Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.     

基于深度强化学习的生鲜产品联合库存控制与动态定价研究

针对生鲜产品的易逝性特征以及复杂多变的现实环境导致生鲜产品的最优订货和定价策略难以获得的问题,提出了基于深度强化学习方法的生鲜产品联合库存控制与动态定价方法,结合生鲜产品特性对问题进行建模并定义为马尔可夫决策过程,然后基于深度强化学习设计了生鲜品联合库存控制和动态定价算法。实验结果表明,基于深度强化学习的联合库存控制和动态定价策略收益表现最佳,因此,基于深度强化学习的联合库存控制和动态定价研究能够提高企业收益,有效促进强化学习在收益管理领域的落地,具有实际应用价值。     

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.     

Optimal dynamic pricing for deteriorating items with reference-price effects

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.     

量子粒子群算法在易逝品多目标定价中的应用

对易逝品的多目标定价问题进行了研究。从利润最大化角度建立易逝品多目标最优定价模型。模型中涉及复杂的需求函数,常规函数极值法不易获得问题解析解,因此引入量子粒子群算法,结合惩罚函数对模型进行演化求解。根据给出的算例分析表明,利用量子粒子群算法,可以快速有效地得到不同订货量下的最优定价与折扣价组合。     

价格影响需求的易变质产品动态定价模型

在产品销售价格影响需求的条件下,利用最优控制理论建立了易变质产品的动态定价模型,目标是最大化产品销售周期内总的销售利润。利用Pontryagin 最大值原理得到了产品销售价格的最优性条件。通过对模型的理论分析得出如果产品销售价格介于单位产品购买费用和产品销售价格上限之间,且产品库存在销售周期结束之前始终为正时,销售周期内各时刻的产品最优销售价格一定大于与相应时刻变质率和产品单位库存成本有关的一个下界,销售周期内各时刻的产品最优库存水平一定小于与相应时刻变质率和产品单位库存成本有关的一个上界。     

Optimal joint replenishment,delivery and inventory management policies for perishable products

In this paper we analyze the optimal joint decisions of when, how and how much to replenish customers with products of varying ages. We discuss the main features of the problem arising in the joint replenishment and delivery of perishable products, and we model them under general assumptions. We then solve the problem by means of an exact branch-and-cut algorithm, and we test its performance on a set of randomly generated instances. Our algorithm is capable of computing optimal solutions for instances with up to 30 customers, three periods, and a maximum age of two periods for the perishable product. For the unsolved instances the optimality gap is always small, less than 1.5% on average for instances with up to 50 customers. We also implement and compare two suboptimal selling priority policies with an optimized policy: always sell the oldest available items first to avoid spoilage, and always sell the fresher items first to increase revenue.     

Dynamic brand-image-based production location decisions

In this paper, we study the dynamic production location decisions of a manufacturer of a certain branded product. Considering brand-image as a form of goodwill, we extend the well-known Nerlove-Arrow dynamic model by adding both country-image and price. Formulating an optimal control problem for a group of countries in which the cost of production is convexly increasing with country-image, we are able to develop optimal decision rules for a manufacturer regarding the location of production and pricing over time. The resulted optimal policy has a very interesting pattern. Assuming that the demand rises by more than the value of the new brand-image in percentage terms, then, if brand-image is increasing toward a stationary value level, the optimal policy should be to initially locate production in countries with high image and set a high price that signals high quality. Later, the production should gradually shift to countries with lower production costs and lower image and the price lowered until the stationary value level is reached. For brand-images beyond the stationary value level, the location of production should start in a country with low costs and country-image while setting prices that signal relatively low quality. Over time, production should be shifted to countries with gradually higher costs and images while setting higher prices until the brand-image approaches the level of stationary value.     

