考虑参照价格效应的易逝品定价与订购策略

在考虑消费者参照价格效应的基础上,构建一个易逝品的定价与订购联合决策模型,其中产品的需求不仅依赖于销售价格还与该产品在消费者心目中的参照价格相关,变质率为常数,系统不允许缺货.分别讨论了对称参照价格效应和非对称参照价格效应两种情况下零售商的最优定价与订购决策问题,证明并得到关于模型结构的一些性质,进而设计了问题的求解算法.通过数值方法分析了参照价格效应参数和变质率对系统最优解的影响,以及两种情况下最优解之间的关系.结果显示:当面对具有参照价格依赖的消费者时,采用适当的营销策略来提高消费者的参照价格对零售商总是有利的;对高变质率产品而言,零售商可保持一个较稳定的订购策略,更多地关注产品的定价策略;面对损失厌恶型消费者,随着消费者参照价格的逐渐提高,零售商的定价与订购策略均应缓慢地改变,而不宜急剧变化.     

Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand

Product perishability is an important aspect of inventory control. To minimise the effect of deterioration, retailers in supermarkets, departmental store managers, etc. always want higher inventory depletion rate. In this article, we propose a dynamic pre- and post-deterioration cumulative discount policy to enhance inventory depletion rate resulting low volume of deterioration cost, holding cost and hence higher profit. It is assumed that demand is a price and time dependent ramp-type function and the product starts to deteriorate after certain amount of time. Unlike the conventional inventory models with pricing strategies, which are restricted to a fixed number of price changes and to a fixed cycle length, we allow the number of price changes before as well as after the start of deterioration and the replenishment cycle length to be the decision variables. Before start of deterioration, discounts on unit selling price are provided cumulatively in successive pricing cycles. After the start of deterioration, discounts on reduced unit selling price are also provided in a cumulative way. A mathematical model is developed and the existence of the optimal solution is verified. A numerical example is presented, which indicates that under the cumulative effect of price discounting, dynamic pricing policy outperforms static pricing strategy. Sensitivity analysis of the model is carried out.     

Optimal pricing policies for services with consideration of facility maintenance costs

For survival and success, pricing is an essential issue for service firms. This article deals with the pricing strategies for services with substantial facility maintenance costs. For this purpose, a mathematical framework that incorporates service demand and facility deterioration is proposed to address the problem. The facility and customers constitute a service system driven by Poisson arrivals and exponential service times. A service demand with increasing price elasticity and a facility lifetime with strictly increasing failure rate are also adopted in modelling. By examining the bidirectional relationship between customer demand and facility deterioration in the profit model, the pricing policies of the service are investigated. Then analytical conditions of customer demand and facility lifetime are derived to achieve a unique optimal pricing policy. The comparative statics properties of the optimal policy are also explored. Finally, numerical examples are presented to illustrate the effects of parameter variations on the optimal pricing policy.     

Optimal price and order size for a reseller under partial backordering

The problem of determining the optimal price and lot size for a reseller is considered in this paper. It is assumed that demand can be backlogged and that the selling price is constant within the inventory cycle. The backlogging phenomenon is modeled without using the backorder cost and the lost sale cost since these costs are not easy to estimate in practice. The case in which the selling price is fixed and therefore, demand is a known constant is also considered. Given the new way of modeling the backlogging phenomenon, the results for the case of constant demand are developed. Analysis is also presented for the reselling situation in which a nonperishable product is sold.Scope and purposePerishable products constitute a sizable component of inventories. A common question in a reselling situation involving a perishable (or a nonperishable) product is: What should be the size of the replenishment? If demand for the product is sensitive to price, then another question is: What should be the selling price? Although the ability to vary price within an inventory cycle is important, in many cases, the reseller may opt for a policy of constant selling price for administrative convenience. In this paper the pricing and/or lot sizing problem faced by a reseller is modeled assuming a general deterioration rate and a general demand function. The model allows for backlogging of demand. When a product is highly perishable, the reseller may need to backlog demand to contain costs due to deterioration. In this sense, perishability and backlogging are complementary conditions. Given that the problem entails revenue and costs, a natural objective function for the model is profit per period. The conventional approach to modeling the backlogging phenomenon requires the use of the backorder cost and the lost sale cost. These costs, however, are difficult to estimate in practice. A new approach is used in which customers are considered impatient. Hence the fraction of demand that gets backlogged at a given point in time is a decreasing function of waiting time. First the subproblem in which price is fixed is solved to determine the optimal inventory policy. The subproblem represents the important case in which the reseller has no flexibility to change the selling price. Then a procedure is developed for determining the optimal quantity and the selling price for the broader problem. The procedure can be implemented on a spreadsheet.     

