End effects in capacity expansion models with finite horizons

Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual-equilibrium method” for ameliorating possible distortions. Although the dual-equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal-equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.     

The procurement problem: An integer programming problem well suited to a solution using duality

A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.     

Joint pricing and ordering policy for exponentially decaying inventory with known demand

This paper is concerned with the problem of simultaneously setting price and production levels for an exponentially decaying product. Such products suffer a loss in utility which is proportional to the total quantity of stock on hand. A continuous review, deterministic demand model is considered. The optimal ordering decision quantity is derived and its sensitivity to changes in perishability and product price is considered. The joint ordering pricing decision is also computed and consideration of parametric changes of these decisions indicates a non-monotonic response for optimal price to changes in product decay. Issues of market entry and extensions to a model with shortages are also analyzed.     

AN ALGORITHM FOR THE SEGREGATED STORAGE PROBLEM

The segregated storage problem involves the optimal distribution of products among compartments with the restriction that only one product may be stored in each compartment. The storage capacity of each compartment, the storage demand for each product, and the linear cost of storing one unit of a product in a given compartment are specified. The problem is reformulated as a large set-packing problem, and a column generation scheme is devised to solve the associated linear programming problem. In case of fractional solutions, a branch and bound procedure is utilized. Computational results are presented.     

Some comparative & design aspects of fixed cycle production systems

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N-1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade-off between increasing the reliability of the line versus adding a buffer stock.     

On the economic application of airlift to product distribution and its impact on inventory levels

In many resupply situations, the decisionmaker has the option of “purchasing” faster replenishment leadtimes. For example, a premium may be paid for delivery by parcel post rather than slower but less expensive delivery by railway express. It may be economically advantageous to pay shipment premiums for faster leadtimes when considering the possible cost reductions in pipeline (on-order) inventory and safety stock levels. This paper develops a decision rule which, for any given item, will indicate whether it is economically advantageous to purchase a faster leadtime. The general methodology is then applied to a peacetime military resupply operation involving several million items, each requiring a decision as to whether the item should be shipped by air or sea.