Integrated customer portfolio selection and procurement quantity planning for a supplier

Abstract

This paper considers a supplier who offers a customized product to multiple potential customers, each with uncertain demand. The supplier’s end items consume common raw materials, which must be ordered far in advance of the selling season due to long procurement lead times, limiting the supplier’s capacity to meet realized demands. As a result of the customization, each customer negotiates an individual agreement with the supplier, leading to customer-specific prices and loss of goodwill costs in case of unsatisfied demands. The supplier aims to select a portfolio of customers and a raw material procurement quantity to maximize its expected profit. We formulate the problem based on echelon stockout costs, and establish optimality conditions and bounds for the newsvendor solution. This formulation, moreover, elegantly generalizes the analysis of the so-called selective newsvendor problem to address settings with lost sales and an uncertain spot market price for expediting. As customer requirements are oftentimes interdependent, we further extend our models to handle correlated customer demands. Lastly, we analyze the setting in which capacity can be reserved with the supplier prior to the selling season. Such contracts may serve as coordination mechanisms to improve overall supply chain profitability. Since the resulting models are in general difficult to solve exactly, we propose conic quadratic programming-based heuristics as well as sampling-based methods. We validate our approach through an extensive numerical study, illustrating the effectiveness of the proposed solution methods, the importance of explicitly considering correlation among customers due to risk pooling effects, and the impact of capacity reservation on both supplier and customer decisions. Finally, to support real-world applicability, we demonstrate the remarkable performance of the solutions obtained assuming normally distributed demands even when the true distributions deviate from this assumption.