Abstract: This paper investigates aportfolio approach to multi-product newsboy problem with budget constraint, inwhich the procurementstrategy for each newsboy product is designed as portfolio contract. A portfoliocontract consists of a fixed-price contract and an option contract. We model the problem as a profit-maximization model, and proposean efficient solution procedure after investigating the structural propertiesof the model. We conduct numerical studies to show the efficiency of theproposed solution procedure, and to compare three models with different procurement contracts,i.e., fixed-pricecontract, option contract, and portfolio contract. Numericalresults are shown to demonstrate the advantage of the portfolio model, and sensitivityanalysis is provided for obtaining some managerial insights.

Keywords: Newsboy;Option contract; Portfolio; Budget constraint; Flexibility

1.Introduction

Multi-product newsboyproblem with budget constraint is a classical inventory management problem,which was firstly introduced by Hadley and Whitin (1963). After Hadley andWhitin’s seminal work, many researchers have investigated different models andsolution methods for multi-product newsboy problems. Khouja (1999) presented agood literature review on these researches. Due to the difficultyfor solving large-scale problems, most recent works have focused on developing efficientsolution methods, e.g., Lau and Lau (1996), Erlebacher (2000), Vairaktarakis (2000),Moon and Silver (2000), and Abdel-Malek et al. (2004). To addressnon-negativity constraints of the order quantities, Abdel-Malek and Montanari(2005) proposed a modified Lagrangian based method by analyzing the solutionspace. Zhang et al. (2009) provided an exact solution method for the problemwith any continuous demand distribution. Zhang and Hua (2008) proposed aunified algorithm for solving a class of convex separable nonlinear knapsackproblems, which include the singly constrained multi-product newsboy problem withbox constraints. Zhang and Du (2010) studied the multi-product newsboy problem withlimited capacity and outsourcing. 

In the classical newsboyproblem, the product is procured from the supplier with fixed-price contract. Underthis procurement strategy, the retailer will undertake the salvage lossresulting from lower realized demand. To avoid this risk, the retailer always doesnot order enough inventories to maximize the supply chain’s total profit underthe fixed-price contract (Cachon, 2003). In order to maximize the supply chain’stotal profit, and share the risk raised from demand uncertainty with supplychain partners, some different contract types are used for encouraging theretailer to increase the order in supply chain management practice, such as buyback contracts, revenue sharing contracts, quantity flexibility contracts, salesrebate contracts and quantity discount contracts (Cachon, 2003).