Inventory model for seasonal demand with option to change the market

In real life, when bulk purchase becomes convenient or even mandatory, it is a common practice for distributors to explore an alternative market in order to maximize the revenue earned. In this paper, we consider an inventory model for a product having seasonal demand with two potential markets, say, primary and alternate. The distributor has a single opportunity of procurement prior to multiple demand seasons in the primary and the alternate market. Both the markets have similar demand patterns, with time lag between their demand seasons. The demand is a price and time dependent function with increasing, constant and declining phases within each demand season. The scale parameter of demand rate depends upon the market. In each market, successive seasons are separated by random time. In one replenishment cycle, the distributor has a single option to exit the primary market by transferring the inventory, with or without change in selling price. This option can be exercised at the end of any complete season at the primary market. Our investigations indicate that it will be beneficial for the distributor to shift to the alternate market even at a slightly lower selling price if demand rate in the alternate market is higher. Optimal number of seasons at the primary market before change of price or market is obtained. Optimal policy is obtained for jointly determining the order quantity and price. Concavity of the profit function is discussed. Solution procedure, numerical examples and sensitivity analysis are presented.     

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.     

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 partially integrated production-inventory model with interval valued inventory costs,variable demand and flexible reliability

This paper formulates a production-inventory model to investigate the effects of partially integrated production and marketing policy of a manufacturing firm. Demand is assumed to be variable and dependent on the selling price and marketing cost. Also, different inventory costs are considered as interval valued. Shortages are permitted and partially backlogged with a rate dependent on the waiting time. Considering that manufacturing process generates defective units four possible cases have been identified and studied. Basically, the optimization problems (maximization problem for Marketing department and minimization problems for Production and Research & Development departments) have been formulated and solved. For solving these optimization problems, an efficient soft computing algorithm based on Particle Swarm Optimization-Constriction factor (PSO-CO) is proposed. In order to illustrate and validate the production-inventory model a numerical example is solved. Finally, a sensitivity analysis is done to study the effect of changes of different system parameters on optimal policies.     

需求依赖广告费用和销售价格的newsboy型产品库存模型

在假定随机需求是关于销售价格和广告费用的一般函数的前提下,提出一个新的ｎｅｗｓｂｏｙ模型,给出了寻求最优广告费用、销售价格及订货量的分析方法,并且还分析了需求的不确定性对最优销售价格和广告策略的影响．最后,通过数值实例验证了模型的求解过程并得到相关管理启示．     

An inventory replenishment policy for deteriorating items with shortages and partial backlogging

It has long been assumed that the shortages in inventory systems are either completely backlogged or totally lost. However, it is more reasonable to characterize that the longer the waiting time for the next replenishment, the smaller the backlogging rate would be. Moreover, the opportunity cost due to lost sales should be considered since some customers would not like to wait for backlogging during the shortage periods. Without considering these two realistic conditions, study on the inventory modeling for deteriorating items with shortages and partial backlogging cannot be complete and general. In the present article we define an appropriate time-dependent partial backlogging rate and introduce the opportunity cost due to lost sales. Numerical examples are also presented to illustrate the effects of changes in backlogging parameter and unit opportunity cost on total cost and the optimal number of replenishments.Scope and purposeIn a recent article published in this Journal, Giri et al. (Comput. Oper. Res. 27 (2000) 495–505) implemented an existing procedure to the inventory problem of Hariga and Al-Alyan (Comput. Oper. Res. 24 (1997) 1075–83) which concerns with lot-sizing heuristic for deteriorating items with shortages allowed in all cycles except the last one. Giri et al. deviated from the traditional practice and suggested a new policy allowing shortages in all cycles over a finite planning horizon. Their numerical results indicated the proposed policy is cheaper to operate with a cost reduction up to 15%. However, they did not consider the opportunity cost due to lost sales that happen because customers would not like to wait for backlogging. Moreover, for many products with growing sales, the length of the waiting time for the next replenishment is the main factor for determining whether the backlogging will be accepted or not, and the backlogging rate is expected to be time-dependent. Thus the assumption made in Giri et al. that the backlogging rate is a fixed fraction of the total amount of shortages is not reasonable.The purpose of this paper is to present a more realistic discussion of the inventory problem for deteriorating items with time-varying demands and shortages over a finite planning horizon. In contrast to the model by Giri et al., we define an appropriate partial backlogging rate and introduce the opportunity cost due to lost sales. We attempt to complement their model as a practical and general solution for inventory replenishment problems. With these extensions, the scope of applications of the present results is expanded.     

