A reward-penalty stochastic pricing and advertising model under demand uncertainty

Document Type : Research Paper


Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran


This paper aims in assessing the effects of governmental policies on a maximal covering location problem facing stochastic demand which is sensitive to both the retail price and facility advertising effort. A reward-penalty two-stage stochastic programming model is proposed to formulate the problem as a supportive approach in a mixed integer non-linear programming form. In particular, a stochastic pricing and advertising dependent demand model in a facility location configuration is developed which sets the retail price for each opened facility and various advertising effort levels based on the zone’s attractiveness. To promote customer welfare and satisfaction, the legislative counterpart of the reward-penalty model is introduced. The legislative model assigns the minimum satisfaction demand level to the model as a constraint. In both models, the firm tries to maximize its net profit according to government decisions. An analytical method based on the L-shaped algorithm is provided to determine the best solutions of the first and second stages with coping nonlinearity term of the proposed models. Finally, numerical examples are developed to illustrate the governmental policies impacts to reach to the most social welfare as well as the least reward-penalty legislation.


Main Subjects

Aksen, Deniz, Necati Aras, and Ayşe Gönül Karaarslan.  2009.  "Design and Analysis of Government Subsidized Collection Systems for Incentive-Dependent Returns."  International Journal of Production Economics 119: 308-27.
Albareda-Sambola, Maria, Antonio Alonso-Ayuso, Laureano F. Escudero, Elena Fernández, and Celeste Pizarro.  2013.  "Fix-and-Relax-Coordination for a Multi-Period Location–Allocation Problem under Uncertainty."  Computers & Operations Research 40: 2878-92.
Albareda-Sambola, Maria, Elena Fernández, and Francisco Saldanha-da-Gama.  2011.  "The Facility Location Problem with Bernoulli Demands."  Omega 39: 335-45.
Alizadeh, Morteza.  2013.  "A Nonlinear Model for a Capacitated Location-Allocation Problem with Bernoulli Demand Using Sub-Sources". 26: 1007-16.
Alizadeh, Morteza, Iraj Mahdavi, Nezam Mahdavi-Amiri, and Saber Shiripour.  2015.  "A Capacitated Location-Allocation Problem with Stochastic Demands Using Sub-Sources: An Empirical Study."  Applied Soft Computing 34: 551-71.
Amini, Farshad, Jasmine Ahmad, and Abdul Rauf Ambali.  2014.  "The Influence of Reward and Penalty on Households’ Recycling Intention."  APCBEE Procedia 10: 187-92.
Araman, Victor, and Ioana Popescu.  2010.  Media Revenue Management with Audience Uncertainty: Balancing Upfront and Spot Market Sales. 12: 190-212.
Asamoah, Emmanuel, and Miloslava Chovancová.  2011.  "The Influence of Price Endings on Consumer Behavior: An Application of the Psychology of Perception."  Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensi.s 59: 29-38.
Aziz, Haris, Hau Chan, Barton Lee, Bo Li, and Toby Walsh.  2019.  "Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives".
Bashir, Aneeza, and Najma Malik.  2010.  "Effects of Advertisement on Consumer Behavior of University Students".
Bentaha, M. L., O. Battaïa, and A. Dolgui.  2013.  "L-Shaped Algorithm for Stochastic Disassembly Line Balancing Problem."  IFAC Proceedings Volumes 46: 407-11.
Berman, Oded, and Jiamin Wang.  2011.  "The Minmax Regret Gradual Covering Location Problem on a Network with Incomplete Information of Demand Weights."  European Journal of Operational Research 208: 233-38.
Bieniek, Milena.  2015.  "A Note on the Facility Location Problem with Stochastic Demands."  Omega 55: 53-60.
Biesinger, Benjamin, Bin Hu, and Günther Raidl.  2016.  "An Integer L-Shaped Method for the Generalized Vehicle Routing Problem with Stochastic Demands." Electronic Notes in Discrete Mathematics 52: 245-52.
