Multilevel Lot-Sizing with Inventory Bounds

We consider a single-item multilevel lot-sizing problem with a serial structure where one of the levels has an inventory capacity (the bottleneck level). We propose a novel dynamic programming algorithm combining Zangwill’s approach for the uncapacitated problem and the basis-path approach for the production capacitated problem. Under reasonable assumptions on the cost parameters the time complexity of the algorithm is O(LT6) with L the number of levels in the supply chain and T the length of the planning horizon. Computational tests show that our algorithm is significantly faster than the commercial solver CPLEX applied to a standard formulation and can solve reasonably sized instances up to 48 periods and 12 levels in a few minutes.</p

Algorithms for single-item lot-sizing problems with constant batch size

The main result of this paper is an O(n(3)) algorithm for the single-item lot-sizing problem with constant batch size and backlogging. We consider a general number of installable batches, i.e., in each time period t we may produce up to m, batches, where the m, are given and time-dependent. This generalizes earlier results as we consider backlogging and a general number of maximum batches. We also give faster algorithms for three special cases of this general problem. When backlogging is not allowed and the costs satisfy the Wagner-Whitin property, the problem is solvable in O(n(2)log n) time. When the production in each period is required to be either zero or equal to the installed capacity, it is possible to solve the problem with and without backlogging in O(n(2)) and O(n log n) time, respectively

Green Lot-Sizing

The lot-sizing problem concerns a manufacturer that needs to solve a production planning problem. The producer must decide at which points in time to set up a production process, and when he/she does, how much to produce. There is a trade-off bet