Issuing for perishable inventory management with a minimum inventory volume constraint

We study a perishable inventory system that requires to maintain a minimum inventory volume at all times, where the minimum amount in the constraint is significant with respect to regular market demand and the traditional Economic Manufacturing Quantity (EMQ) models do not suffice. The problem is motivated by applications in homeland security, which are related to the management of pharmaceuticals in the Strategic National Stockpile (SNS) for emergency preparedness. We use a modified EMQ model to represent the system and consider the issuing policy given a fixed ordering quantity, as well as the joint ordering and issuing policy problem. We aim to maximize the profit of the system under a linearly-decreasing price structure assumption. We first present the optimal issuing policy with a given ordering quantity for this modified EMQ model. Then we demonstrate that maximizing the revenue of the ordering policy with FIFO (first-in, first-out) and LIFO (last-in, first-out) issuing policies can be formulated as a non-convex non-smooth unconstrained optimization problem. The properties of both problems (e.g. optimizing issuing policy with a fixed ordering quantity and optimizing ordering policy with a fixed issuing policy) is analyzed and an efficient exact algorithm is presented to solve the joint ordering and issuing problem. We show that the LIFO issuing policy is optimal with a linearly-decreasing price structure that deteriorates with the age of the item.     

An integrated inventory system for perishable goods with backordering

We present an integrated inventory model for perishable goods in which backorder is allowed. The model considers the impact of marketing strategies such as pricing and advertising as well as backorder decisions on the profitability of the system. We assume that for certain perishable products, it is feasible for managers to plan for periods of shortage during an inventory cycle. A computer program is developed to determine the optimal production quantity (EPQ) and backorder level that maximize the net profit of the system. A numerical example is used to study the behavior of the model.     

Joint production and supply control in three levels flexible manufacturing systems

This paper considers a stochastic optimal control problem of a three stages Flexible Manufacturing System. The supplier (i.e., upstream FMS) and the transformation stage (i.e., FMS) are both subject to random events. Our objective is to find a feedback control policy for the supply and production activities that minimizes the incurred cost. It is shown that the considered joint production and supply control problem is difficult to tackle using a dissociated analytical approach. A simulation based approach is thus proposed to achieve a close approximation of the optimal policy. The advantages of the approach include possible extensions after numerical characterization of the optimal control policy.     

Dynamic ordering and pricing for a perishable goods supply chain

The paper studies the combined problem of pricing and ordering for a perishable product supply chain with one supplier and one retailer in a finite horizon. The lifetime of the product is two periods and demand in each period is random and price-sensitive. In each period, the supplier determines first a wholesale price and then the retailer decides an order quantity and retail prices. We show that the optimal pricing strategy for the non-fresh product depends only on its inventory, and the optimal pricing strategy and the optimal order quantity for the fresh product depend only on the wholesale price and they have a constant relation. Moreover, the game between the retailer and the supplier for finite horizon is equivalent to a one period game with only one order. Thus, the optimal policies are identical at each period. For the additive and multiplicative demands, we further obtain equations to compute the optimal strategies. All of above results are extended into the infinite horizon case and longer lifetime products. Finally, a numerical analysis is given.     

Supply chain pricing and coordination with markdown strategy in the presence of conspicuous consumers

This paper studies the problem of supply chain pricing and coordination with markdown policy in the presence of conspicuous consumption. A two‐period pricing model is proposed to investigate the effect of conspicuous consumption on pricing decisions with markdown pricing policy for a supply chain that consists of a manufacturer and retailer. The optimal pricing strategies for the integrated supply chain and decentralized supply chain are derived respectively. Our results show that an anticipated conspicuous consumption can benefit the supply chain even though the conspicuous consumption aggravates the double marginalization effect. The conspicuous consumption can serve as a level to segment the market and can promote the supply chain revenue. In addition, our results indicate that the supply chain can benefit from rationing. We also introduce a revenue‐sharing contract and prove that it can be applied to coordinate the supply chain with conspicuous consumption. An interval of the revenue‐sharing rate for coordinating with the supply chain can be coordinated without any additional transfer payment being provided.     

