Optimal acquisition and production policy in a hybrid manufacturing/remanufacturing system with core acquisition at different quality levels

We study the acquisition and production planning problem for a hybrid manufacturing/remanufacturing system with core acquisition at two (high and low) quality conditions. We model the problem as a stochastic dynamic programming, derive the optimal dynamic acquisition pricing and production policy, and analyze the influences of system parameters on the acquisition prices and production quantities. The production cost differences among remanufacturing high- and low-quality cores and manufacturing new products are found to be critical for the optimal production and acquisition pricing policy: the acquisition price of high-quality cores is increasing in manufacturing and remanufacturing cost differences, while the acquisition price of low-quality cores is decreasing in the remanufacturing cost difference between high- and low-quality cores and increasing in manufacturing and remanufacturing cost differences; the optimal remanufacturing/manufacturing policy follows a base-on-stock pattern, which is characterized by some crucial parameters dependent on these cost differences.     

Impact of uncertainty in the quality of returns on the profitability of a single-period refurbishing operation

This paper investigates how the profitability of reuse activities is affected by uncertainty regarding the quality of returned products. Specifically, we examine a reverse supply chain consisting of two collection sites and a refurbishing site, which faces stochastic demand for refurbished products in a single-period setting. The quality of returns (refurbishing yield) becomes known only after the transportation of the products to the refurbishing site. We prove that the expected profit function has a unique optimal solution (procurement and production quantities) and we derive the conditions under which it is optimal to use only one of the collection sites. The analysis is supported by numerical results which provide insights regarding the effect of the uncertain yields at the two collection sites and their correlation on optimal decisions and system profitability.     

Robust optimal dynamic production/pricing policies in a closed-loop system

Hybrid manufacturing/remanufacturing systems play a key role in implementing closed-loop production systems which have been considered due to increasingly environmental concerns and latent profit of used products. Manufacturing and remanufacturing rates, selling price of new products, and acquisition price of used products are the most critical variables to optimize in such hybrid systems. In this paper, we develop a dynamic production/pricing problem, in which decisions should be made in each period confronting with uncertain demand and return. The manufacturer is able to control the demand and return by adjusting selling price and acquisition price respectively, also she can stock inventories of used and new products to deal with uncertainties. Modeling a nominal profit maximization problem, we go through robust optimization approach to reformulate it for the uncertain case. Final robust optimization model is obtained as a quadratic programming model over discrete periods which can be solved by optimization packages of QP. A numerical example is defined and sensitivity analysis is performed on both basic parameters and parameters associated with uncertainty to create managerial views.     

Competition for cores in remanufacturing

We study competition between an original equipment manufacturer (OEM) and an independently operating remanufacturer (IO). Different from the existing literature, the OEM and IO compete not only for selling their products but also for collecting returned products (cores) through their acquisition prices. We consider a two-period model with manufacturing by the OEM in the first period, and manufacturing as well as remanufacturing in the second period. We find the optimal policies for both players by establishing a Nash equilibrium in the second period, and then determine the optimal manufacturing decision for the OEM in the first period. This leads to a number of managerial insights. One interesting result is that the acquisition price of the OEM only depends on its own cost structure, and not on the acquisition price of the IO. Further insights are obtained from a numerical investigation. We find that when the cost benefits of remanufacturing diminishes and the IO has more chance to collect the available cores, the OEM manufactures less in the first period as the market in the second period gets larger to protect its market share. Finally, we consider the case where consumers have lower willingness to pay for the remanufactured products and find that in that case remanufacturing becomes less profitable overall.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

需求不确定下应急医疗服务站鲁棒配置模型与算法

大型突发事件发生后需要快速启动应急救灾网络,合理配置应急医疗服务站。本文考虑各应急医疗服务站选址节点需求的不确定性,引入三个不确定水平参数,构建四类不确定需求集合(box, ellipsoid, polyhedron和interval-polyhedron)对应的应急医疗服务站鲁棒配置模型,运用分支-切割算法求解,最后,进行需求扰动比例的灵敏度分析。算例结果表明,四类不确定需求集下的鲁棒配置模型中,ellipsoid不确定需求集合配置模型开放设施较少,总成本最小,鲁棒性较好。决策者还可以根据风险偏好选择不确定水平和需求扰动比例的组合,以使得总成本最小。     

回收率依赖回收产品质量的再制造EOQ模型

研究回收率依赖回收产品质量情况下制造/再制造混合系统的EOQ模型.该模型假设顾客的需求可通过新产品的制造和回收产品的再制造两种方式满足,且这两种产品无质量差异;需求率是确定的、连续的;总成本包括制造和再制造的固定启动成本,可销售产品和回收品的库存成本,以及缺货成本.当假设缺货成本无限大时给出不允许缺货情况下的模型.给出算例验证模型的有效性.     