A multi-warehouse inventory model for items with time-varying demand and shortages

This paper develops a deterministic replenishment model with multiple warehouses (one is an owned warehouse and others are rented warehouses) possessing limited storage capacity. In this model, the replenishment rate is infinite. The demand rate is a function of time and increases at a decreasing rate. The stocks of rented warehouses are transported to owned warehouse in continuous release pattern. The model allows shortages in owned warehouse and permits part of the backlogged shortages to turn into lost sales—which is assumed to be a function of the currently backlogged amount. The solution procedure for finding the optimal replenishment policy is shown. As a special case of the model, the corresponding models with completely backlogged shortages and without shortages are also presented. The models are illustrated with the help of numerical examples. Sensitivity analysis of parameters is given in graphical form.Scope and purposeIn practical inventory management, there exist many factors like an attracted price discount for bulk purchase, etc. to make retailers buy goods more than the capacity of their owned warehouse. In this case, retailers will need to rent other warehouses or to rebuild a new warehouse. However, from economical point of views, they usually choose to rent other warehouses. If there are multiple warehouses available, an important problem faced by the retailers is which warehouses to be selected to hold items replenished, when to replenish as well as what size to replenish. For such a problem, the existing two-warehouse models, based on an unrealistic assumption that the rented warehouse has unlimited storage capacity, presented some procedures for determining the optimal replenishment policy. This paper extends the existing two-warehouse models in three directions. Firstly, the traditional two-warehouse models assumed the storage capacity of the rented warehouse unlimited. The present paper relaxes this impractical assumption and considers the situation with multiple rented warehouses having a limited capacity. Secondly, the traditional two-warehouse models considered a constant demand rate or a linearly increasing demand rate. In this model, the demand rate varies over time and increases at a decreasing rate, which implies an increasing market going to saturation. Thirdly, we extend the two-warehouse models to the case with partially backlogged shortages. The purpose of this paper is to build a multi-warehouse replenishment model to help decision-makers solve the problem of which warehouses to be chosen to store items replenished and how to replenish.     

Dynamic reorder point replenishment strategies for a capacitated supply chain with seasonal demand

Managing inventory and service levels in a capacitated supply chain environment with seasonal demand requires appropriate selection and readjustment of replenishment decision variables. This study focuses on the dynamic adjustment of decision variables within supply chains using continuous-review reorder point (ROP) replenishment. A framework is proposed to adjust reorder points and lot sizes based on optimal settings within different regions of a seasonal demand cycle. This framework also includes the optimal timing of adjustments defining these regions. A discrete-event simulation model of a simple, capacity-constrained supply chain is developed and simulation–optimization experiments are performed, the objective being to minimize the total supply chain inventory subject to a target delivery service level. The performance of ROP systems with optimal static and optimal dynamic decision variable settings are compared using two different seasonal demand patterns. The results confirm that performance with dynamic decision variable adjustment is better. For a given delivery service level, average work-in-process inventory levels are almost the same for both systems. However average finished goods inventory levels decrease significantly and are more stable under dynamic adjustment. The practical implication is that both finished goods holding costs and maximum storage capacity requirements are reduced.     

A note on the inventory model for deteriorating items with trapezoidal type demand rate

In this paper, we study the inventory model for deteriorating items with trapezoidal type demand rate, that is, the demand rate is a piecewise linearly function. We proposed an inventory replenishment policy for this type of inventory model. The numerical solution of the model is obtained and also examined.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.     

