Optimal Pricing and Production Planning for Subscription‐Based Products

Abstract

In this paper, we address the problem of a magazine publishing firm facing stochastic demand over multiple periods. We model the dynamics of customer subscription and retention/attrition. We identify the key decision variables to enhance magazine profitability: production quantity, subscription price and newsstand price.First, we provide a dynamic programming formulation of the firm's problem and then propose a single-stage reduction which admits a classical newsvendor characterization. For both the finite and infinite horizon cases, we characterize the optimal policy of the firm where the decision variables are one, two or all three of the aforementioned variables. Next, we consider the duopolistic setting, where firms benefit from the overflow of the competitor's unmet demand, and we provide analytic solutions in the case of uniform demand distributions. Finally, we report on computational experiments both in the monopolistic and duopolistic settings and provide managerial insights.

A review of discrete-time optimization models for tactical production planning

“…Pricing decisions, hence price-dependent demand levels, are addressed by a group of 10 references (Deng and Yano, 2006;Geunes et al, 2006;Gonzalez-Ramirez et al, 2011;Guan and Philpott, 2011;Haugen et al, 2007;Huh et al, 2010;Merzifonluoglu et al, 2007;Onal and Romeijn, 2010;Smith and Martinez-Flores, 2007;van den Heuvel and Wagelmans, 2006). Moreover, the time window notion is obtained if demands levels are considered between a release (availability) date and a due date.…”

“…Processed food, beverages and dairy industry 2 Ram et al (2006), Christou et al (2007) Pulp and paper industry 2 Rizk et al (2006), Almeder et al (2009) Sawmills, wood and furniture industry 1 Demirli and Yimer (2008) Pharmaceutical company 1 Lukac et al (2008) Pottery company 1 Petrovic and Akoez (2008) Fruit juice and soft drink industry 1 Ferreira et al (2009) Iron factory 1 Pan et al (2009) Semiconductor and electronic devices industry 1 Quadt and Kuhn (2009) Magazine publishing firm 1 Huh et al (2010) Refractory bricks manufacturer 1 Mateus et al (2010) X-ray film producer 1 Aghezzaf et al (2011) Clinical trial 1 Fleischhacker and Zhao (2011) Numerical examples inspired in:…”

“…Demand limitations are described in 37 references. These weaknesses are due to not allowing backorders (Aksen, 2007;Almada-Lobo et al, 2007;Begnaud et al, 2009;Bilgen and Guenther, 2010;Bollapragada et al, 2011;Degraeve and Jans, 2007;Gaglioppa et al, 2008;Goren et al, 2012;Gutierrez et al, 2008;Kanyalkar and Adil, 2007;Lan et al, 2011;Liu and Tu, 2008a;Lusa et al, 2009;Menezes et al, 2011;Wolsey, 2006), lost sales (Bollapragada et al, 2011;Liu and Tu, 2008b), or are owing to not including pricing decisions (Bjork and Carlsson, 2007;Feng et al, 2010;Geunes et al, 2006;Huh et al, 2010;Jayaraman, 2006;Leung et al, 2006;Lu and Qi, 2011;Onal and Romeijn, 2010;Sargut and Romeijn, 2007;Shi et al, 2011;Xue et al, 2011) or discounts (Aksen, 2007;Ho et al, 2007). The other demand limitations reported by authors consider constant selling prices (Feng et al, 2008;van den Heuvel and Wagelmans, 2006), assume monopolistic demand (Haugen et al, 2007), or ignore demand patterns and seasonal demand (Alwan et al, 2008;Zanjani et al, 2010b), segregation of customers or time windows (Absi et al, 2011).…”

“…Moreover, the product structures of Barba-Gutierrez et al (2008), Kim and Xirouchakis (2010) and Ram et al (2006) do not bear in mind possible product commonalities. Supply chain limitations are related to the specific nodes not included in the supply chain structure, such as suppliers (Jung et al, 2008a;Yang and Qi, 2010), more production plants (Guan and Philpott, 2011), warehouses (Guan and Philpott, 2011;Shaikh et al, 2011), distribution centers (Erromdhani et al, 2012;Torabi and Hassini, 2009), vendors (Jung et al, 2008b) or supplying very simple chain networks (Dudek and Stadtler, 2007;Fleischhacker and Zhao, 2011;Huh et al, 2010;Rizk et al, 2006a;Selcuk et al, 2008). Moreover, transport issues and supplier selection are reported as drawbacks in Bilgen and Guenther (2010), Chen and Huang (2010), Gunnarsson and Ronnqvist (2008), Qu and Williams (2008), and Lin et al (2009) and Pal et al (2011).…”

A Note on the Relationship Among Capacity, Pricing, and Inventory in a Make‐to‐Stock System

“…Further references in this stream of literature are surveyed in Elmaghraby and Keskinocak (2003); a deterministic analysis of such problems dates back to Thomas (1974) and Kunreuther and Schrage (1973). Recently, Ketzenberg and Zuidwijk (2009) studied the joint pricing, ordering decisions, and return policies for consumer goods, and Huh et al (2010) studied the optimal pricing and production for subscription-based products.…”