Fredagen den 3 maj kl. 13.15--14.15 talar prof. Robert W. Grubbström, Institutionen för produktionsekonomi, om Application of the Laplace Transform in Material Requirements Planning.
Abstract: In a number of instances, the Laplace Transform together with Input-Output Analysis has been applied for the sake of formulating a basic theoretical description of Material Requirements Planning (MRP).
The transform approach has a threefold use. On the one hand, it is useful for describing time developments of the relevant production, demand, inventory and stockout properties in a compact way including effects of order flows and lead times. Secondly, the transform also captures stochastic properties by functioning as a generating function, and, thirdly, the transform is easily applied for assessing the resulting cash flows when adopting the Net Present Value (NPV) principle (or the Annuity Stream principle which is a variation of NPV).
Input-Output Analysis, in particular the input matrix, is applied for describing multi-level product structures, which makes the analysis compact and distinct.
A finite horizon is considered. There is a stochastic external demand for products assembled from subordinate items according to product structures described by an input matrix H. Production decisions are allowed to be taken individually as regards their lot-sizes and their timing. A continuous time scale is applied (a bucket-less system). Production decisions concerning amounts and their timing will automatically incorporate safety-production decisions.
External demand is assumed to be a renewal process made up of stochastic unit events separated by independent stochastic time intervals with a given probability density function. As our objective function, we choose a variation of the Net Present Value of the in-payments from final products sold and out-payments associated with costs for set-ups and for production.
Problem: To determine the values of the batch sizes and their timing in order to maximise the Annuity Stream (proportional to the Net Present Value) of the cash flow associated with the process.
Result: Solving the problem will determine the optimal safety stock levels.
Steps: 1. Determine the objective function's dependence on decision variables.
2. Determine the optimisation conditions. This results in expressions with contour integrals in the complex plane.
3. Locate where the poles are and evaluate the residues at these poles. 4. Optimise.
5. Study the dependence of parameter values on the results.
Outside of this problem, two separate issues will be addressed briefly, namely (i) a finite term expression for the Bernoulli Numbers, and (ii) some preliminary ideas for studying linear programming structures from a geometrical point of departure (''Vertex Analysis''). Onsdagen den 15 maj kl. 13.15--14.15 talar prof. Stephen J. Gardiner, University College, Dublin, om Harmonic Approximation and the Dirichlet Problem.
Lokal: MAI:s seminarierum
Lars Inge Hedberg