Production Planning Problem of a Two-Level Supply Chain with Production-Time-Dependent Products

This study considers a production planning problem with a two-level supply chain consisting of multiple suppliers and a manufacturing plant. Each supplier that consists of multiple production lines can produce several types of semi-finished products, and the manufacturing plant produces the finished products using the semi-finished products from the suppliers to meet dynamic demands. In the suppliers, different types of semi-finished products can be produced in the same batch, and products in the same batch can only be started simultaneously (at the same time) even if they complete at different times. The purpose of this study is to determine the selection of suppliers and their production lines for the production of semi-finished products for each period of a given planning horizon, and the objective is to minimize total costs associated with the supply chain during the whole planning horizon. To solve this problem, we suggest a mixed integer programming model and a heuristic algorithm. To verify performance of the algorithm, a series of tests are conducted on a number of instances, and the results are presented.

Management strategies for run-of-river hydropower plants: an optimal switching approach

The mathematical theory for optimal switching is by now relatively well developed, but the number of concrete applications of this theoretical framework remains few. In this paper, we bridge parts of this gap by applying optimal switching theory to a conceptual production planning problem related to hydropower. In particular, we study two examples of small run-of-river hydropower plants and provide an outline of how optimal switching can be used to create fully automatic production schemes for these. Along the way, we create a new model for random flow of water based on stochastic differential equations and fit this model to historical data. We benchmark the performance of our model using actual flow data from a small river in Sweden and find that our production scheme lies close to the optimal, within 2 and 5 %, respectively, in a long term investigation of the two plants considered.

The integrated cutting and packing heterogeneous precast beams multiperiod production planning problem

We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the ICP-HPBMPP, as well as a lower bound for its optimal objective function value, which is empirically shown to be closer to the optimal solution value than the bound obtained from the linear relaxation of the model. We also propose a genetic algorithm approach for the ICP-HPBMPP as an alternative solution method. We discuss computational experiments and propose a parameterization for the genetic algorithm using D-optimal experimental design. We observe good performance of the exact approach when solving small-sized instances, although there are difficulties in finding optimal solutions for medium and large-sized problems, or even in finding feasible solutions for large instances. On the other hand, the genetic algorithm is shown to typically find good-quality solutions for large-sized instances within short computing times.