Selected Papers on Pricing Methodology in Manufacturing

With the rapid growth of personalized customers’demands, the traditional manufacturing paradigms have not adapted to the variant market environment. Service-oriented manufacturing (SOM) and cloud manufacturing (CMfg) were provided for maintaining the core competitiveness of business. Pricing decision as a fundamental and crucial business link of the manufacturing companies and customers will affect the operation of SOM and CMfg. However, the existing product pricing methodology mainly depending on the financial and market information is not viable for them. Therefore, aiming to accurately satisfy the various requirements of customers, pricing for the multi-variety and small batch production has become an issue for the researchers and entrepreneurs. The latest studies of pricing are as follows.


  1. A continuous approximation method for dynamic pricing problem under costly price modifications (published online: 13 June 2017)
  2. Price of Fairness for allocating a bounded resource (published online: 10 August 2016)
  3. Implementing Value Engineering based on a multidimensional quality-oriented control calculus within a Target Costing and Target Pricing approach (published online: 9 September 2016)
  4. Joint product variety, pricing and scheduling decisions in a flexible facility (published online: 6 September 2016)
  5. Pricing and capacity planning for product-line expansion and reduction (published online: 7 May 2017)
  6. ICIF: an inter-cloud interoperability framework for computing resource cloud providers in factories of
    the future
     (published online: 16 July 2015)
  7. Line balancing in parallel M/M/1 lines and loss systems as cooperative games (published online: 18 April 2017)
  8. A hybrid framework for integrating multiple manufacturing clouds (published online: 29 December 2015)
  9. Multiproduct price optimization under the multilevel (published online: 3 April 2017)
  10. Improving Profits by Bundling Vertically Differentiated Products (published online: 19 March 2017)

Detailed Information

1. Chen T, Tsai H R. Maintenance in digitalised manufacturing: Delphi-based scenarios for 2030. [J]. Robotics and Computer-Integrated Manufacturing, 2017, 45: 126-132.

ABSTRACT: This paper presents a heuristic method to solve a dynamic pricing problem under costly price modifications. This is an extremely difficult nonlinear problem that has been solved only for a few special instances. Here we provide a new approach that involves an approximate reformulation of the problem, which can subsequently be solved in closed-form using elementary calculus techniques. Numerical results show that the approach is quite accurate; approximating the optimal revenue with errors usually much less than 1%. Moreover, the accuracy rapidly improves as the optimal number of price changes increases, which are precisely the cases conventional approaches would fail.

2. Nicosia G, Pacifici A, Pferschy U. Price of Fairness for allocating a bounded resource. European Journal of Operational Research. 2017 Mar 16;257(3):933-43.

ABSTRACT: We study the problem faced by a decision maker who wants to allocate a scarce resource among several agents in order to maximize the total utility. An optimal solution may present a very unbalanced allocation of the resource to the agents and hence be perceived as unfair. On the other hand balanced allocations may be far from the optimum. In this paper we are interested in assessing the quality of fair solutions, i.e., in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the total utility. This indicator is called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai–Smorodinski and proportional fairness. Our results are twofold. We first formalize a number of properties holding for any general multi-agent problem without any special assumptions on the agent utilities. Then we introduce an allocation problem, in which each agent can consume the available bounded resource in given discrete quantities (items). The utility of each agent is given by the sum of these quantities (weights of allocated items). We distinguish two cases depending on whether disjoint sets or a shared set of items is available to the agents. Clearly, the maximization of the total utility is given by a Subset Sum Problem. For the resulting Fair Subset Sum Problem, in the case of two agents, we provide upper and lower bounds on the Price of Fairness as functions of an upper bound on the items size.

3. Bock S, Pütz M. Implementing Value Engineering based on a multidimensional quality-oriented control calculus within a Target Costing and Target Pricing approach. International Journal of Production Economics. 2017 Jan 31;183:146-58

ABSTRACT: In this paper, a new quality-oriented control approach for Value Engineering is proposed. It is reasonably applied within a Target Costing and Target Pricing concept in order to generate, maintain and process reliable data. On the basis of Target costs and prices, the approach determines the quality program of the relevant product core components as well as of the quality-related production stages. In order to provide decision support for various applications in business, this new approach is based on a discrete quality measure that allows for the mapping of multidimensional dependencies. After mathematically defining the underlying quality planning model, we propose an exact Dynamic Programming approach for determining optimal programs. It is shown that this procedure is strongly polynomial if the number of resulting intermediate product quality levels does not increase exponentially. Subsequently, in order to provide decision support for the level of real-time Value Engineering, a variance analysis scheme for examining the consequences of actual decisions is proposed. In addition to controlling and understanding the process of decision-making in sales and production departments, its iterative application makes it possible to systematically attain insights into the controlled processes and, in doing so, supports decision-oriented management accounting.

4. Chen P, Xu H, Li Y, Zeng L. Joint product variety, pricing and scheduling decisions in a flexible facility. International Journal of Production Research. 2017 Jan 17;55(2):606-20.

ABSTRACT: This paper studies a manufacturer’s optimal product variety, pricing and scheduling decisions in a single flexible production facility when customers have private information in their marginal valuations for product qualities. In addition to determining the product variety and price of each product, the manufacturer needs to optimise a detailed schedule of production (batch sizes and production sequences) to fully utilise the flexibility of this facility. To achieve the second-degree discrimination, the manufacturer provides multiple products and follows a priority rule in the production schedule. To obtain economies of scale, the manufacturer may offer a composite product targeting the whole population, or choose a dedicated product to serve a proportion of customers. Comparing these three production choices, we observe that the optimal product variety strategy is threshold controlled by the relative ratio of customer arrival rates, the relative difference between customers’ marginal valuations and the production technology.

