Abstract
A single-item economic production model is developed in which inventory is depleted not only due to demand but also by deterioration. The rate of deterioration is taken to be time dependent, and the time to deterioration is assumed to follow a two-parameter Weibull distribution. The Weibull distribution, which is capable of representing constant, increasing, and decreasing rates of deterioration, is used to represent the distribution of the time to deterioration. In many real-life situations it is not possible to have a single rate of production throughout the production period. Items are produced at different rates during subperiods so as to meet various constraints that arise due to change in demand pattern, market fluctuations, and so forth. This paper models such a situation. Here it is assumed that demand rate is uncertain in fuzzy sense, that is, it is imprecise in nature and so demand rate is taken as triangular fuzzy number. Then by using 𝛼-cut for defuzzification the total variable cost per unit time is derived. Therefore the problem is reduced to crisp average costs. The multiobjective model is solved by Global Criteria method with the help of GRG (Generalized Reduced Gradient) Technique. In this model shortages are permitted and fully backordered. Numerical examples are given to illustrate the solution procedure of the two models.
Highlights
The classical EOQ Economic Order Quantity inventory models were developed under the assumption of constant demand
In real-life problems the parameters of the stochastic inventory models are fuzzy, that is, not deterministic in nature and this is the case of application of fuzzy probability in the inventory models
The present paper proposes a solution procedure to develop an EPQ inventory model with variable production rate and fuzzy demand
Summary
The classical EOQ Economic Order Quantity inventory models were developed under the assumption of constant demand. Donaldson 1 discussed for the first time the classical no-shortage inventory policy for the case of a linear, positive trend in demand. A unified approach to fuzzy random variables is considered by Kratschmer ; Kao and Hsu discussed a single-period inventory model with fuzzy demand. Fuzzy models for single-period inventory problem were discussed by Li et al. Banerjee and Roy considered application of the Intuitionistic Fuzzy Optimization in the constrained Multiobjective Stochastic Inventory Model. Various types of uncertainties and imprecision are inherent in real inventory problems They are classically modeled using the approaches from the probability theory. This paper considers the modification of EPQ formula in the presence of imprecisely estimated parameters with fuzzy demands where backorders are permitted, yet a shortage cost is incurred. This multiobjective problem is solved by Global Criteria method with the help of GRG Generalized Reduced Gradient technique, and it is illustrated with the help of numerical example
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