Brawley, Otis W.  2017.  "The Role of Government and Regulation in Cancer Prevention."  The Lancet Oncology 18: e483-e93.
C. Petruzzi, Nicholas, and Maqbool Dada.  1999.  Pricing and the Newsvendor Problem: A Review with Extensions.  47: 183-94.
Church, Richard, and Charles R. Velle.  1974.  "The Maximal Covering Location Problem."  Papers in Regional Science 32: 101-18.
Correia, Isabel, and Francisco Saldanha da Gama.  2015.  "Facility Location under Uncertainty."  In Location Science, eds.  Gilbert Laporte, Stefan Nickel and Francisco Saldanha da Gama.  Cham: Springer International Publishing.  177-203.
Correia, Isabel, Stefan Nickel, and Francisco Saldanha-da-Gama.  2018.  "A Stochastic Multi-Period Capacitated Multiple Allocation Hub Location Problem: Formulation and Inequalities."  Omega 74: 122-34.
Farahani, Reza Zanjirani, Nasrin Asgari, Nooshin Heidari, Mahtab Hosseininia, and Mark Goh.  2012.  "Covering Problems in Facility Location: A Review."  Computers & Industrial Engineering 62: 368-407.
Fischetti, Matteo, Ivana Ljubic, and Markus Sinnl. 2016. "Redesigning Benders Decomposition for Large-Scale Facility Location." Management Science. 63.
Gou, Qinglong, Jing Shao, Xin Wang, and Lili Yu.  2020.  "Co-Op Supply Chains with a Local Media Company: Models and Analysis."  Transportation Research Part E: Logistics and Transportation Review 136: 101893.
Gutierrez, Anabel, Simon O'Leary, Nripendra P. Rana, Yogesh K. Dwivedi, and Tatiana Calle.  2019.  "Using Privacy Calculus Theory to Explore Entrepreneurial Directions in Mobile Location-Based Advertising: Identifying Intrusiveness as the Critical Risk Factor."  Computers in Human Behavior 95: 295-306.
Gülpınar, Nalan, Dessislava Pachamanova, and Ethem Çanakoğlu. 2013. "Robust Strategies for Facility Location under Uncertainty." European Journal of Operational Research. 225(1): 21-35.
Habibzadeh Boukani, Fereidoon, Babak Farhang Moghaddam, and Mir Saman Pishvaee. 2016. "Robust Optimization Approach to Capacitated Single and Multiple Allocation Hub Location Problems." Computational and Applied Mathematics. 35(1): 45-60.
He, Yong, Xuan Zhao, Lindu Zhao, and Ju He.  2009.  "Coordinating a Supply Chain with Effort and Price Dependent Stochastic Demand."  Applied Mathematical Modelling 33: 2777-90.
Helmes, Kurt L., and Rainer Schlosser.  2013.  "Dynamic Advertising and Pricing with Constant Demand Elasticities."  Journal of Economic Dynamics and Control 37: 2814-32.
Hosseini, Meysam, and S. A. MirHassani. (2015) "Refueling-Station Location Problem under Uncertainty." Transportation Research Part E: Logistics and Transportation Review. 84: 101-16.
IHS ECONOMICS AND COUNTRY RISK. 2015. " Economic Impact of Advertising in the United States." www.ihs.com.
Kulshreshtha, Praveen, and Sudipta Sarangi.  2001.  "“No Return, No Refund”: An Analysis of Deposit-Refund Systems."  Journal of Economic Behavior & Organization 46: 379-94.
Lee, Gunhak, and Alan T. Murray.  2010.  "Maximal Covering with Network Survivability Requirements in Wireless Mesh Networks."  Computers, Environment and Urban Systems 34: 49-57.
Lei, Chao, Wei-Hua Lin, and Lixin Miao.  2014.  "A Multi cut L-Shaped Based Algorithm to Solve a Stochastic Programming Model for the Mobile Facility Routing and Scheduling Problem."  European Journal of Operational Research 238: 699-710.
