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.

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.

An Ordering Policy for Deteriorating Items with Time-Dependent Quadratic Demand and Salvage Value under Permissible Delay in Payment

The article deals with an economic order quantity (EOQ) inventory model for deteriorating items in which the supplier provides the purchaser a permissible delay in payment. This is so when deterioration of units in the inventory is subject to constant deterioration rate, demand rate is quadratic function of time and salvage value is associated with the deteriorated units. Shortages in the system are not allowed to occur. A mathematical formulation is developed when the supplier offers a permissible delay period to the customers under two circumstances: 1) when delay period is less than the cycle of time;and 2) when delay period is greater than the cycle of time. The method is suitable for the items like state-of-the-art aircrafts, super computers, laptops, android mobiles, seasonal items and machines and their spare parts. A solution procedure algorithm is given for finding the optimal order quantity which minimizes the total cost of an inventory system. The article includes numerical examples to support the effectiveness of the developed model. Finally, sensitivity analysis on some parameters on optimal solution is provided.

Optimal Ordering Policy of Deteriorating Items with Mixed Cargo Transportation Over a Finite Planning Horizon

In this paper, we propose a deteriorating items inventory model with constant demand and deterioration rates, and mixed cargo transportation modes. The transportation modes are full container load (FCL) and less than container load (LCL). Deteriorating items, such as specialty gases which are applied in semiconductor fabrication, deteriorate owing to environmental variation. Exact algorithms are proposed to determine the optimal inventory policies over a finite and an infinite planning horizon. Numerical examples are given to illustrate the proposed solution procedures. In addition, when the deterioration rate is large, the results of the proposed model perform better compared to the inventory model proposed by Rieksts and Ventura (2008).

Analysis of an Inventory System for Items with Stochastic Demand and Time Dependent Three-Parameter Weibull Deterioration Function

In recent times, mathematical models have been developed to describe various scenarios obtainable in the management of inventories. These models usually have as objective the minimizing of inventory costs. In this research work we propose a mathematical model of an inventory system with time-dependent three-parameter Weibull deterioration and a stochastic type demand in the form of a negative exponential distribution. Explicit expressions for the optimal values of the decision variables are obtained. Numerical examples are provided to illustrate the theoretical development.

A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

Optimal Policy and Simple Algorithm for a Deteriorated Multi-Item EOQ Problem

This paper considers a deteriorated multi-item economic order quantity (EOQ) problem, which has been studied in literature, but the algorithms used in the literature are limited. In this paper, we explore the optimal policy of this inventory problem by analyzing the structural properties of the model, and introduce a simple algorithm for generating the optimal solution to this problem. Numerical results are reported to show effi-cacy of the proposed method.

SUPPLY CHAIN PERFORMANCE FOR DETERIORATING ITEMS WITH COOPERATIVE ADVERTISING

To study the effect of cooperative advertising on the supply chain of deteriorating items, this paper establishes a Stackelberg game model for a two-echelon deteriorating items supply chain composed of one manufacturer and one retailer under a given support program with an exogenous participation rate. The manufacturer as the leader determines the wholesale price and production rate, and the retailer as the follower determines the retail price and advertising strategies. The strategies of the players under the decentralized scenario and the centralized scenario are respectively characterized. Numerical simulations and sensitivity analysis are conducted to gain some managerial insights. It is shown that the pricing, advertising and production strategies are negatively correlated to deteriorating coefficient, and both the profit and the channel efficiency decrease with deteriorating coefficient; The interaction between price, advertising investment and production rate results in a higher retail price of the centralized channel compared to that of the decentralized channel; Implementing the cooperative advertising program does improve the performance of the supply chain in some cases and the participation rate roughly at 0.5 is most preferable, but it is also possible to distort incentive and damage the channel performance when the participation rate reaches a relatively high level.

AN OPTIMAL DYNAMIC ADVERTISING MODEL WITH INVERSE INVENTORY SENSITIVE DEMAND EFFECT FOR DETERIORATING ITEMS

This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin＇s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.