Joint pricing and replenishment policies for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint

This study develops an inventory model for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint. The model assumes price sensitive demand when the product has no deterioration and price and time dependent demand when the product has deterioration. Under these considerations, the study attempts to offer best policy for selling price and replenishment cycle for the retailer that aims at maximizing the total profit per unit time. Making use of nearest interval approximation and interval arithmetic, the single objective problem is transformed to multi objective problem. Employing Weighted Sum Method, an analytical approach along with simple algorithm is developed to identify Pareto optimal solution. Finally, the behavior of the model with varied parameters is illustrated in numerical examples.     

Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach

In this article, we consider an infinite horizon, single product economic order quantity where demand and deterioration rate are continuous and differentiable function of price and time, respectively. In addition, we allow for shortages and completely backlogged. The objective is to find the optimal inventory and pricing strategies maximizing the net present value of total profit over the infinite horizon. For any given selling price, 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 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 a couple of numerical examples to illustrate the algorithm.     

考虑体验服务和促销努力的时尚服装库存与定价优化决策

时尚服装受季节性、时尚流行性等因素的影响,其时尚度随时间衰减,致使市场价值不断降低,造成服装行业一直面临高库存问题.鉴于此,研究需求依赖于价格和时尚程度的服装库存模型,考虑体验服务投资可提高服装时尚度、促销降价可改善销售需求的作用,构建一般情形、体验服务投资情形、促销努力情形以及服务与促销联合4种情形下的优化订货和定价模型,分析体验服务投资和促销努力联合时对服装零售商优化决策的影响.研究结果表明:体验服务投资对边际效益的影响是先增后减;服装零售商通过决策折扣促销力度和延后折扣时间点,优化库存水平和定价,可降低库存成本,增加利润;体验服务和促销努力联合作用时,产生利润互补或替代效应,这取决于服装时尚度衰减因子,当其大于某临界值时,体验服务和促销努力两者为互补关系,反之则为替代关系.     

库存水平影响需求下变质品订购、定价和保鲜技术投资的联合决策

研究变质品的订购、定价和保鲜技术投资联合决策问题.假设产品需求同时受价格和库存水平的影响,系统不允许缺货并放松期末库存水平为零的约束,零售商拥有有限的货架空间或存储空间,同时考虑零售商可以通过投资保鲜技术减低产品的变质率,以平均利润最大化为目标构建库存水平影响需求下变质品的订购、定价和保鲜技术投资联合决策模型.首先证明最优策略的存在性和唯一性,并给出零售商建立期末库存的条件;然后利用最优解的相关性质设计一个求解模型的多阶段迭代算法;最后通过具体算例验证展示模型和算法的可行性和实用性,并完成相关参数的敏感性分析,获得一定的管理启示.     

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。     

Dynamic pricing,promotion and replenishment policies for a deteriorating item under permissible delay in payments

We study the problem of dynamic pricing, promotion and replenishment for a deteriorating item subject to the supplier's trade credit and retailer's promotional effort. In this paper we adopt a price- and time-dependent demand function to model the finite time horizon inventory for deteriorating items. The objective of this paper is to determine the optimal retail price, the promotional effort and the replenishment quantity so that the net profit is maximized. We discuss the properties and develop an algorithm for solving the problem described. The numerical analyses show that an appropriate promotion policy can benefit the retailer and that the promotion policy is important, especially for deteriorating items. Furthermore dynamic decision-making is shown to be superior to fixed decision-making in terms of profit maximization. Some special cases, such as with no credit period and for non-deteriorating items, are discussed as is the influence of the time-varying demand, the rate of deterioration and the credit period on the retailer behavior.     

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered supplier’s production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailer’s and holding costs, production cost, transportation cost, setup cost of the supplier’s and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

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.     

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.     