A discrete-in-time deteriorating inventory model with time-varying demand,variable deterioration rate and waiting-time-dependent partial backlogging

A new inventory system is considered for deteriorating items in which unsatisfied demands are partially backlogged depending on the waiting time until the next replenishment and deterioration rates are constant, but different from period to period. Time is considered as a discrete variable, which better represents some real-life scenarios. An optimal solution can be easily derived. A sensitivity study is provided through substantial numerical experiments to illustrate the use and robustness of the proposed model. The sensitivity analysis reveals some useful and significant insights.     

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.     

Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation

This paper deals with an economic order quantity (EOQ) model for non-instantaneous deteriorating items with price and advertisement dependent demand pattern under the effect of inflation and time value of money over a finite planning horizon. In this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This paper aids the retailer in minimising the total inventory cost by finding the optimal interval 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. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented and the implications are discussed in detail.     

An inventory model with Weibull demand rate,finite rate of production and shortages

We develop here an inventory model with time-dependent two-parameter Weibull demand rate, allowing shortages in the inventory. The shortages are completely backlogged. The production rate is assumed to be finite and proportional to the demand rate. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. Sensitivity of the optimal solution with respect to changes in the values of the system parameters is also studied. Special features of time-dependent Weibull demand rate are discussed.     

随机需求下提前期可控的生产-库存联合优化模型

考虑单供应商和单采购商的生产-库存联合优化问题.假设采购商面临正态需求,供应商的提前期可以控制,并基于此建立供应商与采购商联合期望总成本最小化模型.在所建立的模型中允许采购商缺货,且部分缺货可延期交付,部分缺货发生销售损失;同时考虑运输成本,并假设运输成本依赖于订货量和提前期.给出了求解最优生产批量、最优提前期、最优再订货点和订货量的算法,并通过数值算例进行了说明.     

A stochastic approximation algorithm for option pricing model calibration with a switchable market

This paper is concerned with option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, finite-state Markov chain. At any given instance, the price follows either a geometric Brownian motion model or a mean-reversion model, depending on its market mode. Stochastic approximation/optimization algorithms are developed for model calibration. Convergence of the algorithm is proved; rate of convergence is also provided. Option market data are used to predict the future market mode.     

Multi-product multi-chance-constraint stochastic inventory control problem with dynamic demand and partial back-ordering: A harmony search algorithm

In this paper, a multiproduct inventory control problem is considered in which the periods between two replenishments of the products are assumed independent random variables, and increasing and decreasing functions are assumed to model the dynamic demands of each product. Furthermore, the quantities of the orders are assumed integer-type, space and budget are constraints, the service-level is a chance-constraint, and that the partial back-ordering policy is taken into account for the shortages. The costs of the problem are holding, purchasing, and shortage. We show the model of this problem is an integer nonlinear programming type and to solve it, a harmony search approach is used. At the end, three numerical examples of different sizes are given to demonstrate the applicability of the proposed methodology in real world inventory control problems, to validate the results obtained, and to compare its performances with the ones of both a genetic and a particle swarm optimization algorithms.     

Strategic demand forecasts for the tablet PC market using the Bayesian mixed logit model and market share simulations

Since the release of the Apple iPad and the explosion of consumer demand for tablet PCs, a number of companies are entering into the tablet PC market, creating a situation that is becoming more fiercely competitive, complex, and difficult to predict. Under the singularity of the Korean tablet PC market, into which both the iPad and Galaxy Tab (with an Android operating system) were simultaneously released, this study closely analyses consumer preferences for tablet PCs. It uses the Bayesian mixed logit model, which can reflect consumers’ heterogeneous preferences based on data collected from a conjoint method, and using the estimates of the consumer utility function with model verification, it offers forecasts for the tablet PC market under six likely situations.