Designing safety space in a supply chain to handle system‐wide disruptions

In some supply chains serious disruptions are system wide. This happens during periods of severe weather, as when storms cause shuttle tankers serving oil platforms in the North Sea to stop movements of crude oil, barges are frozen in the Mississippi, or all airplanes are grounded after a blizzard. Other notable instances of system‐wide disruption happened after the attack on the World Trade Center when all aircraft were grounded and the natural gas and crude‐oil pipelines were tangled by hurricanes in 2005. We model a situation where shutting down supply facilities is very difficult and expensive because of excessive inventory buildup from an inability to move out the production. We present a planning model that balances the cost of spare capacity versus shutting down production when planning for disruptions. The model uses an assignment model embedded in a simulation. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Integrated capacity,demand, and production planning with subcontracting and overtime options

Models for integrated production and demand planning decisions can serve to improve a producer's ability to effectively match demand requirements with production capabilities. In contexts with price‐sensitive demands, economies of scale in production, and multiple capacity options, such integrated planning problems can quickly become complex. To address these complexities, this paper provides profit‐maximizing production planning models for determining optimal demand and internal production capacity levels under price‐sensitive deterministic demands, with subcontracting and overtime options. The models determine a producer's optimal price, production, inventory, subcontracting, overtime, and internal capacity levels, while accounting for production economies of scale and capacity costs through concave cost functions. We use polyhedral properties and dynamic programming techniques to provide polynomial‐time solution approaches for obtaining an optimal solution for this class of problems when the internal capacity level is time‐invariant. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A comparative study of three tool replacement/operation sequencing strategies in a flexible manufacturing system

This paper studies three tool replacement/operation sequencing strategies for a flexible manufacturing system over a finite time horizon: (1) failure replacement—replace the tool only upon failure, (2) optimal preventive tool replacement for a fixed sequence of operations, and (3) joint scheduling of the optimal preventive tool replacement times and the optimal sequence of operations. Stochastic dynamic decision models are used for strategies 2 and 3. The optimization criterion for strategies 2 and 3 is the minimization of the total expected cost over the finite time horizon. We will show through numerical studies that, with the same amount of information, the total expected costs can be reduced considerably by choosing an optimal strategy. Our conclusion is that in flexible manufacturing, optimal tool replacement and optimal operations sequencing are not separate issues. They should be considered jointly to minimize the expected total cost. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 479–499, 2000     

Optimal stopping problems for differential equations perturbed by a poisson process

We investigate a class of optimal stopping problems for dynamical systems described by one-dimensional differential equations with an additive Poisson disturbance. The rate of the disturbance may depend upon the current state of the system. A dynamic programming equation for the optimal stopping cost is derived along with conditions which must be met at the boundary of the optimal stopping set. These boundary conditions depend upon whether or not the stopping set may be entered by smooth motion.     

Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.     

Economic impact and the notion of compensated procurement

The paper consists essentially of two parts. In the first part a linear economic impact model is presented whose structure is based on subcontracting flows. The structural coefficients are defined in terms of flows per area. The model is derived from two identities that are analogous to the income and expenditure identities of national income accounting. The parameters are prime contracts and when one or several of the prime contracts are changed, the model determines the impacts of such changes on the various regions that have been selected. The impacts can be combined with regional multipliers to derive changes in regional income and regional employment. Fragmentary data for this kind of model have been collected on a one-time basis by DOD in 1965 and some results based on the data are presented. The second part of the paper is concerned with normative economics. A scheme is suggested, called compensated procurement, that outlines how the Department of Defense might employ the impact model in a macroeconomic setting. The basic idea is that a stabilization fund be established to finance an array of potential projects which are contracted for to balance sudden shifts in defense demand. Only short-run stabilization is advocated.     

A tactical warfare simulation program

The Tactical Warfare Simulation Program is a procedure by which the major interactions among opposing military units and terrain features can be treated in a tactical limited warfare situation. It is a critical-area, sequence-of-event model and is programmed in SIM-SCRIPT. In this program a military unit is described by such properties as strength, size, location, velocity, and attrition rates. Some of the events which can occur to a military unit are entering/leaving terrain features, becoming engaged/disengaged with opposing units, retreating, reaching an objective, and breaking. Following a discussion of the general features of the program, a study of a hypothetical war is presented.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

Minimax trees,paths, and cut sets

The notions of minimax paths, trees, and cut sets are defined for undirected graphs; and relationships between these entities are established. Simple solution procedures based on these relationships are presented.