Abstract
The purpose of the paper is to formulate two uncooperative replenishment models with demand and default risk which are the functions of the trade credit period, i.e., a Nash equilibrium model and a supplier-Stackelberg model. Firstly, we present the optimal results of decentralized decision and centralized decision without trade credit. Secondly, we derive the existence and uniqueness conditions of the optimal solutions under the two games, respectively. Moreover, we present a set of theorems and corollary to determine the optimal solutions. Finally, we provide an example and sensitivity analysis to illustrate the proposed strategy and optimal solutions. Sensitivity analysis reveals that the total profits of supply chain under the two games both are better than the results under the centralized decision only if the optimal trade credit period isn’t too short. It also reveals that the size of trade credit period, demand, retailer’s profit and supplier’s profit have strong relationship with the increasing demand coefficient, wholesale price, default risk coefficient and production cost. The major contribution of the paper is that we comprehensively compare between the results of decentralized decision and centralized decision without trade credit, Nash equilibrium and supplier-Stackelberg models with trade credit, and obtain some interesting managerial insights and practical implications.
Highlights
In the past 100 years, a huge of extensions of the traditional Economic Order Quantity (EOQ) model has been proposed by lots of researchers
The main trait of this paper compared to most existing uncooperative inventory model is that the developed model includes the following aspects: (i) Nash equilibrium game and supplier-Stackelberg game; (ii) the results of decentralized decision and centralized decision without trade credit as comparison benchmarks; (iii) the retailer’s capital opportunity cost equal to its opportunity gain; (iv) trade credit period is a decision variable; (v) the demand and default risk both are exponential functions of trade credit period; (vi) lot-for-lot policy; and (vii) the production rate is finite but the replenishment is instantaneous
The major contribution of the paper is that we fully compare between the results of decentralized and centralized decision without trade credit, Nash equilibrium and a supplier-Stackelberg model with trade credit in detail, and obtain some interesting managerial insights and practical implications
Summary
In the past 100 years, a huge of extensions of the traditional Economic Order Quantity (EOQ) model has been proposed by lots of researchers. The International Journal of Production Economics published a special issue “Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris”. Among them, Andriolo et al (2014) and Glock et al (2014) respectively adopted different methodologies to analysis the evolution and main streams of these research emerged from Harris’ seminal lot size during 100 years of history and proposed a new research opportunities for future research, such as, sustainability issue and cash flows Latest works include those by Battini et al (2014), and Marchi et al (2016), among others. One of most important extensions is that incorporating trade credit into the EOQ. It assumes that supplier offers retailer/buyer a permissible delay in payments
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