基于收益管理的MTS和MTO企业的供需管理研究
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摘要
收益管理是一套以收益最大化为目标，以市场细分和需求预测为基础，对有限的供给实行最优定价和最优能力分配策略的管理思想和方法。为了使得有限的供给能够与变化的需求进行匹配，以实现收益最大化，本文将收益管理中的动态定价和存量控制的思想与方法应用到存货生产（Make-to-Stock，MTS）企业和订单生产（Make-to-Order，MTO）企业，采用生产和定价联合策略管理MTS企业的供应和需求，采用订单接受策略管理MTO企业的供应，采用定价和承诺交货期策略管理MTO企业的需求。
对于MTS企业的供需管理，本文首先研究基于线性需求的最优定价和生产策略问题。假设需求是价格的线性函数，且只与当期价格有关。需求形式已知，需求参数未知。采用基于最小二乘法的需求学习的方法来预测未知的需求参数。针对该问题，我们分别不考虑和考虑竞争，分三种情况展开：第一、单一企业，不考虑市场竞争，建立了该企业的最优控制问题，得出了最优定价和最优生产决策，并分析了最优决策和最大利润关于各参数的敏感性。第二、寡头竞争，市场上存在多个相互竞争的企业，研究表明所有企业的最优控制问题是一个广义微分Nash均衡问题，本文将广义微分Nash均衡问题转化为微分变分不等式，证明了这两者的等价性，及广义微分Nash均衡的存在。通过数值分析比较了两种动态定价策略，得出基于需求学习方法的动态定价策略获得的利润要高于基于固定需求参数的动态定价策略获得的利润，然后还讨论了竞争者价格敏感度的变化对企业决策和利润的影响。第三、主从竞争，考虑存在一个领导企业和多个追随企业的竞争市场，研究表明Stackelberg广义微分Nash均衡的存在。通过数值分析展现了领导企业和追随企业的最优决策和利润，比较了寡头竞争和主从竞争下企业利润的大小，得出相比于在寡头竞争的情况下，一个企业成为主从竞争中的领导者将获得更多利润，成为主从竞争中的追随者将获得更少利润。
然后研究了基于需求动态的最优定价和生产问题。不再假设需求是价格的线性函数，而是考虑需求动态，需求不仅与当期价格有关，而且还与过去时期的价格有关。采用进化博弈论动态来建立需求动态模型。需求形式已知，需求参数未知，采用基于马尔可夫链蒙特卡洛法的需求学习算法来预测需求参数。同样考虑了单一企业、寡头竞争和主从竞争三种情况，分别得出了这三种情况下的最优定价和生产决策。对于单一企业，我们还分析了企业最大利润关于各参数的敏感性。对于寡头竞争，我们通过数值分析比较了两种不同的需求学习方法：基于最小二乘法的需求学习方法和基于马尔可夫链蒙特卡洛的需求学习方法，结果表明基于马尔可夫链蒙特卡洛的需求学习方法可以使得企业获得更高利润。对于主从竞争，我们分析了领导企业的价格敏感度的变化对领导企业和追随企业的最优决策和利润的影响。
对于MTO企业的供需管理，本文首先研究了其供应管理策略，先考虑单一资源情况下的订单接受策略。采用收益管理中期望边际座位收益方法a和方法b计算出两种不同等级订单的预订限额，然后根据预订限额决定订单的接受与否。分析结果表明基于方法a和基于方法b的订单接受策略均明显优于先来先接受（First-Come-First-Served，FCFS）策略。然后研究了多资源情况下的订单接受和资源分配策略，考虑了机器资源的易逝性，采用动态规划对问题进行建模，运用逆向递归法进行求解，分析了参数的变化对最大期望利润的影响，并得出本文提出的最优策略要优于FCFS策略。
然后考虑了MTO企业的需求管理，首先研究了顾客下订单后不取消订单的定价策略，将顾客下订单的概率表示为价格的函数，得出了最优定价和订单最大期望利润，分析了这两者关于各参数的敏感性。然后研究了顾客下订单后可能取消订单的定价策略，得出了最优定价和订单最大期望利润，分析了这两者关于各参数的敏感性，并且还讨论了当顾客确实可能取消订单时，决策者忽略顾客可能取消订单这一行为对最大期望利润的影响。最后研究了定价与其它因素的联合策略：(1)定价与承诺交货期联合策略。顾客下订单的概率依赖于价格和承诺交货期，以最大化单个订单的利润为目标，得出了订单的最优定价和承诺交货期决策。(2)定价与生产安排联合策略。这种情况下由顾客决定交货期，其下订单的概率依赖于价格。企业根据顾客期望的交货期，决策出最优定价和生产安排策略。(3)定价与订单接受联合策略。考虑了签约顾客和零散顾客并存的MTO企业，采用动态规划对零散顾客的订单接受问题进行建模，得出了零散顾客的最优订单接受策略。采用遗传算法得出了签约顾客的最优订单定价策略，结果显示本文得出的最优订单接受策略要优于FCFS策略。
Revenue management is a set of strategies and techniques firms use to maximizetheir revenue by setting optimal prices and optimal capacity control for limited capacitybased on market segment and demand forecast. In order to match the limited supply andthe varying demand, and maximize revenue, this paper applies the strategies andtechniques of dynamic pricing and capacity control from revenue management intomake-to-stock (MTS) and make-to-order (MTO) firms. Production and pricingintegrating policies are used to control the supply and demand in MTS firms, orderacceptance policy is employed to manage the supply in MTO firms, and pricing anddelivery date quotation are adopted to control the demand in MTO firms.
