Two Level Storage Inventory Model with Ramp Type Demand under Inflationary Environment with Partial Backordering

A continuous order-level inventory model is developed for deteriorating items with a ramp type demand function of time. A two parameter Weibull distribution is taken to represent the time to deterioration. The model is solved analytically by enumerating two possible shortage models to obtain the optimal solution of the problem. The method is illustrated by two numerical examples and sensitivity analysis of the optimal solutions with respect to the parameters of the system are carried out.

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.

This paper aims to formulate an optimal policy regarding replenishment of inventory models which deteriorate as ramp type demand function and an inspection is made at the time of fulfilment of inventory. Further delayed payments are allowed. The delayed payments help the stockist to make better profits by earning interest on the credit amount for the permissible delayed time. It also encourages the shopkeeper or stockist to reduce losses. These illustrations are explained with the help of numerical examples to keep large inventories. The impact of delayed payments and inspection helps the shopkeeper or stockist to minimize his losses.

In this article, an economic order quantity (EOQ) model for deteriorating items with trade-credit facility is presented. It is assumed that decay rate is two parameter Weibull distributed function of time. Demand rate of the products increases with time. Shortages are allowed and partially backlogged. The whole study is done in inflationary environment. A numerical assessment is done to exemplify the proposed model and sensitivity analysis with respect to the change in system parameters is also carried out.

In this paper, a computational approach to an inventory model with ramp-type demand and linear deterioration has been presented. With possible cost consideration for the model, the total cost function is constructed and subjected to the optimisation which in turn gives us the system of non-linear equations whose solution is obtained by developing the computing algorithm. Numerical demonstration and sensitivity analysis have been carried out for the model to identify the most sensibilities of various parameters involved in the system.

In this paper, we assume that the supplier offers the retailer a credit period (i.e., M) and the retailer purchases a single deteriorating item from the supplier to satisfy the market demand, and shortages are not allowed. With the consideration of trade credit, we develop an inventory model for a single deteriorating item with ramp-type demand rate. Unlike the previous research, on the one hand, we consider both cases of and thoroughly (where is the changing point from linear demand to the constant demand and T is the replenishment cycle time). On the other hand, our objective is to optimal the replenishment cycle time T to minimise the average total cost, while the previous study is to determine the optimal shortage time point. Then, we obtain some theoretical results and employ an alternative approach to find the optimal replenishment policy efficiently. In order to verify whether the credit period offered by the supplier is significant to affect retailer’s ordering behaviour, we make a comparison between models without and with the strategy of delay in payments. Through numerical examples, we show that when the delay period is longer than the changing point , the advantage of the delay in payments is more obvious, and thus it can entice more potential retailers to order more quantities. Therefore, our study can offer a reference for suppliers to set trade credit period reasonably and retailers to order rationally when they deal with a deteriorating item facing ramp-type demand rate.

A Multi-Item EOQ Model for Deterioration Items with Ramp-Type Demand and Partial Backlogging under Carbon Emission and Inflationary Environment

In general, inventory models consider unlimited capacity of warehouses. But in real inventory situations, the capacities of warehouses are limited. So in such cases, to deal with unlimited stocks, one requires additional warehouses. Here a two-warehouse inventory model has been developed for deteriorating items with ramp type demand. Also a corresponding fuzzy model has been developed by considering inventory costs (holding cost, setup cost) and deterioration cost. Subsequently the model has been solved by fuzzy ranking based approach. In both crisp and fuzzy cases, models are being numerically illustrated through examples through a gradient based nonlinear optimization technique (LINGO). Moreover, some sensitivity analysis has been done by taking into consideration the deterioration rate and cost parameters.

Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments

Study’s Excerpt/Novelty This study introduces a novel economic order quantity (EOQ) model for managing non-instantaneous deteriorating items under two-phase demand rates and linear holding costs, incorporating constant partial backlogging and two-level pricing strategies within a trade credit framework. The model uniquely addresses the complexities of time-dependent quadratic demand before deterioration and constant demand afterward, providing optimal solutions for maximizing total profit by determining the best timing for positive inventory, cycle length, and order quantity. The research not only establishes the theoretical existence and uniqueness of these optimal solutions but also demonstrates practical implications through numerical examples and sensitivity analyses, highlighting the critical impact of deterioration rates on inventory management and profitability. Full Abstract This research developed an economic order quantity model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost, constant partial backlogging rate and two-level pricing strategies under trade credit policy. It is assumed that the holding cost is linear time-dependent, the unit selling price before deterioration sets in is greater than that after deterioration sets and the demand rate before deterioration sets in is considered as continuous time-dependent quadratic, after which it is considered as constant up to when the inventory is completely exhausted. Shortages are allowed and partially backlogged. The purpose of the model is to determine the optimal time with positive inventory, cycle length and order quantity such that the total profit of the inventory system has a maximum value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions have been established. Some numerical examples have been given to illustrate the theoretical result of the model. Sensitivity analysis of some model parameters on the decision variables has been carried out and suggestions towards maximising the total profit were also given. , it is seen that the higher the rate of deterioration the lower the optimal time with positive inventory ( ), cycle length order quantity and the total profit and vice versa. This implies that the retailer needs to take all the necessary measures to avoid or reduce deterioration to maximise higher profit. Based on the results application of the model led to an increase in revenue.

This study examines the inventory management problem for deteriorating item with stock level dependent demand and controllable deterioration under trade credit and complete backlogging and derived the objective function which is the total average cost function and minimized it. We applied the optimization problem solver in MATLAB to solve the derived objective function. From the numerical illustrations and sensitivity analysis, it is observed that the optimal total average cost and the optimal order quantity are sensitive to the initial demand rate, stock level and the reduced deteriorating rate parameters.

This research work derives an integrated inventory model for imperfect production/remanufacturing process with time varying demand, production and repair rates under inflationary environment. This inventory model deals with the joint manufacturing and remanufacturing options. There is a collection process devoted to collect used items with the aim to remanufacture them. Both production and repair runs generate imperfect items. The repair process remanufactures used and imperfect items. Further, it is also considered that the remanufactured item that is classified as good has exactly same quality as that of new one. Demand rate is supposed as time dependent. The production rate is assumed to be demand dependent and therefore it is also time dependent. The repair rate is supposed to be a function of time. All system costs are contemplated in uncertain environment. Therefore, the costs are considered as fuzzy nature. Theoretical results are illustrated thru a numerical example. Finally, a sensitivity analysis is performed in order to know the impact of different parameters on the optimal policy.

This book addresses a broad range of problems commonly encountered in the fields of financial analysis, logistics and supply chain management, such as the use of big data analytics in the banking sector. Divided into twenty chapters, some of the contemporary topics discussed in the book are co-operative/non-cooperative supply chain models for imperfect quality items with trade-credit financing; a non-dominated sorting water cycle algorithm for the cardinality constrained portfolio problem; and determining initial, basic and feasible solutions for transportation problems by means of the “supply demand reparation method” and “continuous allocation method.” In addition, the book delves into a comparison study on exponential smoothing and the Arima model for fuel prices; optimal policy for Weibull distributed deteriorating items varying with ramp type demand rate and shortages; an inventory model with shortages and deterioration for three different demand rates; outlier labeling methods for medical data; a garbage disposal plant as a validated model of a fault-tolerant system; and the design of a “least cost ration formulation application for cattle”; a preservation technology model for deteriorating items with advertisement dependent demand and trade credit; a time series model for stock price forecasting in India; and asset pricing using capital market curves. The book offers a valuable asset for all researchers and industry practitioners working in these areas, giving them a feel for the latest developments and encouraging them to pursue further research in this direction. Lifelong 40%

This paper extends the problem in Ouyang, Chen and Chuang [13] and Huang and Goyal [10] to new product introduction, under which demand is assumed to be the ramp type function of time, and supplier off ers retailer a full and partial deferral of payment to choose from. Ultimately, the determination of optimal order quantity and optimal payment policy minimizing total cost per unit time is explored. Six possible cases occur here, among which one of the most commonly seen will be mathematically analyzed, while the others are presented by numerical examples.

Multivariate demand is a practical approach in today's business scenario. The entropy of a system is a measurement of the amount of disorder. Inflation is one of the major factors in inventory modeling. It makes the inventory model to realistic. Permissible delay in payment also plays an important role in a highly competitive market. It is a promotional tool to push the product, which indirectly reduces the selling price of the product. This paper developed an Entropic inventory model of imperfect product quality with multivariate demand and permissible delay in payment under the inflationary environment. The finding of this paper is that cost of entropy behaves the same as the selling price and EOQ. The numerical example is carried out using the software MATHEMATICA12.0. Sensitivity Analysis is carried out to see the behavior of different parameters.