Price Strategy Implementation

Consider a situation in which a company sells several different items to a set of customers. However, the company is not satisfied with the current pricing strategy and wishes to implement new prices for the items. Implementing these new prices in one single step mightnot be desirable, for example, because of the change in contract prices for the customers. Therefore, the company changes the prices gradually, such that the prices charged to a subset of the customers, the target market, do not differ too much from one period to the next. We propose a polynomial time algorithm to implement the new prices in the minimum number of time periods needed, given that the prices charged to the customers in the target market increase by at most a factor 1 + δ, for predetermined δ > 0. Furthermore, we address the problem to maximize the revenue when also a maximum number of time periods is predetermined. For this problem, we describe a dynamic program if the numberof possible prices is limited, and a local search algorithm if all prices are allowed. Also, we present the integer program that models this problem. Finally, we apply the obtained algorithms in a practical study.operations research and management science;

Stackelberg Network Pricing Games

We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of $m$ priceable edges in a graph. The other edges have a fixed cost. Based on the leader's decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader's prices. The leader receives as revenue the total amount of prices paid by the followers for priceable edges in their solutions, and the problem is to find revenue maximizing prices. Our model extends several known pricing problems, including single-minded and unit-demand pricing, as well as Stackelberg pricing for certain follower problems like shortest path or minimum spanning tree. Our first main result is a tight analysis of a single-price algorithm for the single follower game, which provides a $(1+\epsilon) \log m$-approximation for any $\epsilon >0$. This can be extended to provide a $(1+\epsilon)(\log k + \log m)$-approximation for the general problem and $k$ followers. The latter result is essentially best possible, as the problem is shown to be hard to approximate within \mathcal{O(\log^\epsilon k + \log^\epsilon m). If followers have demands, the single-price algorithm provides a $(1+\epsilon)m^2$-approximation, and the problem is hard to approximate within \mathcal{O(m^\epsilon) for some $\epsilon >0$. Our second main result is a polynomial time algorithm for revenue maximization in the special case of Stackelberg bipartite vertex cover, which is based on non-trivial max-flow and LP-duality techniques. Our results can be extended to provide constant-factor approximations for any constant number of followers

Optimal Bundle Pricing with Monotonicity Constraint

We consider the problem to price (digital) items in order to maximize the revenue obtainable from a set of bidders. We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we derive a PTAS. We also discuss a special case, the highway pricing problem.operations research and management science;

Optimal Bundle Pricing for Homogeneous Items

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation for the requested bundle that we assume to be known to the seller. The task is to find an envy-free pricing such as to maximize the revenue of the seller. We derive several complexity results and algorithms for several variants of this pricing problem. In fact, the settings that we consider address problems where the different items are `homogeneous'' in some sense. First, we introduce the notion of affne price functions that can be used to model situations much more general than the usual combinatorial pricing model that is mostly addressed in the literature. We derive fixed-parameter polynomial time algorithms as well as inapproximability results. Second, we consider the special case of combinatorial pricing, and introduce a monotonicity constraint that can also be seen as `global'' envy-freeness condition. We show that the problem remains strongly NP-hard, and we derive a PTAS - thus breaking the inapproximability barrier known for the general case. As a special case, we finally address the notorious highway pricing problem under the global envy-freeness condition.operations research and management science;

Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

РЕЗУЛЬТАТЫ МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ ДЕЯТЕЛЬНОСТИ ГОРНОДОБЫВАЮЩЕГО ПРЕДПРИЯТИЯ

The economy of Russia is based around the mineral-raw material complex to the highest degree. The mining industry is a prioritized and important area. Given the high competitiveness of businesses in this sector, increasing the efficiency of completed work and manufactured products will become a central issue. Improvement of planning and management in this sector should be based on multivariant study and the optimization of planning decisions, the appraisal of their immediate and long-term results, taking the dynamic of economic development into account. All of this requires the use of economic mathematic models and methods. The object of research is the work of OAO “Uchalinsky GOK” which is the leading plant in the extraction and enrichment of copper-zinc ores in the Ural region. Production capacity is the most important technical-economical indicator established to substantiate the feasibility of exploration and further development of a site for the design of new and reconstruction of old mining processing plants. The optimal production capacity is the capacity at which ore is extracted with the most favorable indicators of workforce productivity, production costs and overhead costs. Applying an economic-mathematic model to determine optimal ore mine production capacity, we receive a figure of 4,712,000 tons. The production capacity of the Uchalinsky ore mine is 1560 thousand tons, and the Uzelginsky ore mine – 3650 thousand. Conducting a corresponding analysis of the production of OAO “Uchalinsky Gok”, an optimal production plan was received: the optimal production of copper – 77961,4 rubles; the optimal production of zinc – 17975.66 rubles. The residual production volume of the two main ore mines of OAO “UGOK” is 160 million tons of ore.Экономика России в наибольшей степени ориентирована на минерально-сырьевой комплекс. Горнодобывающая промышленность является приоритетным и важным направлением. В условиях высокой конкурентоспособности предприятий данной отрасли центральным становится вопрос о повышении эффективности выполняемых работ и выпускаемой продукции. Совершенствование планирования и управления в данной отрасли должно осуществляться на основе многовариантной проработки и оптимизации плановых решений, оценки их непосредственных и отдаленных во времени результатов с учетом динамики развития экономики. Все это требует применения экономико-математических моделей и методов. Объект исследования – деятельность ОАО «Учалинский ГОК», который является ведущим предприятием по добыче и обогащению медно-цинковых руд в Уральском регионе. Важнейшим технико-экономическим показателем, который устанавливается для обоснования целесообразности освоения и дальнейшей разработки месторождения в целях проектирования новых и реконструкции действующих горно-обогатительных предприятий, является производственная мощность. Оптимальная производственная мощность характеризует мощность, при которой руда добывается с наиболее благоприятными для данного месторождения показателями производительности труда, себестоимости и приведенных затрат. Применяя экономико-математическую модель определения оптимальной производственной мощности рудника, получен показатель, равный 4712000 тонн. Производственная мощность Учалинского рудника – 1560 тыс. тонн, а Узельгинского рудника – 3650 тыс. тонн. Проведя соответствующий анализ производства ОАО «Учалинский ГОК», был получен оптимальный план производства: оптимальное производство меди – 77961,4 рублей; оптимальное производство цинка – 17975,66 рублей. Остаточный объем производства двух основных рудников ОАО «УГОК» составляет 160 млн тонн руды

Revenue Management In Manufacturing: A Research Landscape

Revenue management is the science of using past history and current levels of order activity to forecast demand as accurately as possible in order to set and update pricing and product availability decisions across various sales channels to maximize profitability. In much the same way that revenue management has transformed the airline industry in selling tickets for the same flight at markedly different rates based upon product restrictions, time to departure, and the number of unsold seats, many manufacturing companies have started exploring innovative revenue management strategies in an effort to improve their operations and profitability. These strategies employ sophisticated demand forecasting and optimization models that are based on research from many areas, including management science and economics, and that can take advantage of the vast amount of data available through customer relationship management systems in order to calibrate the models. In this paper, we present an overview of revenue management systems and provide an extensive survey of published research along a landscape delineated by three fundamental dimensions of capacity management, pricing, and market segmentation