# A Coordinated Supply Contract for a Two-Echelon Supply Chain Considering Learning Effects
## 6 Conclusions  
The reduction in production costs due to learning effects is a widely observed phenomenon across various industries. However, the majority of existing supply contracts are based on static production costs, thus missing out on the potential benefits derived from learning effects within the supply chain. This paper has explored a two-echelon supply chain, taking into account the impact of the learning effects. We have introduced a coordinated supply contract where learning effects are integrated into the contract-building process. Our findings reveal that the proposed contract with the learning effects can generate additional profits for both the manufacturer and the retailer compared to the existing coordinated contracts with static production costs. Furthermore, our study addresses the complexities arising from diverse bargaining powers among supply chain members, illustrating how contract parameters are determined for different profit-distribution cases. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Wholesale** & \
\begin{tabular}{c} **Revenue-Sharing** \\ **without LC** \\ \end{tabular} &
\begin{tabular}{c} **Revenue-Sharing** \\ **with LC** \\ \end{tabular} \\ \hline \(Q^{*}\) & 180 & 220 & 263 \\ \(w\) & 40 & 22.17 & 13.79 \\ \(\phi\) & - & 0.6739 & 0.5101 \\ \(\pi_{r}\) & 2800 & 2922 & 3053 \\ \(\pi_{m}\) & 1800 & 1878 & 1958 \\ \(\pi_{c}\) & 4600 & 4800 & 5011 \\ \hline \hline \end{tabular} \(Q^{*}\): the optimal order quantity when a set of \(w\) and \(\phi\) is given.  
\end{table} 
Table 2: The optimal solution of wholesale contract and revenue-sharing contracts with and without LC effects. The results reveal that the new supply contract with learning effects can accommodate any profit distribution structure through the appropriate manipulation of contract parameters. The current study is subject to several limitations, which pave the way for potential future research avenues:  
* The proposed contract is based on the log-linear learning-curve model. Further research is needed to explore the implications of other learning-curve models, as various alternative models also exist;
* Our study only considers risk-neutral supply-chain participants. Investigating risk-averse and risk-seeking participants would be an interesting research avenue;
* While we examine revenue-sharing contracts to coordinate the supply chain under learning-curve effects, exploring other contract types like option contracts and buyback contracts with learning effects is warranted;
* We solely consider learning effects, neglecting forgetting effects. Future research incorporating both learning and forgetting effects would provide a more comprehensive understanding of production efficiencies over time;
* This study focuses on the two-echelon supply-chain structure. Investigating the impact of the learning effects on various supply-chain structures, especially those involving multiple echelons or complex network relationships, could provide deeper insights into the applicability of coordination strategies across different supply-chain models;
* Further analyses could also be conducted, incorporating psychological factors such as retailers' overconfidence in supply-chain decisions for enhanced supply-chain coordination. In conclusion, our study offers valuable insights into the impact of learning effects on supply-chain efficiency and provides practical implications for supply-chain practitioners. Addressing the identified limitations in future research endeavors would contribute to advancing the field of supply-chain management. Conceptualization, Z.-J.T. and P.-H.K. ; methodology, Z.-J.T. and P.-H.K. ; software, Z.-J.T. ; validation, Z.-J.T. and P.-H.K. ; formal analysis, Z.-J.T. ; resources, P.-H.K. ; data curation, Z.-J.T. ; writing--original draft preparation, Z.-J.T. ; writing--review and editing, Z.-J.T. and P.-H.K. ; supervision, P.-H.K. ; funding acquisition, P.-H.K. All authors have read and agreed to the published version of the manuscript.