Abstract
The demand for a product is one of the important components of inventory management. In most cases, it is not constant; it may vary from time to time depending upon several factors which cannot be ignored. For any seasonal product, it is observed that at the beginning of the season, demand escalates over time, then it is stable and after that, it decreases. This type of demand is known as the trapezoidal type. Also, due to the uncertainty of customers’ behavior, inventory parameters are not always fixed. Combining these two concepts together, an inventory model is formulated for decaying items in an interval environment. Preservative technology is incorporated to preserve the product from deterioration. The corresponding mathematical formulation is derived in such a way that the profit of the inventory system is maximized. Consequently, the corresponding optimization problem is converted into an interval optimization problem. To solve the same, different variants of quantum-behaved particle swarm optimization (QPSO) techniques are employed to determine the duration of stock-in time and preservation technology cost. To illustrate and also to validate the model, three numerical examples are considered and solved. Then the computational results are compared. Thereafter, to study the impact of different parameters of the proposed model on the best found (optimal or very close to optimal) solution, sensitivity analysis are performed graphically.
Highlights
In the literature of inventory, it is observed that several investigators drew their attention to investigate the impact of trapezoidal type demand rate on the different inventory systems
Wu et al [10] formulated an inventory model with trapezoidal demand and the rate of decaying is dependent on the maximum lifetime of an item along with trade credit facilities
Interval valued salvage value ($)/unit pU < CpL ) Preservation cost ($)/unit/unit time Preservation technology function Replenishment cost ($) Interval valued inventory holding cost ($)/unit/unit time Selling price ($)/unit Stock-in period Cycle length Maximum shortage level Time points of trapezoidal demand in which the demand becomes constant during the time period [γ1, γ2] Sales revenue Interval valued shortage cost/unit/unit time Interval-valued lost-sale cost Backlogging rate Crisp valued total system cost ($) Interval-valued total cost of the system ($) Crisp/ Interval valued average profit ($)
Summary
In the literature of inventory, it is observed that several investigators drew their attention to investigate the impact of trapezoidal type demand rate on the different inventory systems. Wu et al [8] developed two inventory models with trapezoidal demand, time-dependent deterioration, and completely backlogged shortages. Garai et al [11] proposed a fuzzy inventory model with time-varying holding cost under price-dependent demand. Kumar [13] investigated a fuzzy inventory model with trapezoidal demand and time-varying holding costs under shortages. Dutta and Kumar [21] developed a deteriorating inventory model along with time-varying holding cost and demand. Mondal et al [27] introduced an ameliorating inventory model for deteriorating items in crisp and interval environments They have solved the corresponding optimization problem with the help of different variants of quantumbehaved particle swarm optimization techniques. Saha and Sen [38] proposed a price-dependent inventory model for deteriorating items considering shortages. Dye [42] proposed a non-instantaneous decaying inventory model considering preservation facility
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