Optimal Solutions of Economic Lot Scheduling Problem with Energy and Power Costs

This paper proposes a new planning method for a cyclic production of many different products with steady demand and variable production rates, which minimises energy consumption while reducing and equalising power demand. The problem is modelled as the Economic Lot Scheduling Problem (elsp), with a common production cycle for all products. This paper shows that the problem can be optimally solved by a general-purpose mathematical programming solver in a short time by reformulating the general non-linear model into a Mixed-Integer Quadratically Constrained Programming (miqcp) model. This way, there is no need to develop a specialised algorithm, which requires a high level of expertise and is very labour-intensive. The proposed approach is also the only method that allows finding optimal solutions for the general case of the common-cycle elsp with variable production rates. For a problem instance known from the literature, the optimal solution ensured a reduction in the power demand cost by 10.7%, and in the total cost by 3.3%. Moreover, experiments proved that production rate lower bounds are critical for the choice of solution.