For the supply and demand management in MTS firms, we first study the pricingand production policies based on linear demand. Assume demand is a linear function ofprices, and demand only depends on the current prices. The function of demand isknown, but with unknown demand parameters. A demand learning approach based onleast square method is applied to learn the unknown demand parameters. We considerthe optimal pricing and production problem without and with competition:(1) Singlefirm. We model the firm’s optimal control problem without considering competition,and obtain the optimal pricing and production policy. We also analyze the sensitivitiesof the maximum profit on the parameters;(2) Oligopolistic competition. There areseveral firms competing with each other. We show that all firms’ optimal controlproblem yields a generalized differential Nash equilibrium problem, which isrepresented as a differential variational inequality. We prove the equivalence betweenthe two and a generalized-differential-Nash equilibrium exists. Through the numericalexamples, two dynamic pricing policies are compared, and we obtain that the policybased on demand learning method can generate higher profit than the one based onfixed demand parameters. We also discuss the impact of competitor’s price sensitivityon the optimal policies and profit;(3) Stackelberg competition. There are one leader andmultiple followers. We prove that a Stackelberg-generalized-differential-Nashequilibrium exists. The numerical examples show the optimal prices and production policies of the leader and the followers. And we compare the profit of each firm underoligopolistic and Stackelberg competition, and find out that a firm can yield higherprofit to be the leader in the Stackelberg game, however achieve lower profit to be thefollower in the Stackelberg game, than in oligopolistic game.
Next, we consider the pricing and production problem based on demanddynamics. Instead of assuming demand is a linear function of prices, we considerdemand dynamics. Demand depends not only on the current prices, but also on theprices of the past periods. We express the demand dynamics based on evolutionarygame theory with known function and unknown demand parameters. A demand learningapproach based on Markov chain Monte Carlo method is used to predict the unknowndemand parameters. We also consider the problem under the three cases: single firm,oligopolistic and Stackelberg competition. The optimal pricing and production policiesare obtained under each case. For the single firm, we analyze the sensitivities of themaximum profit on the parameters. For the oligopolistic game, through the numericalexample, we compared two different demand learning methods, the one based on leastsquare method and the one based on Markov chain Monte Carlo method. The resultshows that the latter demand learning method can generate higher profit. For theStackelberg game, we show the impact of the leader’s price sensitivity on the optimalpolices and the profits of the leader and the follower.