Optimal Decision Rule of the inventory Problem for Deteriorating items with Shortages and Time－varying Demand

In this paper, we consider the general inventory problem for deteriorating items having time-varying demand and shortages. An optimal order policy is obtained for determining the number of reorders and the time of the reorder points and shortage points in order to minimize the total cost of system. Several fundamental theoretical results are established for this model. The corresponding cases for no-deterioration and no-shortage is also discussed. To illustrate the solution procedure,numerical examples are shown for the special case of linear increasing demand.

Sustainable Integrated Inventory Model for Substitutable Deteriorating Items Considering Both Transport and Industry Carbon Emissions

Sustainable integrated inventory management policy focuses on reducing the environmental impact of the manufacturing and transport sector.This study develops an integrated single-manufacturer single-buyer inventory model for substitutable deteriorating items considering transport and industry carbon emissions.This article categorizes carbon emissions into two parts:direct and indirect emissions.We also assume two mutually substitutable items,and substitution is considered on the buyer's side.If one of the items is out of stock,the demand for that item can be partially satisfied by the stock of the other item;else,demand will be lost.The purpose of this study is to minimize the integrated cost of the supply chain with total carbon emissions produced by industry and transport sectors and to determine the optimal number of deliveries,order level and carbon emission quantity.A solution procedure is developed to find the optimal values of the policy.Numerical experiments and sensitivity analyses are presented to demonstrate the proposed model.

碳减排约束下二级易腐品供应链的博弈模型

针对单一制造商和单一零售商组成的二级易腐品供应链,建立碳限额与交易政策下制造商为主导的斯坦伯格博弈模型.当市场需求依赖于制造商的减排技术水平、零售商的促销努力、销售价格以及库存水平时,分析模型最优解的相关性质并设计算法求解制造商的最优减排技术水平和批发价格以及零售商的最优订购时间、订购次数、销售价格与促销努力.利用数值算例验证理论结果并分析相关参数对供应链成员利润及碳排放的影响.研究结果表明:在碳限额与交易政策下,增加碳配额取值有利于制造商获得更多的利润而增加碳排放权交易价格则会使制造商的利润降低;碳配额对零售商的利润没有影响但增加碳排放权交易价格能够使其利润增加;碳配额对供应链的碳排放没有影响但增加碳排放权价格能够减少碳排放;制造商更愿意对变质率大的产品投资减排技术来降低碳排放.

Inventory Policy for a Deteriorating Item with Time-Varying Demand Under Trade Credit and Inflation

It’s often the case that the supplier will provide the retailer with a permissible delay period in payments, during which the supplier charges the retailer no interest and the retailer accumulates interest earned from investment return. As a type of price reduction and an alternative to price discount,trade credit helps the supplier encourage the retailer’s ordering. This paper develops an inventory replenishment model for a deteriorating item with time-varying demand and shortages, taking account of trade credit and time value of money under inflation over a finite time horizon. This model is an extension and development of the existing studies related to the inventory system considering trade credit and time value of money and offers a more general model with more flexibility and resilience to handle the situation where demand of the end market is non-decreasing with regard to time.

短保质期变质产品的两次订货策略研究

一类短保质期变质产品,如生鲜蔬菜、水果等,增加其库存展示量能为顾客提供更多的拣选机会,从而刺激顾客增加购买量.对此,在综合分析已有变质库存基本模型的基础上,建立了一个更能准确反映当前存货水平和需求率、变质率的关系的库存模型.考虑到计划期可能不是最优订货周期的整数倍,从一般意义上研究了基于保质期约束和计划期可修正的变质产品最后两次订货策略.结论表明,最优订货周期须超过一个保质期.在计划期的一定变动范围内,订货周期越短越有利于增加利润和增强经营的社会外部性,并在计划期的上界达到最优;超过计划期的合理变动范围,则须将不完整订货周期控制在一个保质期内,且越接近保质期越好,否则随着计划期延长,变质量增加而利润却逐渐降低.

