{'fraction_non_alphanumeric': 0.02502360717658168, 'fraction_numerical': 0.0, 'mean_word_length': 5.124277456647399, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Long-Term Service Agreement in Electricity Supply Chain with Renewable Energy Penetration

Problem Definition: We study a long-term service agreement (LTSA) between an OEM of conventional power generators and a power plant operator (utility firm) in the electricity supply chain. The OEM offers maintenance based on the LTSA which specifies the service fee and the maintenance interval. The utility firm dynamically chooses among different resources (conventional, renewable, or emergency) to meet energy demand. 
 
Academic/Practical Relevance: Although being widely used in power systems, LTSA has not been studied in the OM literature. Different from traditional supply chain contracts, LTSA contracts on a generator’s long-term production schedule (i.e., usage time and number of starts). A good understanding of LTSA provides guidance on how to design such a complex contract. 
 
Methodology: We use game theory to model the LTSA between the OEM and the utility firm and use dynamic programming to study the utility firm’s power generation decision. 
 
Results: We first characterize that the conventional generator’s optimal operating mode (i.e., on or off) follows a two-threshold policy which shows a hysteresis phenomenon. Then the optimal output from different resources can be obtained by minimizing the utility firm’s cost of the current period. We show that the OEM’s optimal LTSA design on the maintenance interval and service fee can be solved sequentially, and capture the OEM’s tradeoﬀ between the service margin and the usage of conventional generator. 
 
Managerial Implications: We ﬁnd that the OEM does not have incentives to signiﬁcantly reduce the maintenance cost of a generator start, while both OEM and utility firm prefer greater generator flexibility. While overall availability of renewable output is important, renewable source characteristics such as autocorrelation and variation do not have a significant impact on the equilibrium outcomes. By incorporating the number of starts into the contract, LTSA is effective in preventing the utility firm from frequently cycling the equipment.