A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimisation

This paper deals with a deterministic inventory model for linear trend in demand under inflationary conditions with different rates of deterioration in two separate warehouses (owned and rented warehouses). The replenishment rate is infinite. The stock is transferred from the rented warehouse to owned warehouse in continuous release pattern and the associated transportation cost is taken into account. At owned warehouse, shortages, if any, are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of the next lot. The corresponding problems have been formulated as nonlinear constrained optimisation problems for two different policies (inventory follows shortage (IFS) and shortage follows inventory (SFI)). Finally, the model has been illustrated with a numerical example and to study the effects of changes of different system parameters on initial stock level, maximum shortage level and cycle length with the minimum cost of the system, sensitivity analyses have been carried out by changing one parameter at a time and keeping the others at their original values.     

需求依赖库存且短缺量部分拖后的促销商品库存模型

促销商品是商场吸引顾客前往购买消费的一种重要手段,它可以有效带动其他商品的销售从而提高商场销售收入。考虑促销商品在缺货期间价格和时间对顾客等待行为的影响,构造了一个与销售价和等待时间相关的短缺量拖后率,建立了多次订货下两阶段存货影响需求和顾客等待的促销商品库存模型,并利用仿真方法分析价格和时间敏感因子、存货影响需求临界点、销售价格对销售商订货策略和系统总利润的影响。结果表明：价格和时间敏感因子对各周期服务水平影响显著,存货影响需求临界点对订货次数影响较大;当销售价在一定范围时,销售商只需调整各周期服务水平,而当销售价过高或过低时,销售商则需同时调整各周期服务水平和订货次数     

需求依赖库存且有时变短缺拖后率的非立即变质物品库存模型

研究了时变短缺部分拖后条件下非立即变质性物品的库存补给模型,其中物品的变质率随时间变化而变化。当库存水平为正值时,市场需求受销售价格影响;当库存为负值时,不能满足的需求被部分拖后,拖后率与在缺货期间已经发生的缺货量有关。通过考虑短缺拖后率和变质率同时随时间变化对库存补给策略的影响,建立具有短缺量部分拖后的非立即变质性物品的库存模型,并且给出模型最优解存在的必要条件,得到一类更加符合实际情形的库存模型。最后,用数值算例说明模型的实际应用。     

An economic production lot size model with increasing demand, shortages and partial backlogging

In this paper, an economic production quantity model is developed for a production–inventory system where the demand rate increases with time, the production rate is finite and adjustable in each cycle over an infinite planning horizon and shortages are permitted. The cost of adjusting the production rate depends linearly on the magnitude of the change in the production rate. During the stock‐out period, a known fraction of the unsatisfied demands is backordered while the remaining fraction is lost. The model is formulated taking the demand rate as a general increasing function of time and the optimal production policy is obtained for the special case of a linearly increasing demand rate. The proposed model is also shown to be suitable for a prescribed time horizon. A procedure to find approximately the minimum total cost of the system over a finite time horizon is suggested. A numerical example is taken to illustrate the solution procedure of the developed model.     

A general model for EOQ inventory systems with partial backlogging and linear shortage costs

We present a mathematical model which generalises several known deterministic Economic Order Quantity (EOQ) inventory systems with partial backlogging. This inventory model considers purchasing cost, holding cost, shortage costs and replenishment cost. Shortage costs (backorder cost and lost sales cost) are both made up of a fixed cost and a variable cost which depends on the length of the waiting time for the next replenishment. The optimal policy is characterised through a sequential optimisation procedure. To illustrate the model, numerical examples and sensitivity results are given.     

修改D-W分解求具有需求时间窗和投机性成本的批量问题

研究多产品具有能力约束、需求时间窗、允许延期交货和投机性成本的批量问题.分析无能力约束凸包极点的特征,采用修正的Dantzig-Wolfe分解对原问题进行等价变换.使用列生成获得下界,同时采用启发式分支定界寻找近优解.对随机算例进行了测试与比较,计算结果表明上界与下界之间的间隙非常小;另外分析了当能力参数和订单规模变化时解的质量和计算时间.     

Optimal replenishment policy for perishable items with stock-dependent selling rate and capacity constraint

In this paper, a deterministic inventory model is developed for deteriorating items with stock-dependent demand and finite shelf/display space. Furthermore, we allow for shortages and the unsatisfied demand is partially backlogged at the exponential rate with respect to the waiting time. We provide solution procedures for finding the maximum total profit per unit time. In a specific circumstance, the model will reduce to the case with no shortage. Further, we use numerical examples to illustrate the model.     

A distribution-free newsvendor problem with nonlinear holding cost

In this paper, we analyse a single-period newsvendor model to determine the optimal order quantity where the customers’ balking occurs.This scenario occurs when the customers are opposed to buy a product for various reasons, such as decreasing quality of product, product is not as good as fresh when it reaches under a threshold level, etc. The model is investigated by assuming that the holding cost function depends on order quantity and the inventory level at which customer balking occurs depends on holding cost. The model allows partial backlogging and permits part of the backlogged shortages to turn into lost sales. We develop the model without taking any specific distributional form of demand, only assuming the mean and the variance of the distribution of demand. Finally, we illustrate the model by numerical examples and compare our distribution-free model with the specific distributional form of demand.     

考虑消费者缺货容忍的变质品订购与信用期策略研究

考虑消费者存在缺货容忍行为,研究变质品的联合订购和信用期决策问题.假设延迟订购消费者面对缺货等待时存在一个容忍期限(即在该容忍期限内零售商无需支付缺货成本),同时考虑市场需求受商业信用期的影响,库存系统允许缺货且短缺量部分延迟订购.以零售商的平均利润最大化为目标,分两种情形构建变质品的订购和信用期决策模型.从理论上证明...     

An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate

In this paper, we formulate a deteriorating inventory model with stock-dependent demand by allowing preservation technology cost as a decision variable in conjunction with replacement policy. Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of preservation technology cost when the replenishment schedule is given. We then provide a simple algorithm to find the optimal preservation technology cost and replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model.