Urban district heating and cooling (DHC) systems operate large freezers, 
heat exchangers, and boilers to supply hot and cold water, steam etc. stably 
and economically, based on customers demand. 
We formulate an operation-planning problem as a nonlinear integer programming problem 
for an actual DHC plant.
To reflect actual decision making appropriately, we incorporate  contract-violation penalties 
into the running cost consisting of fuel and arrangements expenses. 
Since a yearly operation plan is necessary for checking whether 
the minimum gas consumption contract is fulfilled or not, we need to solve 
long-term operation-planning problems. 
To solve long-term operation-planning problems fast 
and approximately, we propose a decomposition approach using coarse 
(monthly) approximate operation-planning problems.