Production-location problems with demand considerations

The production-location problem of a profit maximizing firm is considered. A model is developed for a single firm, facing the joint problems of determining the optimal plant location, the optimal input mix, and the optimal plant size. A homothetic production function is used as the model of the production technologies, and the existence of a sequential “separability” between the production, or input mix, problem and the location problem is demonstrated.     

An inventory model with finite-range stochastic lead times

This article considers an inventory model with constant demand and stochastic lead times distributed over a finite range. A generalization of the EOQ formula with backorders is derived and ranges for the decision variables are obtained. The results are illustrated with the case of uniformly distributed lead time.     

On queueing systems with variable service capacities

In some queueing systems the total service capacity utilized at any given time is a variable under the control of a decision maker. Management doctrines are examined which prescribe the actual service capacity as a function of the queue length and the recent history of the system. Steady state probabilities, expected queue lengths and frequencies of change in capacity are evaluated for a wide class of possible control schemes. Optimization procedures are outlined.     

Evaluation of force structures under uncertainty

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade-offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.     

Computation of constrained optimum quantities and reorder points for time-weighted backorder penalties

The purpose of this paper and the accompanying tables is to facilitate the calculation of constrained optimum order quantities and reorder points for an inventory control system where the criterion of optimality is the minimization of expected inventory holding, ordering, and time-weighted backorder costs. The tables provided in the paper allow the identification of the optimal solution when order quantities and/or reorder points are restricted to a set of values which do not include the unconstrained optimal solution.     

Dynamic server assignment policies for assembly‐type queues with flexible servers

We seek dynamic server assignment policies in finite‐capacity queueing systems with flexible and collaborative servers, which involve an assembly and/or a disassembly operation. The objective is to maximize the steady‐state throughput. We completely characterize the optimal policy for a Markovian system with two servers, two feeder stations, and instantaneous assembly and disassembly operations. This optimal policy allocates one server per station unless one of the stations is blocked, in which case both servers work at the unblocked station. For Markovian systems with three stations and instantaneous assembly and/or disassembly operations, we consider similar policies that move a server away from his/her “primary” station only when that station is blocked or starving. We determine the optimal assignment of each server whose primary station is blocked or starving in systems with three stations and zero buffers, by formulating the problem as a Markov decision process. Using this optimal assignment, we develop heuristic policies for systems with three or more stations and positive buffers, and show by means of a numerical study that these policies provide near‐optimal throughput. Furthermore, our numerical study shows that these policies developed for assembly‐type systems also work well in tandem systems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λ_j,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λ_j,k‐number of ∏ K for pairwise relatively prime integers t₁ < t₂ < … < t_q, t₁ ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005