| Economically cutting a bill of material out of stock sheets is a common problem encountered in the metal, leather, glass, electronic, shipbuilding, and lumber industries. This research investigates a part of this problem called the portfolio problem. The portfolio problem can be defined as the determination of the best combination of sheets to stock in inventory in order to minimize material wastage given that the bill of material is random.; Three approaches to the solution of this stochastic optimization problem are examined: stochastic quasigradient methods, simulated annealing, and optimization homotopy. Simulated annealing is modified in order to extend this deterministic procedure to our stochastic problem. A comparative analysis of the effectiveness of each of these three methods is made. In addition, application of optimization homotopy to the simpler assortment problem is made (fixed bill of material).; Finally, at the expense of large amounts of computer time, numerical representations of response surfaces are made and used as a tool in developing some general engineering guidelines for the proper portfolio selection. |