Optimizing supply chain network for perishable products using improved bacteria foraging algorithm

In a supply chain environment, time delay has a significant impact on the success of perishable products. A major concern is therefore aimed at development of a holistic optimized approach in a supply chain environment for perishable products. Thus, integration of production, inventory and, distribution of perishable products in a supply chain environment are the challenging tasks for practitioners and researchers. In general, the standard optimal supply chain model cannot work for perishable products. There is therefore, a need for a holistic model that focuses on the consolidation of the processes. Shorter product shelf-life, temperature control, requirement of strict tractability, large number of product variants, and a large volume of goods handled are the major challenges in a supply chain environment for perishable products. The present work focuses on the development of a holistic model which uses improved bacteria forging algorithm (IBFA) for solving the formulated model. We have proposed and analyzed some general properties of the model and, finally applied it to a three-stage supply chain problem using an IBFA. Two case studies have been considered for support and demonstration of the integrated perishable supply chain network problem. Results obtained from IBFA reveal that the proposed model is more useful for decision makers while considering optimal supply chain network for perishable products. Finally, validation of results has been carried out using bacteria forging algorithm (BFA). The computational performance of the proposed algorithm proves that IBFA is instrumental in effectively handling the proposed approach.     

Optimization of some dynamic industrial control processes by analog simulation

The analog computer has, for several years, been used to simulate the dynamic behaviour of some electrical systems such as servomechanisms and other control systems. In this paper some dynamic industrial processes are first formulated and solved as an optimal control problem via the Pontryagin's maximum principle. The resulting policy will be either bang-bang or continuous in time depending on whether there is a constraint on the policy or not. Two cases of short-time dynamic industrial processes are considered. One is an inventory control process and the other a production scheduling problem. These processes are both simulated on an analog computer. The results obtained seem to be rather reasonable and predictable in accordance to the actual practice.     

基于提前支付的非瞬时变质产品批量订货定价策略

当供应商处于供应链节点的买方市场时,通常要求零售商提前支付一定比例购置成本作为订金.针对该问题研究零售商促销努力下存在随机需求的非瞬时变质产品批量订货定价策略,考虑零售商提前支付策略,允许部分缺货.在一定条件下可得零售商最优补货周期和局部最优定价策略,随之提出相应的求解算法.数值计算结果表明:若提前支付购置成本占比或利率增大,则零售商利润将显著减少;提前支付期限和期数均对最优利润产生消极影响;零售商采取积极促销策略可有效提升自身利润.     

Interference-Based Dynamic Pricing for WCDMA Networks Using Neurodynamic Programming

We study the problem of optimal integrated dynamic pricing and radio resource management, in terms of resource allocation and call admission control, in a WCDMA network. In such interference-limited network, one's resource usage also degrades the utility of others. A new parameter noise rise factor, which indicates the amount of interference generated by a call, is suggested as a basis for setting price to make users accountable for the congestion externality of their usage. The methods of dynamic programming (DP) are unsuitable for problems with large state spaces due to the associated ldquocurse of dimensionality.rdquo To overcome this, we solve the problem using a simulation-based neurodynamic programming (NDP) method with an action-dependent approximation architecture. Our results show that the proposed optimal policy provides significant average reward and congestion improvement over conventional policies that charge users based on their load factor.     

A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems

In a capacitated multi-item dynamic pricing problem one maximizes the profit by choosing a proper production level as well as pricing policy, where the latter depends on a satisfied demand. The objective function involves inventory, production and setup costs, and revenue functions. The products are required to satisfy joined production capacities. We consider a bilinear reduction of the linear mixed integer formulation of the problem and prove that the problem is equivalent to finding a global maximum of the bilinear problem. A heuristic algorithm is proposed, based on the reduction technique. Numerical experiments confirm the efficiency of the proposed technique.     

A simulation‐based algorithm for optimal pricing policy under demand uncertainty

We propose a simulation‐based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high‐dimensional parameters, it uses the efficient smoothed functional gradient estimator.     

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.