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.     

不确定环境下再制造生产调度研究

针对再制造过程中存在的再制造件质量状况和加工时间不确定性调度问题,分别采用随机数和三角模糊数表示质量状况和加工时间的不确定性。在满足工序顺序、机器等限制下,将各自带有权重系数的最大完工时间和总成本之和最小值当做目标函数,构造不确定环境下再制造生产调度模糊模型且转换成确定的单目标非线性规划模型。应用多层编码遗传算法求解某个再制造子系统算例得到,决策者对于最大完工时间和总成本的重视程度不同,调度方案不同,其需要根据自身关注的重点做出决策,选择合适的调度方案。并且调度结果会受到决策者消极或积极态度的影响,态度越积极,结果越好,反之,态度越消极,结果越差,从而检验了再制造生产调度模型的正确性。希望为再制造实现产业化,规模化提供相关参考意见。     

Flexible long-term capacity planning in closed-loop supply chains with remanufacturing

We deal with long-term demand-driven capacity planning policies in the reverse channel of closed-loop supply chains (CLSCs) with remanufacturing, under high capacity acquisition cost coupled with uncertainty in actual demand, sales patterns, quality and timing of end-of-use product returns. The objective is to facilitate the decision-making when the management faces the dilemma of implementing either a strategy of early large-scale investments to benefit from economies of scale and capacity readiness, or a flexible strategy of low volume but more frequent capacity expansions. We consider a CLSC with two sequential product-types. We study the system’s response in terms of transient flows, actual/desired capacity level, capacity expansions/contractions and total supply chain profit, employing a simulation-based system dynamics optimization approach. Extensive numerical investigation covers a broad range of real-world remanufacturable products under alternative scenarios in relation to the market preference over product-types. The key findings propose flexible policies as improved alternatives to large-scale capacity expansions/contractions in terms of adaptability to the actual pattern of end-of-use product returns and involved risk in the investments’ turnover. Flexible policies are also proposed as practices to avoid overcapacity phenomena in collection and remanufacturing capacity and as robust policies to product demand. Their implementation is revealed to be even more important for the case of remanufacturing, when a high capacity acquisition unit-cost ratio (remanufacturing/collection) is coupled with strong economies of scale. Finally, results under different information sharing structures show changes in remanufacturing policies, thus justifying the importance of coordination between the decision-maker and the distributor.     

Master disassembly scheduling in a remanufacturing system with stochastic routings

Remanufacturing is an important source of sustainable development. Remanufactured products have proven to be high quality and low cost. Due to their unique characteristics, remanufacturing processes have many differences compared to manufacturing processes. These characteristics, which make remanufacturing complex, require good performance from Production Planning and Control (PPC) activities. The goal of the paper is to propose a mathematical model for disassembly master production scheduling considering stochastic routings in the remanufacturing environment. The proposed model is based on stochastic dynamic programming and it is applied to a real case of automotive clutch remanufacturing. The results contribute to the development of theory and practice by filling a gap in knowledge of the use of PPC systems, developing a mathematical method that can be easily implemented in a spreadsheet. The findings also show some decisions that are counterintuitive. For example, in some situations disassemble more products than necessary to meet the demand can result in a lower expected total cost.     

需求不确定性对闭环供应链系统决策的影响分析

在由一个制造商与一个销售商组成的闭环供应链系统中,构建了市场需求不确定环境下废旧产品回收率为外生变量和零售商决策变量两种情形的闭环供应链系统决策模型,并通过数值仿真得到了各模型供应链成员的最优定价和订货策略以及最终利润,进一步分析了两种情形下市场需求不确定性对零售商、制造商决策行为及利润的影响,最后对两种情形进行了对比分析.     

Loss-averse newsvendor problem with supply risk

Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor’s loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker’s optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.     

“酒店+OTA”双渠道供应链超订策略研究

为解决市场需求不确定环境下,酒店和在线旅行网站(Online Travel Agency,OTA)合作时的能力超订量与在线房间预留量的决策问题,建立了基于佣金合作模式的数学模型,给出了实现酒店整体期望收益最大化的在线房间预留量与能力超订量。借助数值分析,进一步研究了佣金率与需求不确定性对最优决策的影响。结果表明,当佣金率与门店需求不确定性较小时,酒店采取双渠道策略并且实施超订;当佣金率与门店需求不确定性很大时,酒店采取门店单渠道策略但不实施超订。另外,在线房间预留量随着佣金率、门店需求不确定性的增大而减小。     

基于不确定需求与产出的计划生产量决策

在复杂多交的市场环境下和生产过程易受多种随机因素影响,产品的需求和产出往往具有不确定性.考虑不确定需求和产出的情况,建立起以最小期望成本(包括生产成本、缺货成本和超产成本)为目标函数,计划生产量为决策变量的决策模型.通过利用费马定理和极值第二充分条件对计划生产量决策模型分析,提出了最优计划生产量必须满足的方程和证明了模型是凹函数,存在着最小期望成本.最后通过数值实例验证了模型的有效性.     

