An integrated stochastic model and algorithm for constrained multi-item newsvendor problems by two-stage decision-making approach

Abstract

In this paper, we first build a model for a complicated newsvendor problem, which is involved with optimization to preseason production quantity with random yields and outsourcing quantity with supplier quantity discounts. Different from the existing models, a two-stage decision-making strategy is proposed for the retailer such that the possible loss, caused by the uncertainty of production, is reduced in virtue of dynamically choosing the outsourcing quantities and sales prices. Additionally, the cross-elasticity of prices is incorporated into formulating the random and price-dependent demand function in our model. Consequently, the mathematical model is expressed by a parameterized optimization problem, and a cyclic coordinate descent algorithm (CCD), combined with a feasible direction method and a parameters-choosing procedure, is developed to obtain optimal solutions of the original problem. Both substitute and complementary scenarios for different products are further investigated by numerical simulation. Main managerial implications are summarized as follows: (1) The two-stage policy of decision-making brings more benefits than a static policy for the complicated newsvendor problems. (2) The budget available is a critical constraint for the small-and-medium sized business, the maximum expected profit increases as the budget becomes greater, but remains at the same level after it reaches a threshold value. (3) The cross elasticity relationship between the products plays a critical role in choosing optimal quantities of preseason production, sales prices and outsourcing quantities.