部分延迟订购的易变质品联合定价与生产策略

构建了一个需求同时依赖于销售价格和库存水平,生产率和变质率均为常数,允许缺货且缺货量部分延迟订购的易变质品联合定价与生产控制模型。首先证明了在销售价格给定的情况下,系统的总利润函数是关于生产计划的严格凹函数,平均利润函数是严格的伪凹函数,即存在唯一的最优解,并给出其充分条件。接着给出问题的一个数值求解算法。最后通过算例,展示了模型及相关算法的应用,并对相关参数进行了灵敏度分析,结果显示:当产品的生产成本、缺货成本和机会成本增加时,系统的平均利润将下降;生产成本和延迟订购阻力系数对最优定价和生产策略以及平均利润的影响较大。     

基于收益共享的多周期易变质产品供应链协调模型

研究了单个供应商与单个零售商组成的易变质产品供应链系统在有限计划期内的协调问题。考虑到市场需求会同时受到多种因素的影响,构建了市场需求率依赖于销售价格与当前库存水平且随时间呈现一般连续变化的需求函数。将零售商的订购次数、销售价格以及供应商的批发价格作为决策变量,分别求解了集中式与分散式供应链系统下的最优策略。通过与分散式决策的利润值进行比较,得出集中式决策能够使得供应链系统的利润值至少增加1/3。利用收益共享契约机制协调此系统,求解了供应链实现完美协调时收益共享因子的取值区间。最后通过算例验证了理论结果并分析了相关参数变化对系统协调的影响。     

Optimal pricing,production, and inventory for deteriorating items under demand uncertainty: The finite horizon case

This paper aims to investigate the joint dynamic pricing and production decisions of deteriorating items with uncertain demand over a finite selling season, where the demand is price sensitive and the potential demand is characterized by a stochastic process. The stocks deteriorate physically at a constant fraction of the on-hand inventory. A joint dynamic pricing and production problem to maximize the total expected profit is modeled as a stochastic optimal control problem. We derive the closed-form solutions, which are in time-dependent linear feedback form of the inventory level when it is either positive or negative. It is shown that the manufacturer always benefits from a reduction in the volatility of potential market demand. In addition, to highlight the effectiveness of the joint dynamic strategy, we also consider the case of optimal production with a static price. A numerical example is presented to illustrate the validity of the optimal control policy, and sensitivity analysis on major parameters is performed to provide more managerial insights into deteriorating items.     

具有定价和开机成本的生产-库存系统的最优(s,d,S)策略

考虑一个具有有限容量和开机成本的连续盘点生产-库存系统, 其控制策略为(s,d,S)策略. 未被满足的需求都会丢失. 当机器处于关闭状态时,库存产品可以两个不同的价格进行销售. 当机器处于开机状态时,库存只能以较高的价格进行销售. 研究了如何发现该系统下的最优(s,d,S)策略,并开发了用于计算最优控制参数的有效算法.     

允许缺货且带数量折扣的腐烂物质库存模型

在短缺量拖后率是等待时间的负指数函数、订购成本是批量的线性函数的条件下,建立了带数量折扣的腐烂物质库存模型,目标是优化总平均利润.在给定销售价格的情况下,证明了库存系统的最优补货策略存在且唯一;且若采用最优补货策略,平均利润函数是销售价格的凹函数;最后给出了模型的算法,并用数值例子说明了模型和算法的有效性.     

Optimal inventory policies for profit maximizing EOQ models under various cost functions

In this paper, we establish and analyze three EOQ based inventory models under profit maximization via geometric programming (GP) techniques. Through GP, we find optimal order quantity and price for each of these models considering production (lot sizing) as well as marketing (pricing) decisions. We also investigate the effects on the changes in the optimal solutions when different parameters are changed. In addition, a comparative analysis between the profit maximization models is conducted. By investigating the error in the optimal price, order quantity, and profit of these models, several interesting economic implications and insights can be observed.     