Li, Can, and Ignacio E. Grossmann.  2018.  "An Improved L-Shaped Method for Two-Stage Convex 0–1 Mixed Integer Nonlinear Stochastic Programs."  Computers & Chemical Engineering 112: 165-79.
Li, Xueping, Zhaoxia Zhao, Xiaoyan Zhu, and Tami Wyatt.  2011.  "Covering Models and Optimization Techniques for Emergency Response Facility Location and Planning: A Review."  Mathematical Methods of Operations Research 74: 281-310.
Liu, Bin, Xindi Ma, and Rong Zhang.  2014.  "Joint Decision on Pricing and Advertising for Competing Retailers under Emergency Purchasing."  Economic Modelling 39: 257-64.
Madansky, Albert.  1960.  "Inequalities for Stochastic Linear Programming Problems."  Management Science 6: 197-204.
Maiti, T., and B. C. Giri.  2017.  "Two-Period Pricing and Decision Strategies in a Two-Echelon Supply Chain under Price-Dependent Demand."  Applied Mathematical Modelling 42: 655-74.
Mestre, Ana Maria, Mónica Duarte Oliveira, and Ana Paula Barbosa-Póvoa. 2015. "Location–Allocation Approaches for Hospital Network Planning under Uncertainty." European Journal of Operational Research. 240(3): 791-806.
Mirzapour Al-e-hashem, Seyed M. J., Yacine Rekik, and Ebrahim Mohammadi Hoseinhajlou.  2019.  "A Hybrid L-Shaped Method to Solve a Bi-Objective Stochastic Transshipment-Enabled Inventory Routing Problem."  International Journal of Production Economics 209: 381-98.
Mišković, Stefan, Zorica Stanimirović, and Igor Grujičić. 2017. "Solving the Robust Two-Stage Capacitated Facility Location Problem with Uncertain Transportation Costs." Optimization Letters. 11(6): 1169-84.
Mitra, Supriya, and Scott Webster.  2008.  "Competition in Remanufacturing and the Effects of Government Subsidies."  International Journal of Production Economics 111: 287-98.
Nickel, Stefan, Francisco Saldanha-da-Gama, and Hans-Peter Ziegler.  2012.  "A Multi-Stage Stochastic Supply Network Design Problem with Financial Decisions and Risk Management."  Omega 40: 511-24.
Niu, Baozhuang, Lei Chen, and Jie Zhang.  2017.  "Punishing or Subsidizing? Regulation Analysis of Sustainable Fashion Procurement Strategies."  Transportation Research Part E: Logistics and Transportation Review 107: 81-96.
Ortiz-Astorquiza, Camilo, Ivan Contrerasn, and Gilbert Laporte.  2017.  "Multi-Level Facility Location Problems."  European Journal of Operational Research.
Plambeck, Erica, and Qiong Wang.  2009.  "Effects of E-Waste Regulation on New Product Introduction."  Management Science 55: 333-47.
Plastria, Frank, and Lieselot Vanhaverbeke.  2007.  "Aggregation without Loss of Optimality in Competitive Location Models."  Networks and Spatial Economics 7: 3-18.
Plastria, Frank, and Lieselot Vanhaverbeke. 2009.  "Maximal Covering Location Problem with Price Decision for Revenue Maximization in a Competitive Environment."  OR Spectrum 31: 555-71.
Rad, Mona Ahmadi, Farid Khoshalhan, and Christoph H. Glock.  2016.  "Optimal Production and Distribution Policies for a Two-Stage Supply Chain with Imperfect Items and Price- and Advertisement-Sensitive Demand: A Note."  Applied Mathematical Modelling.
Ray, Saibal.  2005.  "An Integrated Operations–Marketing Model for Innovative Products and Services."  International Journal of Production Economics 95: 327-45.
Schlicher, Loe, Marco Slikker, and Geert-Jan van Houtum.  2017.  "A Note on Maximal Covering Location Games."  Operations Research Letters 45: 98-103.
Schlosser, Rainer.  2016.  "Joint Stochastic Dynamic Pricing and Advertising with Time-Dependent Demand."  Journal of Economic Dynamics and Control 73: 439-52.
