Generalized quasi-variational inequalities in infinite-dimensional normed spaces
Journal of Optimization Theory and Applications
Mathematics of Operations Research
Differential games in economics and management science
Differential games in economics and management science
Nash equilibria, variational inequalities, and dynamical systems
Journal of Optimization Theory and Applications
Operations Research
A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders
Mathematical Programming: Series A and B
A Robust Optimization Approach to Inventory Theory
Operations Research
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In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor's strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.