易变质性产品生产商和销售商库存协调模型

本文基于如下假定:1)生产商的生产率为有限值且采取两阶段生产供货模式;2)生产的产品具有易变质性.在此假定下,建立了单生产商单销售商生产销售协调模型.讨论了如何利用价格折扣策略来激励销售商的订货行为.在保证销售商利润不减的前提下,给出了求解使得生产商利润达到最大化的最优价格折扣算法,同时给出了生产商的最优供给批量和销售商的最优订货批量.最后,用数值实例来验证模型的求解过程.

信用期下时滞变质品供应链库存和定价的Stackelberg均衡策略

在允许缺货和考虑资金机会成本情况下,根据时滞变质品的基本库存模型,分别构建了信用期下供应商为领导者(SL)和零售商为领导者(RL)的Stackelberg博弈模型。通过分析SL和RL下的Stackelberg博弈模型唯一均衡解,得到两个模型中均衡解的解析表达式。最后,根据数值算例分析得出:(1)在SL供应链中信用期并不总使整个供应链协调,然而在RL供应链中信用期的协调效果较好;(2)延长信用期或增加零售价格均能刺激零售商多订货;(3)在两个模型中,零售价格均随变质时刻递增,且整条供应链达到Pareto改进;(4)SL中供应商变动信用期与RL中零售商变动价格相比,SL供应链收益更高;而当信用期和价格固定,其他参数变动时,RL供应链收益更大。

等级信用支付策略下变质性产品的库存优化模型

基于两层次和等级信用支付策略构建了变质性产品的库存模型,即模型假设上游供应商给予下游零售商一个固定的信用支付期,同时零售商对客户实施带有等级区别的信用支付策略.零售商给予信用好的客户全额贸易信贷且不需要任何押金,相反对信用不好的客户不给予贸易信贷的优惠.讨论了模型最优解的存在性与唯一性,并提供了寻求系统最优订货策略的简单方法.最后,给出了具体数值算例和主要参数的灵敏度分析.

弹性需求条件下具有库存损耗的经济订货批量模型

为了寻求零售商面临数量折扣时的最优订货策略,在库存损耗,以及库存与时间相关的基础上,研究了弹性需求条件下考虑数量折扣的易变质物品经济订货批量问题。折扣前零售商按照常规订货,需求率与时间呈线性关系;折扣后订货量超过常规订货量。为了保证在一个周期内产品完全售出,提出了需求率是时间和库存的函数关系。根据这两种情况,分别建立了经济订货批量模型,运用最优性原理证明了最优解的存在,同时进行了仿真寻优计算,并分析了相关参数的灵敏度。最后,通过对两种模型的比较,得出了零售商可以选择合适的订货策略的结论。

多分销渠道下易变质产品的联合库存与定价模型

研究了电子商务环境下零售商具有多分销渠道的联合库存与定价策略问题。有限计划期内,零售商从上游供应商订购易变质类产品后,通过实体商店满足传统销售渠道下的即期市场需求,同时利用网上商店满足在线销售渠道下的远期市场需求。当销售价格为在线渠道下市场需求率的主要影响因素而当前库存水平与销售价格则是传统渠道下市场需求率的主要影响因素时,针对零售商订购固定成本具有学习效应行为的情形,以计划期内的总利润最大为目标建立了优化模型。通过分析最优解的相关性质,设计了求得最优订购次数,最优订购时间以及最优销售价格的有效算法。最后对武汉市某零售连锁超市关于易变质水果的订购策略进行了实证分析,验证了理论结果并进一步得出了相关参数变化对于最优库存策略与销售价格的影响。

随机需求情形下单一易变质产品库存模型的订购与定价策略

在无限时间范围内,需求率为随机波动函数且依赖于产品销售价格时,研究了单一易变质产品的联合订购与定价策略.采用周期盘点的(T,S)库存策略,即每隔相同的订购周期时长T,将库存水平补充到S,缺货完全补足.在不考虑固定订购成本及订购提前期的前提下,建立了库存模型.采用Aggoun等提出的直接法(Directapproach)及泰勒级数展开对此模型进行了近似.针对需求率为一类特定形式时,分析了易变质产品最优订购与定价策略的求解方法.给出算例并进行仿真,得到了问题的近似最优解.