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The paper deals with a single machine scheduling problem with job processing times dependent on continuously-divisible resource, e.g. gas, power, energy, raw materials, catalyzer, financial outlay. Ready and delivery times are also given for each job. The problem is to find a schedule of jobs and resource allocation that minimize the time by which all jobs are delivered. Genetic approach, using some proved problem properties is constructed to solve the problem being strongly NP-hard. Analysis of some computational experiment and conclusion remarks are also given.