Coordination-based inventory management for deteriorating items in a two-echelon supply chain with profit sharing

This study develops a model for inventory management consisting of a two-echelon supply chain (SC) with profit sharing and deteriorating items. The retailer and the supplier act as the leader and follower, in which the supplier faces a huge setup cost and economic order quantity ordering strategy. The market demand is affected by the sale price of the product, and the inventory has a deterioration rate following a Weibull distribution. The retailer executes three profit-sharing mechanisms to motivate the supplier to participate in SC optimisation and to extend the life cycle of the product. A search algorithm is developed to determine the solutions as using the profit-sharing mechanisms. The outcomes from numerical experiments demonstrate the profitability of the proposed model.     

Decision process for multiobjective,multi-item production-inventory system via interactive fuzzy satisficing technique

Multiobjective and single-objective inventory models of stochastically deteriorating items are developed in which demand is a function of inventory level and selling price of the commodity. Production rate depends upon the quality level of the items produced and unit production cost is a function of production rate. Deterioration depends upon both the quality of the item and duration of time for storage. The time-related deterioration function follows a two-parameter Weibull distribution in time. In these models, results are derived for both without shortages and partially backlogged shortages. Here, objectives for profit maximization for each item are separately formulated with different goals and compromise solutions of the multiobjective production/inventory problems are obtained by goal programming method. The models are illustrated with numerical examples and results for different formulations are compared. The results for the models assuming them to be a single house integrated business are also obtained using a gradient-based optimization technique and compared with those obtained from the respective decentralized models. Taking man-machine interaction into consideration, interactive solutions are derived for one of the said models—multiobjective model with shortages using interactive fuzzy satisficing method. Pareto optimum and satisficing results are derived for some numerical data.     

Joint pricing and ordering policy for a deteriorating inventory

An inventory model is developed for a deteriorating item with a price-dependent demand rate. The rate of deterioration is taken to be time-proportional and a power law form of the price-dependence of demand is considered. The model is solved analytically and is illustrated with a numerical example.     

Optimizing the Location of a Production Firm

A facility needs to be located in the plane to sell goods to a set of demand points. The cost for producing an item and the actual transportation cost per unit distance are given. The planner needs to determine the best location for the facility, the price charged at the source (mill price) and the transportation rate per unit distance to be charged to customers. Demand by customers is elastic and assumed declining linearly with the total charge. For each customer two parameters are given: the demand at charge zero and the decline of demand per unit charge. The objective is to find a location for the facility in the plane, the mill price charged to customers and the unit transportation rate charged to customers such that the company’s profit is maximized. The problem is formulated and an algorithm that finds the optimal solution is designed and tested on randomly generated problems.     

Data science and reinforcement learning for price forecasting and raw material procurement in petrochemical industry

Petrochemical industry is one of the major sectors contributing to the world-wide economy and the digital transformation is urgent to enhance core competence. In general, ethylene, propylene and butadiene, which are associated with synthetic chemicals, are the main raw materials of this industry with around 70–80% cost structure. In particular, butadiene is one of the key materials for producing synthetic rubber and used for several daily commodities. However, the price of butadiene fluctuates along with the demand–supply mismatch or by the international economy and political events. This study proposes two-stage data science framework to predict the weekly price of butadiene and optimize the procurement decision. The first stage suggests several the price prediction models with a comprehensive information including contract price, supply rate, demand rate, and upstream and downstream information. The second stage applies the analytic hierarchy process and reinforcement learning technique to derive an optimal policy of procurement decision and reduce the total procurement cost. An empirical study is conducted to validate the proposed framework, and the results improve the accuracy of price forecasts and the procurement cost reduction of the raw materials.     

Disruption management for a dominant retailer with constant demand-stimulating service cost

In this paper, we consider coordination model of a one-manufacturer and multi-retailer supply chain with a dominant retailer’s sales promotion opportunity and possible demand disruption. An appropriate contractual scheme can be used to fully coordinate the supply chain even if the demand disruption occurs. In our study, we also analyze how the demand disruption affects the coordination mechanism. When the demand is disrupted, the manufacturer only needs to adjust the maximum variable wholesale price and the subsidy rate under the linear quantity discount scheme. For each case of the demand disruption, we find that the higher the market share of the dominant retailer, the lower its average wholesale price will be. Meanwhile, the higher service cost leads to the higher subsidy rate provided by the manufacturer. The optimal wholesale/retail price, order quantity and subsidy rate can be greatly influenced by the demand disruption. If the disrupted amount of demand is sufficiently small, however, the manufacturer needs to take some special measures to prevent the retailers from deviating the order quantity of the original plan. To demonstrate these findings, we illustrate our propositions by numerical examples.