Impact of Trapezoidal Demand and Deteriorating Preventing Technology in an Inventory Model in Interval Uncertainty under Backlogging Situation

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.

Keywords

• trapezoidal type demand
• interval-valued inventory costs
• deterioration
• preservation technology
• QPSO algorithms