On the convexity of newsvendor games

This study considers a simple newsvendor situation that consists of n retailers, all selling the same item with common purchasing costs and common selling prices. Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand. The resulting newsvendor games are shown to have non-empty cores in the literature. This study investigates convexity of newsvendor games. We focus our analysis on the class of newsvendor games with independent symmetric unimodal demand distributions after providing several examples outside this class that are not convex. Several interesting subclasses, containing convex games only, are identified. Additionally, we illustrate that these results cannot be extended to all games in this class.Game theory Inventory centralization Newsvendor Convexity

A collaborative decentralized distribution system with demand forecast updates

In this paper, we study inventory pooling coalitions within a decentralized distribution system consisting of a manufacturer, a warehouse (or an integration center), and n retailers. At the time their orders are placed, the retailers know their demand distribution but do not know the exact value of the demand. After certain production and transportation lead time elapses, the orders arrive at the warehouse. During this time, the retailers can update their demand forecasts. We first focus on cooperation among the retailers – the retailers coordinate their initial orders and can reallocate their orders in the warehouse after they receive more information about their demand and update their demand forecasts. We study two types of cooperation: forecast sharing and joint forecasting. By using an example, we illustrate how forecast sharing collaboration might worsen performance, and asymmetric forecasting capabilities of the retailers might harm the cooperation. However, this does not happen if the retailers possess symmetric forecasting capabilities or they cooperate by joint forecasting, and the associated cooperative games have non-empty cores. Finally, we analyze the impact that cooperation and non-cooperation of the retailers has on the manufacturer’s profit. We focus on coordination of the entire supply chain through a three-parameter buyback contract. We show that our three-parameter contract can coordinate the system if the retailers have symmetric margins. Moreover, under such a contract the manufacturer benefits from retailers’ cooperation since he can get a share of improved performance

On the convexity of newsvendor games

This study considers a simple newsvendor situation that consists of n retailers, all selling the same item with common purchasing costs and common selling prices.Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand.The resulting newsvendor games are shown to have non-empty cores in the literature.This study investigates convexity of newsvendor games.We focus our analysis on the class of newsvendor games with independent symmetric unimodal demand distributions after providing several examples outside this class that are not convex.Several interesting subclasses, containing convex games only, are identified.Additionally, we illustrate that these results can not be extended to all games in this class

Cooperation between multiple newsvendors with warehouses

This study considers a supply chain that consists of n retailers, each facing a newsvendor problem, and m warehouses. The retailers are supplied with a single product via some warehouses. In these warehouses, the ordered amounts of goods of these retailers become available after some lead time. At the time that the goods arrive at the warehouses, demand realizations are known by the retailers. The retailers can increase their expected joint profits if they can coordinate their orders and make allocations after demand realization. For this setting, we consider an associated cooperative game between the retailers. We show that this associated cooperative game has a nonempty core. Finally, we introduce a noncooperative game, where the retailers decide on their order quantities individually, and show that the set of payoff vectors resulting from strong Nash equilibria corresponds to the core of the associated cooperative game

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.Inventory Relaxation Stochastic non-stationary demand Mixed integer programming Service level Static-dynamic uncertainty

Cooperative newsvendor games : a review

In this survey, we review some of the main contributions to the cooperative approach of newsvendor situations. We show how newsvendor situations with several retailers can be modeled as a transferable-utility cooperative game and we concentrate on one solution concept: the core. First, we examine the basic model and then we consider several variations that are of interest from a theoretical and an applied viewpoint