Abstract
In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting, where demand depends linearly on the price. Our goal is to address demand uncertainty using various robust and stochastic optimization approaches. For each of these approaches, we first introduce closed-loop formulations (adjustable robust and dynamic programming), where decisions for a given time period are made at the beginning of the time period, and uncertainty unfolds as time evolves. We then describe models in an open-loop setting, where decisions for the entire time horizon must be made at time zero. We conclude that the affine adjustable robust approach performs well (when compared to the other approaches such as dynamic programming, stochastic programming and robust open loop approaches) in terms of realized profits and protection against constraint violation while at the same time it is computationally tractable. Furthermore, we compare the complexity of these models and discuss some insights on a numerical example.
Highlights
In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system
Decisions for all time periods must be taken at the beginning of the time horizon
In a closed-loop setting for linear programs, Ben-Tal et al [8] and Guslitzer [31] extend their robust optimization methodology to formulations where some variables may be determined after the realization of uncertain parameters. These variables are called adjustable. They address the difficulty of solving the adjustable robust counterpart problem by restricting adjustable variables to be affine functions of the uncertain data
Summary
We assume that firms are profit maximizing In this model, multiple products share a single common production capacity K(t). We assume that the production costs are quadratic with the production rate with a coefficient γi(t), and that the holding costs are linear with the inventory level, with coefficient hi(t). These types of costs have been used often in the literature on inventory control. Clark and Scarf [24] introduce the Multi-Echelon Inventory Problem which includes linear holding costs This model was used extensively in the literature
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