An EPQ model with variable production,probabilistic deterioration and partial backlogging under inflation

This paper develops an economic production quantity(EPQ)model under the effect of inflation and time value of money.The rate of replenishment is considered to be a variable and the generalized unit production cost function is formulated by incorporating several factors,such as raw material,labour,replenishment rate,advertisements and other factors of the manufacturing system.The selling price of a unit is determined by a mark-up over the production cost.We have considered three types of continuous probabilistic deterioration function,and also considered that the holding cost of the item per unit time is assumed to be an increasing linear function of time spent in storage.In addition,shortages are allowed and partially backlogged.This model aids in minimizing the total inventory cost by finding the optimal cycle length and the optimal production quantity.The optimal solution of the model is illustrated with the help of numerical examples.

Two-warehouse inventory model for non-instantaneous deteriorating items with optimal credit period and partial backlogging under inflation

This paper analyses an inventory model for non-instantaneous deteriorating items under a two-warehouse system with the effect of inflation and time value of money.We propose the model from the seller’s prospective by incorporating the fact that granting the trade credit from the seller to its buyer not only increases sales and revenue but also opportunity cost and default risk.Moreover,in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The purpose of this study is to determine the optimal credit period and the optimal order quantity such that the total profit of the seller is maximised.Some numerical examples are presented for illustrating the proposed inventory model.Furthermore,sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.

An EOQ model for non-instantaneous deteriorating items with timedependent demand under partial backlogging

This article discusses an economic order quantity model for non-instantaneous deteriorating items in which the demand is assumed to be a linear function of time over an infinite planning horizon.In addition,the salvage value associated with the deteriorated units is also considered.The shortages are allowed and partially backlogged.A mathematical model is framed to obtain the replenishment policy which aids the retailer to minimize the total inventory cost.The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity.The theory developed in this article is illustrated using numerical examples.A computational algorithm is designed to find the optimal solution.Sensitivity analysis is carried out to study the changes in the effect on the optimal solutions and some managerial insights are obtained.

Two-warehouse inventory model with non-instantaneously deteriorating items,stock-dependent demand,shortages and inflation

In this paper,a two-warehouse economic order quantity(EOQ)model for noninstantaneously deteriorating items with stock-dependent demand under the effects of inflation and the time value of money is presented.Also in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal intervals and the optimal order quantity.An algorithm is designed to find the optimum solution of the proposed model.Numerical examples are given to demonstrate the results.Sensitivity analysis of the model with respect to several system parameters has been carried out and some managerial inferences are obtained.

Pricing and inventory decisions for non-instantaneous deteriorating items with price and promotional effort stochastic demand

This study investigates an inventory model for a non-instantaneous deteriorating item with partial backlogging wherein the demand is stochastic in nature and depends on price and promotional effort whereas the deterioration rate is time proportional.Under these settings,a mathematical model is developed with the objective to maximise the expected profit per unit time by determining the optimal price and the length of replenishment cycle.Some useful theoretical results are established to deduce the optimal replenishment schedule.An effective algorithmic procedure is developed to find the optimal solutions to the proposed model.The applicability of the proposed model is illustrated by numerical example.Sensitivity analysis of the optimal solution with respect to key parameters has been carried out and the implications are discussed.The study indicates that though promotional effort stimulates the market demand,it is beneficial in an economic sense when it applies in a conservative manner.

Multi-item EOQ model for fresh fruits with preservation technology investment,time-varying holding cost,variable deterioration and shortages

In a fruit wholesale shop,a fruiterer needs to maintain huge inventory of different ranges of fruit items for customers because of uncertainty in consumer preferences and behaviour.But demand of them may differ and different EOQ models for each item are required for optimal level of EOQ.This paper presents a single inventory model to assimilate these varieties.It is assumed that many fruit items bear constant rate of deterioration,some are with time proportional deterioration and some do not deteriorate.To control deterioration of the units in inventory,the advanced preservation technology is considered.The proposed single inventory model of this paper incorporates composite and heterogeneous features of multiple items and presents analysis for obtaining optimal level for output model parameters.

Trade Credit Policy Between Supplier-Manufacturer-Retailer for Ameliorating/Deteriorating Items

This paper is related to the advancement of the inventory models for ameliorating items and focused on the real-life business situation as with the time the deterioration rate of ameliorating items is increased.In the global world,every supply chain entities as suppliers/manufacturers/retailers want to increase the consumption of their goods without any losses.For this,he/she tries to lure manufacturer/retailers by offering some discounts,i.e.credit period for settling the account.The problem states that the manufacturer purchases the ameliorating items from the supplier,where the supplier offers his/her credit period to settle the account.The manufacturer purchases ameliorating items(like pigs,fishes,ducklings,etc.)and take those items as rawmaterial;when the livestock matures the manufacturer sells it to the retailer and offer credit time for settling the account.Reason to propose the model is when the quantities of livestock become larger,then the manufacturer faces difficulty in maintaining all the livestock.In such a situation,the traditional method(without offering credit period)fails to provide the maximum profit to the manufacturer.Therefore,in order to get maximum profit,the manufacturer needs some more realistic scientific outlook for making decisions.The proposed model provides a more realistic assumption of business markets,by offering credit policy.In the introduced model,manufacturer faces amelioration and deterioration rate simultaneously due to the growth and the death of livestock.The amelioration and deterioration rates are assumed as theWeibull distribution type.Shortages allowed only for the retailer,which is partially backlogged.The main goal of this paper is to minimize the total relevant inventory cost for both the manufacturer and the retailers,by finding the optimal replenishment policy.Themathematical formulation with optimal solutions for manufacturer and retailers are given.Convexity and existence of the proposed model via numerical examples and graphical representations are explained.Finally,the conclusions with some future research direction are discussed.