Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model

Abstract

A generalized newsvendor model is developed to analyze the coordinated quantity decisions between the manufacturer and the buyer. The manufacturer and the buyer operate to meet random demand of one product with a short lifecycle. The analytical results for the general newsvendor model are obtained. Our analysis of the generalized newsvendor model developed yields the insights into the coordination structure between the manufacturer and the buyer. Quantity discount policies are developed as incentive policies, which the manufacturer may use to induce the buyer to order the coordinated quantity.

Introduction

Shortened product lifecycles and the accompanying rapid price depreciation of products impel both manufacturers and buyers to better coordinate their decisions (see, e.g., Fisher and Raman, 1996; Fites, 1996; Webster and Weng, 2000). In this paper, we consider the scenario of two parties––one manufacturer and one buyer––operating to meet random demand of a single product with a short lifecycle. The manufacturer and the buyer may coordinate order quantity decisions. The paper aims to study the coordination structure between the manufacturer and the buyer. The optimal coordinated ordering policies that maximize expected profits of the manufacturer and the buyer are developed. The coordination strategy (an all) units quantity discount policy––as well as the necessary condition for it to prevail are developed.

The order quantity coordination problem under consideration can be briefly described as follows. Consider a manufacturer, for example, a consumer electronics manufacturer, that produces a variety of products with short product lifecycles. The manufacturer does not hold inventory and activates production with a fixed production setup cost when the buyer places an order. The buyer receives the order from the manufacturer before the beginning of the period. At the end of the period, if demand exceeds stock on hand, the buyer may place a second order from the manufacturer. For such a setting, we develop a generalized newsvendor model to analyze the impact of coordination on the expected profits of the manufacturer and the buyer, on the number of units produced by the manufacturer and on the amount of stock held by the buyer. The model is constructed to focus on coordination issues. Of course, the model developed in this paper represents an abstraction of the real world scenarios under consideration.

Coordinating ordering decisions in distribution channels with deterministic demand and an infinite time horizon have been studied from the viewpoints of production management, marketing channel coordination, and economics. Works in the economic literature (e.g., Oren et al., 1983; Tirole, 1993) mainly study price discrimination due to quantity discounts on vertical channel integration. Research in the production management literature focuses on analyzing the impact of joint ordering and inventory policies for a given quantity discount on minimizing the buyer’s and the supplier’s operating costs (including the purchasing, ordering and inventory holding costs). Studies in the marketing literature focus on the coordination mechanism provided by quantity discounts in the channels of distribution. A generalization of the above two streams of research is provided in Weng, 1995a, Weng, 1995b and examples of recent works on channel coordination include Jeuland and Shugan (1983), Lal and Staelin (1984), and Kohli and Park (1994). Interested readers may also consult the following literature review papers: Munson and Rosenblatt (1998), Benton and Park (1996), and Goyal and Gupta (1989).

This study represents a departure from the existing literature by studying the effect of coordination between the manufacturer and the buyer on the order quantities under a generalized newsvendor model. The model developed is a general one; it can be used to model various managerial scenarios where either all demands have to be satisfied, or any additional demand exceeding stock on hand is satisfied only if the resulting profit is positive, or no additional demand exceeding stock on hand is met.

The paper is organized as follows. Problem descriptions, assumptions, and notations are presented and the general model is developed in Section 2. In Section 3, we develop the coordinated optimal ordering policies and the buyer’s optimal ordering policies without coordination. This is followed in Section 4 by the analysis of the impact of coordination on the expected profits of both parties. The coordination strategy that causes the optimal coordinated policy to prevail is developed. Finally, discussion and concluding remarks in Section 5 close the paper.