Optimal policies for inventory systems with two types of product sharing common hardware platforms: Single period and finite horizon

In this paper, we consider an inventory system whose products share a common hardware platform but are differentiated by two types of software. Choice of different software results in different installation cost and different selling price of the whole product. Product with different software also faces different customer demand. We investigate the optimal proportion of an order to be installed with software 1 or 2, that maximizes expected profit in the single and multiple period scenarios, respectively. The optimal policy is analytically obtained and proved to be an order-up-to policy in each scenario. Our investigation reveals that whether to replenish, and how much to replenish each product depend not only on its own initial inventory level, and system parameters, but also the initial inventory level of the other product. We perform numerical experiments using the optimal policies we have derived in the paper.     

Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging

In this paper, a deterministic inventory model for deteriorating items with price-dependent demand is developed. The demand and deterioration rates are continuous and differentiable function of price and time, respectively. In addition, we allow for shortages and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. Under these assumptions, for any given selling price, we first develop the criterion for the optimal solution for the replenishment schedule, and prove that the optimal replenishment policy not only exists but also is unique. If the criterion is not satisfied, the inventory system should not be operated. Next, we show that the total profit per unit time is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use numerical examples to illustrate the algorithm.     

Effect of declining selling price: profit analysis for a single period inventory model with stochastic demand and lead time

In this paper, considering the empirical trend for sales and price of fashion apparels as prototype, optimal ordering policy for a single period stochastic inventory model is investigated. The impact of the presence of random lead time and declining selling price on the profitability of the retailer is explored. Existence of unique optimal solutions for net profit functions is proved. Numerical examples are presented to illustrate the method of identifying profitable levels of inventory holding and penalty costs. Percentage profit per unit investment in inventory is obtained in order to assist managers in taking business decisions, specifically to the extent of whether or not to take up a particular business under known constraints. It is demonstrated that the optimal inventory policy in the absence of price decline and lead time differs considerably from that when lead time and price decline are simultaneously considered.     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

销售率线性依赖瞬时库存水平的两货栈决策模型

在成熟期的存货影响销售环境下,考虑销售率线性依赖瞬时库存水平,不允许缺货,研究了一类非变质性物品的两货栈库存决策问题.建立了以系统平均总利润最大为目标的决策模型,分析了系统最优库存策略的存在性和唯一性,并给出了求解模型的有效方法.分析结果表明,库存管理者利用租用货栈进行订货决策时,除了要充分考虑企业自身的库存容量外,还取决于自有货栈产品相关参数对库存系统绩效的边际贡献率.     

Hierarchical decision making in production and repair/replacement planning with imperfect repairs under uncertainties

In this paper, we analyse an optimal production, repair and replacement problem for a manufacturing system subject to random machine breakdowns. The system produces parts, and upon machine breakdown, either an imperfect repair is undertaken or the machine is replaced with a new identical one. The decision variables of the system are the production rate and the repair/replacement policy. The objective of the control problem is to find decision variables that minimize total incurred costs over an infinite planning horizon. Firstly, a hierarchical decision making approach, based on a semi-Markov decision model (SMDM), is used to determine the optimal repair and replacement policy. Secondly, the production rate is determined, given the obtained repair and replacement policy. Optimality conditions are given and numerical methods are used to solve them and to determine the control policy. We show that the number of parts to hold in inventory in order to hedge against breakdowns must be readjusted to a higher level as the number of breakdowns increases or as the machine ages. We go from the traditional policy with only one high threshold level to a policy with several threshold levels, which depend on the number of breakdowns. Numerical examples and sensitivity analyses are presented to illustrate the usefulness of the proposed approach.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

Optimal pricing and ordering policy for non-instantaneous deteriorating items under inflation and customer returns

This paper deals with an economic production quantity inventory model for non-instantaneous deteriorating items under inflationary conditions considering customer returns. We adopt a price- and time-dependent demand function. Also, the customer returns are considered as a function of both price and demand. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal replenishment cycles, and the optimal production quantity simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution. Finally, numerical examples are provided to solve the presented inventory model using our proposed algorithm, which is further clarified through a sensitivity analysis. The results of analysing customer returns provide important suggestions to financial managers who use price as a control to match the quantity sold to inventory while maximizing revenues. The paper ends with a conclusion and an outlook to future studies.     