5. Mishra BK, Prasad A, Srinivasan D, ElHafsi M. Pricing and capacity planning for product-line expansion and reduction. International Journal of Production Research. 2017 May 7:1-8.

ABSTRACT: We investigate optimal pricing and capacity planning decisions for product-line settings such as introducing a new product or dropping an existing one. We consider a two-product, two-period model with stochastic demands, where price and capacity decisions are made at the outset. Investment in capacity must be traded-off against the possibility of buying at higher spot market prices due to shortage in capacity or charging a higher price to manage the demand. Prior studies argue that introducing an additional product to the product-line strains capacity, resulting in an increase in the price of an existing product. In contrast, we find that introducing a new product can also result in a drop in price of an existing product, enabling strategic pricing by firms. The necessary condition for this to occur is that the demand uncertainties for the products are of similar magnitude and negatively correlated. Similar insights are obtained for the setting where an existing product is dropped from the product-line. Hence, product-market decisions and contextual factors play a role in capacity planning, capacity cost allocation and pricing.

6. Nodehi T, Jardim-Goncalves R, Zutshi A, Grilo A. ICIF: an inter-cloud interoperability framework for computing resource cloud providers in factories of the future. International Journal of Computer Integrated Manufacturing. 2017 Jan 2;30(1):147-57.

ABSTRACT: Factories of the future (FoF) is a relatively new topic focusing on developing competitive manufacturing. Exploiting cloud services is a vital area for FoF. The collaboration between different cloud vendors can provide better quality of service at a lower price. This paper discusses a framework which supports inter-cloud interoperability in a heterogeneous computing resource cloud environment with the goal of dispatching the workload to the most effective clouds available at runtime. Moreover, a genetic algorithm (GA)–based job-scheduler is proposed as a part of the interoperability framework offering workload migration with the best performance at the least cost. The resource selection model is evaluated using agent-based simulation approach.

7. Anily S, Haviv M. Line balancing in parallel M/M/1 lines and loss systems as cooperative games. Production and Operations Management. 2017 Aug 1;26(8):1568-84.

ABSTRACT: We consider production and service systems that consist of parallel lines of two types: (i) M/M/1 lines and (ii) lines that have no buffers (loss systems). Each line is assumed to be controlled by a dedicated supervisor. The management measures the effectiveness of the supervisors by the long run expected cost of their line. Unbalanced lines cause congestion and bottlenecks, large variation in output, unnecessary wastes and, ultimately, high operating costs. Thus, the supervisors are expected to join forces and reduce the cost of the whole system by applying line-balancing techniques, possibly combined with either strategic outsourcing or capacity reduction practices. By solving appropriate mathematical programming formulations, the policy that minimizes the long run expected cost of each of the parallel-lines system, is identified. The next question to be asked is how to allocate the new total cost of each system among the lines’ supervisors so that the cooperation’s stability is preserved. For that sake, we associate a cooperative game to each system and we investigate its core. We show that the cooperative games are reducible to market games and therefore they are totally balanced, that is, their core and the core of their subgames are non-empty. For each game a core cost allocation based on competitive equilibrium prices is identified.

8. Yang C, Shen W, Lin T, Wang X. A hybrid framework for integrating multiple manufacturing clouds. The International Journal of Advanced Manufacturing Technology. 2016 Sep 1;86(1-4):895-911.

ABSTRACT: Cloud manufacturing (CMfg) adopts and extends the concept of cloud computing to make mass Manufacturing Resources and Capabilities (MR/Cs) more widely integrated and accessible to users through the Internet. However, a single manufacturing cloud (MC) has limited MR/Cs, due to both economic and technical constraints, and can only provide limited manufacturing services in terms of function, price, and reliability, etc. Using the aggregated MR/Cs or services of multiple MCs is a natural evolution, i.e., MCs can satisfy peak demands for MR/Cs through collaboration, while users can have a wider selection of services from multiple MCs. To address such requirements, we propose a hybrid framework for integrating multiple MCs. The key functional modules and the business models of the proposed framework are presented to guide future integration of MCs. The enabling technologies, such as semantic web and ontologies, intelligent agents, service-oriented architecture, and materials handling and logistics technologies are also discussed. A case study is given, showing the feasibility and rationality of the proposed approach.

9. Jiang H, Chen R, Sun H. Multiproduct price optimization under the multilevel nested logit model. Annals of Operations Research. 2017 Jul 1;254(1-2):131-64.

ABSTRACT: We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce the multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.

10. Honhon D, Pan XA. Improving Profits by Bundling Vertically Differentiated Products. Production and Operations Management. 2017 Mar 1.

ABSTRACT: We consider a firm managing a category of vertically differentiated goods, that is, products which differ with respect to an attribute for which all consumers prefer more to less. The goods can be sold individually, in which case they are referred to as components, or in bundles. The firm chooses the assortment of components and bundles and their selling prices to maximize profit. We show that each bundling strategy (pure components, pure bundling or mixed bundling) can be optimal and obtain closed-form expressions for the optimal selling prices. We provide insights on the structure of the optimal assortment and prices. In particular, we show that, when consumers benefit from consuming the components jointly, the products in the optimal assortment form nested sets. When consumers do not benefit from the joint consumption of components, the bundles should be offered at a positive discount. We find that bundling vertically differentiated products can significantly improve profits, even if consumers do not benefit from consuming the components jointly. The value of bundling comes from increased sales: a firm, which understands that its customers may buy multiple types of components, offers bundles of components, incentivizing customers to buy more.



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