Joint Control of Emissions Permit Trading and Production Involving Fixed and Variable Transaction Costs

Quan Yuan, Youhua (Frank) Chen, Jian Yang, Yun Zhou

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The use of permit markets to mitigate harmful emissions is on the rise. When participating in such a market, an emitting firm needs to acquire from it permits that cover emissions resulting from production. Thus, it has to simultaneously cope with fluctuating permit prices and random demand, and also juggle between the activities of permit trading and permit-consuming production. We shed light on this complex dynamic control problem, while confronting difficulties brought on by fixed as well as variable transaction costs associated with permit trading. We exploit K-convexity variants that are suitable for two-dimensional control, and achieve the partial characterization of optimal control policies. When the selling of permits is prohibited, we prescribe an (s, S)-type permit purchasing policy. For the more general case involving two-way trading, we find it optimal to carry out trading in a three-interval fashion. Heuristics, including one based on the uncoupling of trading and production activities, are introduced. Their effectiveness has been illustrated in computational studies.

Original languageEnglish (US)
Pages (from-to)1420-1454
Number of pages35
JournalProduction and Operations Management
Issue number8
StatePublished - Aug 2018

All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation


  • (s, S) policy
  • dynamic programming
  • emissions permit trading
  • fixed and variable transaction costs
  • production planning


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