Recently, various deterministic inventory models were developed for deteriorating items with the uniform demand pattern (either increasing or decreasing) throughout the cycle. However, such types of models are not suitable for many real business problems. In particular, the demand patterns of various items are not steady throughout the cycle. In many inventory models, ordinarily, the demand rises first, then it becomes static and finally decreases, and such types of demands can be portrayed by considering trapezoidal functions. Moreover, the costs associated with the inventory become imprecise due to several socio-economical factors.  As a result, the optimal solution obtained by the classical inventory model may not fit the actual scenario. Keeping this in view, we develop here an inventory model for deteriorating items having the trapezoidal type of demand function in both crisp and fuzzy environments by considering three possible cases of shortages which are completely backlogged. Furthermore, in view of the comparative study of both scenarios, different data sets of constraints are examined for optimal results. Also, it is observed that the optimal results of the fuzzy model are more appropriate to real-world inventory problems. Finally, in order to strengthen the present investigation, the managerial insight of fluctuation in parameters is presented analytically via sensitivity analysis.

Cost optimization inventory model for deteriorating items with trapezoidal

demand rate under completely backlogged shortages in crisp and fuzzy environment

Management of inventory and its control for the retailers involves the procurement and storage of items for the smooth functioning of day-to-day business affairs. The procurement of goods depends on lead time and the payment mechanism. Thus, these components have a vital role in the optimal strategy for inventory control and management. As a result, these two components have a very high priority in recent developments on inventory models. However, a few researchers investigated such inventory problems with the integration of these components. Also, most of the researchers overlooked the impreciseness of different parameters while developing the inventory models. Thus, it is highly required to consider lead-time, payment strategy, and the impreciseness of parameters for inventory problems to provide an insight into real practice. Therefore, keeping these aspects in view, we develop two inventory models for Weibull deteriorating items having selling-price-dependent demand with positive lead-time in prepayment, interim payment, and post-payment scenarios. In the first model (crisp), the inventory constraints and costs are assumed to be deterministic. However, in the second model (fuzzy), only cost parameters are considered as imprecise, and the rest are all deterministic in nature. We first describe the solution strategies for obtaining the optimality of both crisp and fuzzy models. Subsequently, we perform numerical experiments with various sets of inventory constraints to investigate the efficiency of the proposed models. Finally, through sensitivity analysis of crucial parameters, we provide a ready reference to managerial insights making essential decisions in handling various circumstances which arise during the inventory cycle due to alteration of different constraints or parameters. 

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Retailer’s Optimal Ordering Policy for Deteriorating Inventory having Positive Lead Time under Pre-Payment Interim and Post-Payment Strategy

An economic order quantity (EOQ) model is developed for the deteriorating items with two-staged demand: The demand is assumed to be a generalized demand in the stage of the cycle.For the rest of th...

Formulation of an optimal ordering policy with generalised time-dependent demand, quadratic holding cost and partial backlogging

Technology drives many fields to improve the quality of items during the supply of the products. Despite proficient planning in the industrial system and the presence of sophisticated techniques, there may be some defective items in the lots. This paper deals with the inventory model that determines economic order quantity (EOQ) with learning effect for decaying defective quality items under the inflationary condition and credit financing policy. The objective of the work is to analyze the impact of credit financing policy, learning, and inflationary condition on the order quantity and retailer profits. Results revealed that the trade-credit policy will be beneficial for the retailer. Conclusively, sensitive analysis has been presented to understand the robustness of the models.

https://www.igi-global.com/ViewTitle.aspx?TitleId=304368&isxn=9781683180241

Impact of Inflation and Credit Financing Policy on the Supply Chain With Learning

This paper focuses an optimal policy of an inventory model for deteriorating items with trapezoidal type demand rate and the three-parameter Weibull distribution deterioration rate. The model allows shortages which are completely backlogged in order to achieve better preserving amenity. The authors present some optimal solutions which leads to determine the total inventory cost in which the collective behavior of customers hinges on the waiting time. An easy-to-use optimization technique is included to find the shortage time point and order quantity to minimize the total system cost. Taking into account the above-mentioned assumptions, different kinds of numerical examples are considered to illustrate the theoretical behavior of the framed optimization model. The sensitivity analysis is made for this problem with variation of parameters. The study shows that the optimal solution not only exists but also is unique and is less expensive to operate if the factors of three-phase variation, representing the growth, the steady, and the decline phases of demand with respect to time are considered.

Hadibandhu Pattnaik

Papers

An Optimal Policy for Deteriorating Items With Generalized Deterioration, Trapezoidal-Type Demand, and Shortages