For the supply and demand management in MTO firms, we first study the supplymanagement. We consider the order acceptance policy under the single resource case.Expected Marginal Seat Revenue-a and Expected Marginal Seat Revenue-b (EMSR-aand EMSR-b) are used to calculate the two different booking limits for different classes.Then according to the booking limit, we decide to accept or reject an order. Theexample results show that the order acceptance policies based on EMSR-a and EMSR-bperform better than the First-Come-First-Served (FCFS) policy. Then we address theorder acceptance and allocating problem under multiple resources case considering theperishability of the machine resource. The problem is modeled by dynamicprogramming approach, and solved by reverse recursive method. Through an example,we anaylze the effect of the parameters on the maximum expected profit and find outour optimal policy outperforms the FCFS policy.
Then we study the demand management. First, we consider the pricing policy when a customer never cancel order after he places it. The probability that the customerwill place an order depends on price. We obtain the optimal price and the maximumexpected profit, and analyze the sensitivities of the two on all parameters. Then weaddress the pricing problem when the customer may cancel the order after he places it.We also obtain the optimal price and the maximum expected profit, and analyze thesensitivities of the two on all parameters, and discuss the impact of ignoring ordercancellation on the optimal profit, when customers indeed cancel orders with aprobability. At last we consider the pricing and other factors integrating policies:(1)Pricing and delivery date quotation problem. The probability that customer will placeorder is a function of price and the quoted delivery date. With the objective ofmaximizing a single order’s profit, we obtain the optimal prices and the quoted deliverydate.(2) Pricing and production scheduling problem. In this case, customer determinesthe delivery date, and the probability that he will place order depends on price.According to the customer’s expected delivery date, we obtain the optimal pricing andproduction scheduling policy.(3) Pricing and order acceptance problem. Consider aMTO firm with contractual customers and fill-in customers. We use the dynamicprogramming to model the order acceptance problem for fill-in customers, and gain theoptimal order acceptance policy. And the optimal pricing policy for contractualcustomers is obtained by using genetic algorithm. The result shows that the optimalorder acceptance policy is better than the FCFS order acceptance policy.