Schlosser, Rainer. 2017.  "Stochastic Dynamic Pricing and Advertising in Isoelastic Oligopoly Models."  European Journal of Operational Research 259: 1144-55.
Sheu, Jiuh-Biing, and Yenming J. Chen.  2012.  "Impact of Government Financial Intervention on Competition among Green Supply Chains."  International Journal of Production Economics 138: 201-13.
Sheu, Jiuh-Biing, Yi-Hwa Chou, and Chun-Chia Hu.  2005.  "An Integrated Logistics Operational Model for Green-Supply Chain Management."  Transportation Research Part E: Logistics and Transportation Review 41: 287-313.
Shutao, Mu, and Niu Jiangao.  2011.  "An Analysis of the Effect of Government-Enterprise Game in the Government–Leading Industrial Energy Saving Model."  Energy Procedia 5: 633-37.
Shy, O.  2008.  "How to Price: A Guide to Pricing Techniques and Yield Management".
Slyke, R. M. Van, and Roger Wets.  1969.  "L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming."  SIAM Journal on Applied Mathematics 17: 638-63.
Snyder, Lawrence V.  2006.  "Facility Location under Uncertainty: A Review."  IIE Transactions 38: 547-64.
Vatsa, Amit Kumar, and Sachin Jayaswal.  2016.  "A New Formulation and Benders Decomposition for the Multi-Period Maximal Covering Facility Location Problem with Server Uncertainty."  European Journal of Operational Research 251: 404-18.
Wang, Wenbin, Yu Zhang, Yuanyuan Li, Xuejuan Zhao, and Mingbao Cheng.  2017.  "Closed-Loop Supply Chains under Reward-Penalty Mechanism: Retailer Collection and Asymmetric Information."  Journal of Cleaner Production 142, Part 4: 3938-55.
Wang, Wenbin, Yu Zhang, Kai Zhang, Tuo Bai, and Jennifer Shang.  2015.  "Reward–Penalty Mechanism for Closed-Loop Supply Chains under Responsibility-Sharing and Different Power Structures."  International Journal of Production Economics 170: 178-90.
Wojanowski, Rico, Vedat Verter, and Tamer Boyaci.  2007.  "Retail–Collection Network Design under Deposit–Refund."  Computers & Operations Research 34: 324-45.
Wu, Zhengping, Wanshan Zhu, and Pascale Crama.  2011.  The Newsvendor Problem with Advertising Revenue. 13: 281-96.
Xiao, Dan, Yong-Wu Zhou, Yuanguang Zhong, and Wei Xie.  2019.  "Optimal Cooperative Advertising and Ordering Policies for a Two-Echelon Supply Chain."  Computers & Industrial Engineering 127: 511-19.
Yang, Deyan, and Tiaojun Xiao.  2017.  "Pricing and Green Level Decisions of a Green Supply Chain with Governmental Interventions under Fuzzy Uncertainties."  Journal of Cleaner Production 149: 1174-87.
Zhang, Bo, Jin Peng, and Shengguo Li.  2017a.  "Covering Location Problem of Emergency Service Facilities in an Uncertain Environment."  Applied Mathematical Modelling 51: 429-47.
Zhang, Huiming, Yu Zheng, Jie Cao, and Yueming Qiu.  2017b.  "Has Government Intervention Effectively Encouraged the Use of Waste Cooking Oil as an Energy Source? Comparison of Two Chinese Biofuel Companies."  Energy 140: 708-15.
Zhao, Li, Changwei Wang, Haiying Gu, and Chengyan Yue.  2017.  "Market Incentive, Government Regulation and the Behavior of Pesticide Application of Vegetable Farmers in China."  Food Control.
Volume 13, Issue 1 - Serial Number 1
January 2020
Pages 111-135
  • Receive Date: 02 March 2020
  • Revise Date: 14 April 2020
  • Accept Date: 24 April 2020
  • First Publish Date: 16 August 2020