ResearchFields of Research
Production Planning

Production Planning

In dynamic lot-sizing, the number of units of one product manufactured without interruption must be determined such that the total costs consisting of setup and holding costs are minimized. Demand varys over time. Scarce capacities and incomplete information on demand complicate the planning situation.


Exemplary production plan determined with the multi-stage approach

Stochastic capacitated lot sizing aims at determining optimal production quantities for products to be produced without interruption on a single machine, when a setup procedure is necessary to prepare for the production, which is costly and/or takes some time and thereby reduces the capacity available for production. The objective is the minimization of total costs for setup activities, inventory holding and overcapacity. For practical applications it is crucial to consider several parameters as uncertain. In many cases the future demand is not known with certainty. In those cases the demand is predicted using forecasting methods to determine the parameters of the distribution of expected demand. In those cases a planning algorithm which allows some flexibility to adjust the production plans when unexpected demand realizations are observed is beneficial, while also a certain amount of stability is necessary to avoid nervousness in the production system. Another relevant aspect for practical application is the reduction of variability of the distribution of the objective function value, which can be achieved by applying methods from risk averse optimization.


Due to the long-term planning horizon of decisions regarding the design of supply networks, decisions are based on uncertain information, e.g., demand information. The robust supply network planning seeks a network that yields a satisfying solution for the decision maker, regardless of the realization of the uncertain parameters. Therefore, uncertainties need to be considered in mathematical models for supply network planning and the induced financial risk has to be accounted for in the objective function. Furthermore, adaptions of the network design to possible changes in the environment of a company should be incorporated. Such changes could include spatial shift in demand or in the cost structure. To enable a fast adaption, the concept of relocatable modular capacities is used. The production capacity of a facility is then split into modular capacities that can easily be shifted between production facilities. A robust plan for the purchase, relocation and selling of these modular capacities is necessary.