Abstract
Inventory models with integrated time-dependent demands for deteriorative items are considered in this study. The demand models found in the literature include constant, linear, quadratic, exponential, price dependent, and stock dependent among others. To wit, no study exists that uses integrated time-dependent demands. Three models are developed: The first model uses continuously compounded demands, the second model uses linear demands integrated with continuously compounded demands, and the third model uses quadratic demands integrated with continuously compounded demands. Mathematical models are delineated for each model and relevant examples are provided to elucidate the proposed procedure. The objective herein is to obtain optimum order quantities and order intervals concerning the overall cost. Sensitivity analysis is provided for each of the three models. The necessary data was generated using Visual Basic 6.0.
Highlights
Inventory models are of primary significance in industries that require manufacturing, distribution, and retail infrastructure
There is a positive relationship between the increase in the rate of deterioration for items μ and setup costs, deteriorating costs, and total costs, while there is a negative relationship between the increase in the rate of deterioration for items μ and cycle time, optimum quantity, and holding cost
(1) There is a positive relationship between the increase in the setup costs per set (SC) and the cycle time, the optimum quantity, setup costs, holding costs, deteriorating costs, and total costs
Summary
Inventory models are of primary significance in industries that require manufacturing, distribution, and retail infrastructure. Addressing changing demand involves research in two aspects of inventory planning models; the deterioration of inventory items, and variation in the demand rate over time It is, obvious that demand is not constant; it may be time-dependent. Trailogyanath Singh et al [21] developed an inventory model to determine the EOQ for a deteriorating item with a linear time function for the demand rate, a time–proportional deterioration rate, and shortages not allowed. They implement the concept of integrated demands in a higher-order equation for forms of demands such as linear or quadratic continuously compounded demand.
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