A solution algorithm for multi-period bi-level channel optimization with dynamic price-dependent stochastic demand

• Published in: Omega (Oxford) Vol. 102; p. 102297
• Main Authors: Gholami, Reza Azad, Sandal, Leif Kristoffer, Ubøe, Jan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2021
• Subjects: Bi-level optimization; Channel optimization; Game theory; Newsvendor problem; Perishable commodity; Price-dependent demand; Stochastic demand; Time-dependent demand; Time-dependent demand; Bi-level optimization; Channel optimization; Stochastic demand; Perishable commodity; Newsvendor problem; Game theory; Price-dependent demand
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2020.102297

•Explicit solution algorithm for dynamic bi-level channel optimization is provided.•Multi-period newsvendor problem with general additive-multiplicative demand structure is solved.•Full non-autonomy of the ensuing equilibrium problems: all the variables and parameters are time-dependent.•Memory functions are embedded in demand: demand is dependent on pricing history.•Diverse market scenarios are covered in the example section. We extend the single-period decentralized channel optimization problem with stochastic demand into a multi-period, non-autonomous one and propose an efficient general solution algorithm for it. A supply channel composed of two price-setting agents in a bi-level (Stackelberg) framework has to address an uncertain dynamic demand for a perishable good at different times. The stochastic demand model is general (additive-multiplicative). A class of price-dependent memory functions is embedded in the proposed representation of uncertain demand such that they carry the effect of demand level at present over to the demand in the future. Due to this dependence of the current demand to the pricing history, the state space of the ensuing games becomes highly nested. The proposed iterative algorithm decouples the nested equilibria into separate yet interdependent sub-problems and provides explicit solutions. All the model variables and parameters are considered explicitly time-dependent enabling the model to cover cases with finite and infinite time-horizons. Flexibility and generality of our solution scheme make it applicable to a wide variety of economic contexts. In a series of examples we demonstrate how, fed by different market specifications and memory functions, the solution algorithm can find equilibrium results for a diverse set of scenarios at different times.