Optimal Job Scheduling with Day-ahead Price and Random Local Distributed Generation: A Two-stage Robust Approach

In this paper, we consider a job scheduling problem with random local generation, in which some jobs must be scheduled day-ahead while the others can be scheduled in a real time fashion. To capture the randomness of the local distributed generation, we develop a two-stage robust optimization model by assuming an uncertainty set without probability information. Given that the problem is challenging, a nested primal cut algorithm is implemented to exactly solve it. A preliminary computational study, along with management insights, is presented to show the effectiveness of the proposed model. NOMENCLATURE Indices n Time period, n = 0, ..., N − 1 i Jobs, i = 0, ..., I − 1 k Working mode, k = 0, ....,K − 1 t Segments of job, t = 0, ..., Lik − 1 Parameters C n Base electricity price at time n C n Non-base electricity price at time n Ai Earliest start time for job i Bi Due time for job i P n Local generation at time period n Lik Length of job i in mode k Dikt Workload of job i in mode k at segment t P n Consumption limit at base price at time n Ri Whether job i is interruptible or not Decision variables θiktn Binary variable, 1 if the segment t in mode k of job i is assigned to period n yik Binary variable, 1 if job i runs in mode k xi Integer variable, start time of job i zi Integer variable, completion time of job i fn The consumption at period n pin The consumption of job i at period n w n The billed consumption at base price at time n w n The billed consumption at extra price at time n