Data File for Capacitated Lot Sizing Problem with Periodic Carbon Emission Constraints and Multiple Resources by E.Koca and G.I. Koksalan

In this paper, we study the single item capacitated lot sizing problem with multiple resources and periodic carbon emission constraints that define an upper bound for the average emission per product produced in any period. The uncapacitated version of this problem was introduced by Absi et al.(2013) and solved in polynomial time. We show that the generalization of the problem considering the resource capacities is NP-Hard, in general, and present important structural properties for the optimal solutions of the problem. We consider the special cases with two resources and under non-speculative costs, construct the piecewise linear total production cost function when the resource capacities, and the emission and cost parameters are time-invariant, and develop a polynomial time dynamic programming algorithm to solve them. Then, we generalize the procedure to construct the total production cost function and the dynamic programming algorithm for the general setting with fixed number of capacitated resources. In our computational experiments, we test our algorithm for problem instances with different characterizations, and compare it with a commercial solver and the dynamic programming algorithm of Koca et al.(2014).