The value of dynamic pricing for cores in remanufacturing with backorders

In remanufacturing, the supply of used products and the demand for remanufactured products are usually mismatched because of the great uncertainties on both sides. In this paper, we propose a dynamic pricing (DP) policy to balance this uncertain supply and demand. Specifically, we study a remanufacturer’s problem of pricing a single class of cores with random price-dependent returns and random demand for the remanufactured products with backlogs. We model this pricing task as a continuous-time Markov decision process, which addresses both the finite and infinite horizon problems, and provide managerial insights by analysing the structural properties of the optimal policy. We then use several computational examples to illustrate the impacts of particular system parameters on pricing policy and the benefit of DP. In addition, the models are extended to account for the price adjustment costs. We show through numerical example that the nice structural properties do not exist any longer, and find when DP is better than static pricing.     

需求不确定的强势零售商的闭环供应链决策

建立了需求不确定下两个竞争的生产商和一个强势零售商组成的具有产品再制造的闭环供应链模型.利用逆向归纳法对不同废旧品回收渠道下的模型进行分析,然后通过算例分析了不同模型的回收成本和新增回收率对零售价格、回收模式决策、供应链系统及成员期望利润的影响.结果表明:回收成本的增加导致生产商和系统的期望利润降低,零售商领头下只有在零售商负责回收的模式中,零售商的期望利润才是增加的;新增回收率的增加,可降低产品的零售价,增加供应链成员的期望利润,继而提高整个供应链系统的利润.     

The impact of uncertain yield on capacity acquisition in process plant networks

In this paper, we consider the case of process plant networks, which consolidate production of components. It is well known that such networks take advantage of process commonalities thereby accruing economies of scale advantages. It has also been shown in recent work that besides scale economies, process plant networks also enjoy risk-pooling advantages which are a direct outcome of network structure. In this research, motivated by real-world examples, we study capacity acquisition in a process plant network when demand and process yield are both uncertain. We show that the optimal capacity acquired in such situations may be considerably higher or lower than that acquired when yield is assumed perfect. We develop distribution-free policies for optimal capacity acquisition. We illustrate our results by means of a numerical example and study the sensitivity to important model parameters. For specific distributional assumptions we also provide closed-form results for the optimal capacity acquisition. We consider our work as perhaps the first to bridge the gap between operational level quality control studies and strategic level network configuration research. Overall, we believe that this paper opens up several avenues for future research integrating these two important areas.     

基于鲁棒二阶随机占优的投资组合优化模型研究

本文主要考虑一类经典的含有二阶随机占优约束的投资组合优化问题,其目标为最大化期望收益,同时利用二阶随机占优约束度量风险,满足期望收益二阶随机占优预定的参考目标收益。与传统的二阶随机占优投资组合优化模型不同,本文考虑不确定的投资收益率,并未知其精确的概率分布,但属于某一不确定集合,建立鲁棒二阶随机占优投资组合优化模型,借助鲁棒优化理论,推导出对应的鲁棒等价问题。最后,采用S&P 500股票市场的实际数据,对模型进行不同训练样本规模和不确定集合下的最优投资组合的权重、样本内和样本外不确定参数对期望收益的影响的分析。结果表明,投资收益率在最新的历史数据规模下得出的投资策略,能够获得较高的样本外期望收益,对未来投资更具参考意义。在保证样本内解的最优性的同时,也能取得较高的样本外期望收益和随机占优约束被满足的可行性。     

Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

不确定环境下的单周期最优订货量决策具有重要且广泛的应用价值。与传统的仅考虑需求不确定性的报童模型不同,本文考虑市场价格恒定,但成本和需求随机变化且相关联下的报童决策问题。为此,采用Copula函数构建成本和需求之间的关联,考虑决策者可能具有的风险态度,建立了相应的Copula-CVaR模型,证明了模型解的存在性和唯一性,并将模型离散化为易求解的线性规划问题。最后,通过不同的风险水平和多种Copula函数下的仿真,分析了随机成本与需求的相关性和波动性对最优决策结果影响,并得到相关结论,为相关企业决策提供依据。