The paper addresses the unit commitment in multi-period combined heat and power (CHP) production planning under the deregulated power market. In CHP plants (units), generation of heat and power follows joint characteristics, which means that production planning must be done in coordination. We introduce in this paper the DP-RSC1 algorithm, which is a variant of the dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units and sequential commitment of units one by one. The time complexity of DP-RSC1 is proportional to the number of generating units in the system, the number of periods over the planning horizon and the time for solving a single-period economic dispatch problem. We have compared the DP-RSC1 algorithm with realistic power plants against the unit decommitment algorithm and the traditional priority listing method. The results show that the DP-RSC1 algorithm gives somewhat more accurate results (0.08-0.5% on average, maximum 10% for the individual sub-case) and executes 3-5 times faster on average than the unit decommitment algorithm. It is not surprising that the solution quality of the DP-RSC1 algorithm is much better than that of the priority listing method.