A Two-phase Heuristic for the Two-dimensional Cutting-stock Problem

The two-dimensional cutting-stock problem consists of laying out a specified list of rectangular pieces on rectangular sheets, in such a way as to minimize the number of sheets used. A pattern is a combination of piece widths whose sum does not exceed the sheet's width. We present a new heuristic algorithm for this problem based on an approach with two phases: strategic phase and tactical phase. The first phase takes a global view of the problem and proposes a list of patterns to the second phase, which in turn is in charge of actually laying out these patterns on sheets. The strategic module relaxes the global problem to a one-dimensional cutting-stock problem and solves it using linear programming, while the tactical module is a recursive algorithm based on repeated knapsack operations and other heuristics.     

Nursing care demand prediction based on a decomposed semi-markov population model

The semi-markovian population model introduced by Kao for the planning of progressive care hospitals is adapted to the prediction of nursing care demand at the level of a care unit in a general hospital. Assuming a feedback admission policy which refills the unit as soon as discharges occur, it is shown that the care unit can be decomposed into B independent subsystems corresponding to each of the B beds in the unit.For each bed the semi-Markov model permits the computation of the expected care demand and its variance for each of the seven forthcoming days. The model permits also the prediction of admissions of new patients. A prediction formula can thus be obtained where the expected care demand is expressed as a linear function of the expected number of admissions in the forthcoming days.Finally this methodology is illustrated on real data obtained in the gynaecology department of the Montreal Jewish General Hospital.     

Leader–Follower Dynamic Game of New Product Diffusion

The objective of this paper is to study optimal pricing strategies in a duopoly, under an asymmetric information structure, where the appropriate solution concept is the feedback Stackelberg equilibrium. In order to take into account effects such as imitation (e.g., word of mouth) and saturation, the demand (state equation) is assumed to depend on past cumulative sales, market potential, and both players' prices. We assume also that the unit production cost decreases with cumulative production (learning effects). Each player maximizes his total discounted profit over the planning horizon.The problem is formulated as a two-player discrete-time finite-horizon game. Existence results are first obtained under rather mild conditions. Since the solution of this problem is intractable by analytical methods, we use a numerical approach. Thus, we design a numerical algorithm for the computation of feedback Stackelberg equilibria and use it to obtain strategies in various representative cases. The numerical results presented are intented to give some insights into the optimal pricing strategies in the context of an asymmetrical feedback information structure.