# A Coordinated Supply Contract for a Two-Echelon Supply Chain Considering Learning Effects
## 2 Literature Review
### The Application of Learning Effect to Supply-Chain Management
#### 2.2.2 Supplier Selection and Outsourcing
The existing literature has emphasized the significant role of learning effects in supply-chain management and production decision making, investigating the implications of these effects on supplier selection, procurement strategies, outsourcing decisions, production and scheduling decisions, and pricing strategies. However, few studies exist on coordinated supply-contract-design models in situations where LC effects exist. [PERSON] and [PERSON] [5] investigate a supplier-retailer supply chain where the retailer's promotional efforts affect the sales amount, and sales-learning effects exist on the retailer side. They present a model featuring the promotion costs shared between the supplier and retailer while considering the time-based sales-learning effect. It is demonstrated that the promotion-cost-sharing strategy increases profits for all parties, leading to channel coordination. However, their study pertains to sales costs, not the production costs that are the focus of our study. [PERSON] et al. [3] address channel coordination problems for a two-period supply chain under learning effects. They examine the impact of the learning rate on the pricing strategies of the channel members, on the manufacturer's production decisions, and on the retailer's procurement decisions. They demonstrate that the double marginalization problem becomes more severe as the learning rate increases. They present a coordinated contract scheme by using the concept of revenue sharing within each period. They assume that learning effects on production costs occur only between two periods and not within a period. This study addresses the research gap by incorporating the learning effect in developing supply contracts. We address channel coordination contracts in supply chain situations where production costs decrease as production volume increases. Specifically, we aim to provide a coordinated supply contract scheme for a two-stage supply chain under LC effects. The supply chain under consideration consists of two independent parties, a single manufacturer, and a single retailer. It is assumed that the manufacturer acts as a Stackelberg game leader who takes the first move by designing and offering the contract. The contract is designed in a way that the retailer orders a quantity amount that aligns with the globally optimal solution. Our work differs from the existing literature in three aspects:  
1. We investigate the coordination of supply contracts by integrating the learning effect in revenue-sharing contracts. By integrating the learning effect into the design of supply contracts, our aim is to pinpoint strategies that enhance the profitability of individual stakeholders while also bolstering the overall profitability of the entire supply chain;
2. We consider the bargaining power between the manufacturer and the retailer in contract-building processes. This consideration is essential in understanding how the distribution of profits is affected by the negotiation strength of each party, further enhancing the real-world applicability of our findings;
3. We use a numerical method, Newton-Raphson method, to find the optimal order quantity in the system with learning-curve effects. We will demonstrate that this approach is a simple and efficient solution method for the problem in this study.