post hoc paired comparison is applied and the out performance of the RSGAs.

An Improved Genetic Algorithm and Its Application in Constrained Solid TSP in Uncertain Environments

In this paper, we propose an improved genetic algorithm (IGA) to solve Constrained Solid Travelling Salesman Problems (CSTSPs) in crisp, fuzzy, rough, and fuzzy-rough environments. The proposed algorithm is a combination of probabilistic selection, cyclic crossover, and nodes-oriented random mutation. Here, CSTSPs in different uncertain environments have been designed and solved by the proposed algorithm. A CSTSP is usually a travelling salesman problem (TSP) where the salesman visits all cities using any one of the conveyances available at each city under a constraint say, safety constraint. Here a number of conveyances are used for travel from one city to another. In the present problem, there are some risks of travelling between the cities through different conveyances. The salesman desires to maintain certain safety level always to travel from one city to another and a total safety for his entire tour. Costs and safety level factors for travelling between the cities are different. The requirement of minimum safety level is expressed in the form of a constraint. The safety factors are expressed by crisp, fuzzy, rough, and fuzzy-rough numbers. The problems are formulated as minimization problems of total cost subject to crisp, fuzzy, rough, or fuzzy-rough constraints. This problem is numerically illustrated with appropriate data values. Optimum results for the different problems are presented via IGA. Moreover, the problems from the TSPLIB (standard data set) are tested with the proposed algorithm.