Ordering and pricing of service products in an advance sales system with price-dependent demand

This investigation addresses a service inventory control problem in which a firm orders and sells a service which will be used or consumed by customers on a specific future date. The firm sells the product through an advance booking system, aiming to optimize product price to maximize the total expected profit. Considering situations in which product demand is price-dependent and customers with reservations may cancel advance orders, this work develops a continuous-time model to simultaneously determine the order quantity and selling prices. The analytical results reveal that the optimal ordering quantity and prices are derived via closed-form solutions. In addition, sensitivity analysis of the optimal prices with respect to the system parameters is also conducted to illustrate optimal decision characteristics.     

The implications of costs, capacity, and competition on product line selection

We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal.     

可再生能源配额制下异质权力发电商的绿色生产决策研究

基于可再生能源配额的政策背景,本文构造了发电商三种不同市场权力结构下的绿色生产决策模型。讨论了敏感参数对异质权力发电商最优决策结果的影响,基于参数范围分析了不同权力结构下的最优决策效果。通过消费者效用、发电成本、环境保护的社会福利函数,识别出了参数最优取值范围内的最优决策效果的市场结构。结果显示:当绿证交易价格、最低配额比例超过最低临界值时,绿色发电商能够实现最优决策效果,但对传统发电商的最大利润产生了显著的“挤出”效应。若绿证交易价格和电力需求价格弹性系数在最佳区间内,则传统和绿色发电商既能够达到最优决策效果,又可以最大限度促进社会福利效用的单调增加,即存在绿色发电商主导的最优市场决策结构,但不存在最优纳什决策结构。     

Impact of RFID technology on inventory control policy

RFID application can improve operation performance in a supply chain by reducing or eliminating inventory misplacement and shrinkage. In this paper, we present a periodic review inventory model to investigate and characterize the multiperiod inventory control policies in both non-RFID and RFID cases when the firm encounters misplacement and shrinkage. The optimal inventory control policy is proved to be a two-control limit policy. The control limits in both the non-RFID case and the RFID case are analyzed and examined, while considering the impact of shrinkage and misplacement on inventory policies. A critical inventory level is determined to identify the relationship of higher inventory level control limits between the RFID case and the non-RFID case. An intensive numerical study with sensitivity analysis of selling price, misplacement rate, shrinkage rate, inventory recovery rate, and tag price is conducted. We find that when RFID technology is adopted, the inventory control policy in the RFID case is much more stable than that of the non-RFID case, as the misplaced inventory can be recovered perfectly and instantly for sale and the inventory shrinkage can be reduced by RFID technology. In addition, one of our intriguing findings is that when the shrinkage rate is below a threshold value which is independent of parameters, RFID application has no effect on inventory control policy if the misplaced inventory can be recovered in a timely manner by physical audit, which has not been revealed in previous studies.     

The effect of supply uncertainty in price-setting newsvendor models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the input quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.     

A production–recycling–inventory system with imprecise holding costs

This paper presents an optimal control recycling production inventory system in fuzzy environment. The used items are bought back and then either put on recycling or disposal. Recycled products can be used for the new products which are sold again. Here, the rate of production, recycling and disposal are assumed to be function of time and considered as control variables. The demand inversely depends on the selling price. Again selling price is serviceable stock dependent. The holding costs (for serviceable and non-serviceable items) are fuzzy variables. At first we define the expected values of fuzzy variable, then the system is transferred to the fuzzy expected value model. In this paper, an optimal control approach is proposed to optimize the production, recycling and disposal strategy with respect so that expected value of total profit is maximum. The optimum results are presented both in tabular form and graphically.