Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers

Luis A. Guardiola, Ana Meca, Justo Puerto

TL;DR

The paper develops a cooperative game-theoretic framework for supply chains with multiple retailers and multiple bounded-capacity suppliers. By formulating the problem as multi-retailer-multi-supplier (MRS) games, it proves that grand coalitions are beneficial, the coalitional value is positive and superadditive, and the core is nonempty (balanced). It introduces the Supplier Compensation (SC) allocation, a stable core allocation that compensates suppliers for cooperation, and provides a uniqueness result under five stability properties; it also analyzes the unbounded production case, showing when the SC-allocation reduces to the altruistic allocation or requires a modified form to compensate a single optimal supplier. These results yield stable, profit-sharing rules applicable to decentralized supply chains with capacity constraints and offer practical guidance for designing collaboration among retailers and suppliers. The work extends prior single-supplier results to the multi-supplier setting and highlights how capacity constraints influence coalition formation and fair profit allocation.

Abstract

The coordination of actions and the allocation of profit in supply chains under decentralized control play an important role in improving the profits of retailers and suppliers in the chain. We focus on supply chains under decentralized control in which noncompeting retailers can order from multiple suppliers to replenish their stocks. Suppliers' production capacity is bounded. The goal of the firms in the chain is to maximize their individual profits. As the outcome under decentralized control is inefficient, coordination of actions between cooperating agents can improve individual profits. Cooperative game theory is used to analyze cooperation between agents. We define multi-retailer-supplier games and show that agents can always achieve together an optimal profit and they have incentives to cooperate and to form the grand coalition. Moreover, we show that there always exist stable allocations of the total profit among the firms upon which no coalition can improve. Then we propose and characterize a stable allocation of the total surplus induced by cooperation.

Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers

TL;DR

The paper develops a cooperative game-theoretic framework for supply chains with multiple retailers and multiple bounded-capacity suppliers. By formulating the problem as multi-retailer-multi-supplier (MRS) games, it proves that grand coalitions are beneficial, the coalitional value is positive and superadditive, and the core is nonempty (balanced). It introduces the Supplier Compensation (SC) allocation, a stable core allocation that compensates suppliers for cooperation, and provides a uniqueness result under five stability properties; it also analyzes the unbounded production case, showing when the SC-allocation reduces to the altruistic allocation or requires a modified form to compensate a single optimal supplier. These results yield stable, profit-sharing rules applicable to decentralized supply chains with capacity constraints and offer practical guidance for designing collaboration among retailers and suppliers. The work extends prior single-supplier results to the multi-supplier setting and highlights how capacity constraints influence coalition formation and fair profit allocation.

Abstract

The coordination of actions and the allocation of profit in supply chains under decentralized control play an important role in improving the profits of retailers and suppliers in the chain. We focus on supply chains under decentralized control in which noncompeting retailers can order from multiple suppliers to replenish their stocks. Suppliers' production capacity is bounded. The goal of the firms in the chain is to maximize their individual profits. As the outcome under decentralized control is inefficient, coordination of actions between cooperating agents can improve individual profits. Cooperative game theory is used to analyze cooperation between agents. We define multi-retailer-supplier games and show that agents can always achieve together an optimal profit and they have incentives to cooperate and to form the grand coalition. Moreover, we show that there always exist stable allocations of the total profit among the firms upon which no coalition can improve. Then we propose and characterize a stable allocation of the total surplus induced by cooperation.
Paper Structure (7 sections, 10 theorems, 37 equations, 3 tables)

This paper contains 7 sections, 10 theorems, 37 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problems with a retailer and multiple suppliers
  4. Cooperation in problems with multiple retailers and suppliers
  5. An allocation rule that compensates suppliers
  6. MRS-games with unbounded production
  7. Concluding remarks

Key Result

Lemma 4.1

Let $(N,M,W,C,P,\overline{Q})$ be a MRS-situation, and $i\in R\subseteq N$. Then, for all $S,T\subseteq M$ and such that $T\subseteq S:$

Theorems & Definitions (22)

  • Lemma 4.1
  • Definition 4.2
  • Proposition 4.3
  • Lemma 4.4
  • Theorem 4.5
  • Example 4.6
  • Theorem 5.1
  • Proposition 5.2
  • Example 5.3
  • Example 5.4
  • ...and 12 more