对于MTS企业的供需管理，本文首先研究基于线性需求的最优定价和生产策略问题。假设需求是价格的线性函数，且只与当期价格有关。需求形式已知，需求参数未知。采用基于最小二乘法的需求学习的方法来预测未知的需求参数。针对该问题，我们分别不考虑和考虑竞争，分三种情况展开：第一、单一企业，不考虑市场竞争，建立了该企业的最优控制问题，得出了最优定价和最优生产决策，并分析了最优决策和最大利润关于各参数的敏感性。第二、寡头竞争，市场上存在多个相互竞争的企业，研究表明所有企业的最优控制问题是一个广义微分Nash均衡问题，本文将广义微分Nash均衡问题转化为微分变分不等式，证明了这两者的等价性，及广义微分Nash均衡的存在。通过数值分析比较了两种动态定价策略，得出基于需求学习方法的动态定价策略获得的利润要高于基于固定需求参数的动态定价策略获得的利润，然后还讨论了竞争者价格敏感度的变化对企业决策和利润的影响。第三、主从竞争，考虑存在一个领导企业和多个追随企业的竞争市场，研究表明Stackelberg广义微分Nash均衡的存在。通过数值分析展现了领导企业和追随企业的最优决策和利润，比较了寡头竞争和主从竞争下企业利润的大小，得出相比于在寡头竞争的情况下，一个企业成为主从竞争中的领导者将获得更多利润，成为主从竞争中的追随者将获得更少利润。
然后研究了基于需求动态的最优定价和生产问题。不再假设需求是价格的线性函数，而是考虑需求动态，需求不仅与当期价格有关，而且还与过去时期的价格有关。采用进化博弈论动态来建立需求动态模型。需求形式已知，需求参数未知，采用基于马尔可夫链蒙特卡洛法的需求学习算法来预测需求参数。同样考虑了单一企业、寡头竞争和主从竞争三种情况，分别得出了这三种情况下的最优定价和生产决策。对于单一企业，我们还分析了企业最大利润关于各参数的敏感性。对于寡头竞争，我们通过数值分析比较了两种不同的需求学习方法：基于最小二乘法的需求学习方法和基于马尔可夫链蒙特卡洛的需求学习方法，结果表明基于马尔可夫链蒙特卡洛的需求学习方法可以使得企业获得更高利润。对于主从竞争，我们分析了领导企业的价格敏感度的变化对领导企业和追随企业的最优决策和利润的影响。
对于MTO企业的供需管理，本文首先研究了其供应管理策略，先考虑单一资源情况下的订单接受策略。采用收益管理中期望边际座位收益方法a和方法b计算出两种不同等级订单的预订限额，然后根据预订限额决定订单的接受与否。分析结果表明基于方法a和基于方法b的订单接受策略均明显优于先来先接受（First-Come-First-Served，FCFS）策略。然后研究了多资源情况下的订单接受和资源分配策略，考虑了机器资源的易逝性，采用动态规划对问题进行建模，运用逆向递归法进行求解，分析了参数的变化对最大期望利润的影响，并得出本文提出的最优策略要优于FCFS策略。
然后考虑了MTO企业的需求管理，首先研究了顾客下订单后不取消订单的定价策略，将顾客下订单的概率表示为价格的函数，得出了最优定价和订单最大期望利润，分析了这两者关于各参数的敏感性。然后研究了顾客下订单后可能取消订单的定价策略，得出了最优定价和订单最大期望利润，分析了这两者关于各参数的敏感性，并且还讨论了当顾客确实可能取消订单时，决策者忽略顾客可能取消订单这一行为对最大期望利润的影响。最后研究了定价与其它因素的联合策略：(1)定价与承诺交货期联合策略。顾客下订单的概率依赖于价格和承诺交货期，以最大化单个订单的利润为目标，得出了订单的最优定价和承诺交货期决策。(2)定价与生产安排联合策略。这种情况下由顾客决定交货期，其下订单的概率依赖于价格。企业根据顾客期望的交货期，决策出最优定价和生产安排策略。(3)定价与订单接受联合策略。考虑了签约顾客和零散顾客并存的MTO企业，采用动态规划对零散顾客的订单接受问题进行建模，得出了零散顾客的最优订单接受策略。采用遗传算法得出了签约顾客的最优订单定价策略，结果显示本文得出的最优订单接受策略要优于FCFS策略。
Revenue management is a set of strategies and techniques firms use to maximizetheir revenue by setting optimal prices and optimal capacity control for limited capacitybased on market segment and demand forecast. In order to match the limited supply andthe varying demand, and maximize revenue, this paper applies the strategies andtechniques of dynamic pricing and capacity control from revenue management intomake-to-stock (MTS) and make-to-order (MTO) firms. Production and pricingintegrating policies are used to control the supply and demand in MTS firms, orderacceptance policy is employed to manage the supply in MTO firms, and pricing anddelivery date quotation are adopted to control the demand in MTO firms.
For the supply and demand management in MTS firms, we first study the pricingand production policies based on linear demand. Assume demand is a linear function ofprices, and demand only depends on the current prices. The function of demand isknown, but with unknown demand parameters. A demand learning approach based onleast square method is applied to learn the unknown demand parameters. We considerthe optimal pricing and production problem without and with competition:(1) Singlefirm. We model the firm’s optimal control problem without considering competition,and obtain the optimal pricing and production policy. We also analyze the sensitivitiesof the maximum profit on the parameters;(2) Oligopolistic competition. There areseveral firms competing with each other. We show that all firms’ optimal controlproblem yields a generalized differential Nash equilibrium problem, which isrepresented as a differential variational inequality. We prove the equivalence betweenthe two and a generalized-differential-Nash equilibrium exists. Through the numericalexamples, two dynamic pricing policies are compared, and we obtain that the policybased on demand learning method can generate higher profit than the one based onfixed demand parameters. We also discuss the impact of competitor’s price sensitivityon the optimal policies and profit;(3) Stackelberg competition. There are one leader andmultiple followers. We prove that a Stackelberg-generalized-differential-Nashequilibrium exists. The numerical examples show the optimal prices and production policies of the leader and the followers. And we compare the profit of each firm underoligopolistic and Stackelberg competition, and find out that a firm can yield higherprofit to be the leader in the Stackelberg game, however achieve lower profit to be thefollower in the Stackelberg game, than in oligopolistic game.
Next, we consider the pricing and production problem based on demanddynamics. Instead of assuming demand is a linear function of prices, we considerdemand dynamics. Demand depends not only on the current prices, but also on theprices of the past periods. We express the demand dynamics based on evolutionarygame theory with known function and unknown demand parameters. A demand learningapproach based on Markov chain Monte Carlo method is used to predict the unknowndemand parameters. We also consider the problem under the three cases: single firm,oligopolistic and Stackelberg competition. The optimal pricing and production policiesare obtained under each case. For the single firm, we analyze the sensitivities of themaximum profit on the parameters. For the oligopolistic game, through the numericalexample, we compared two different demand learning methods, the one based on leastsquare method and the one based on Markov chain Monte Carlo method. The resultshows that the latter demand learning method can generate higher profit. For theStackelberg game, we show the impact of the leader’s price sensitivity on the optimalpolices and the profits of the leader and the follower.
For the supply and demand management in MTO firms, we first study the supplymanagement. We consider the order acceptance policy under the single resource case.Expected Marginal Seat Revenue-a and Expected Marginal Seat Revenue-b (EMSR-aand EMSR-b) are used to calculate the two different booking limits for different classes.Then according to the booking limit, we decide to accept or reject an order. Theexample results show that the order acceptance policies based on EMSR-a and EMSR-bperform better than the First-Come-First-Served (FCFS) policy. Then we address theorder acceptance and allocating problem under multiple resources case considering theperishability of the machine resource. The problem is modeled by dynamicprogramming approach, and solved by reverse recursive method. Through an example,we anaylze the effect of the parameters on the maximum expected profit and find outour optimal policy outperforms the FCFS policy.
Then we study the demand management. First, we consider the pricing policy when a customer never cancel order after he places it. The probability that the customerwill place an order depends on price. We obtain the optimal price and the maximumexpected profit, and analyze the sensitivities of the two on all parameters. Then weaddress the pricing problem when the customer may cancel the order after he places it.We also obtain the optimal price and the maximum expected profit, and analyze thesensitivities of the two on all parameters, and discuss the impact of ignoring ordercancellation on the optimal profit, when customers indeed cancel orders with aprobability. At last we consider the pricing and other factors integrating policies:(1)Pricing and delivery date quotation problem. The probability that customer will placeorder is a function of price and the quoted delivery date. With the objective ofmaximizing a single order’s profit, we obtain the optimal prices and the quoted deliverydate.(2) Pricing and production scheduling problem. In this case, customer determinesthe delivery date, and the probability that he will place order depends on price.According to the customer’s expected delivery date, we obtain the optimal pricing andproduction scheduling policy.(3) Pricing and order acceptance problem. Consider aMTO firm with contractual customers and fill-in customers. We use the dynamicprogramming to model the order acceptance problem for fill-in customers, and gain theoptimal order acceptance policy. And the optimal pricing policy for contractualcustomers is obtained by using genetic algorithm. The result shows that the optimalorder acceptance policy is better than the FCFS order acceptance policy.
引文
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