Scheduling multiple products on parallel machines with setup costs

We consider a class of production scheduling models with m identical machines in parallel and k different product types. It takes a time p_i to produce one unit of product type i on any one of the machines. There is a demand stream for product type i consisting of n_i units with each unit having a given due date. Before a machine starts with the production of a batch of products of type i a setup cost c is incurred. We consider several different objective functions. Each one of the objective functions has three components, namely a total setup cost, a total earliness cost, and a total tardiness cost. In our class of problems we find a relatively large number of problems that can be solved either in polynomial time or in pseudo‐polynomial time. The polynomiality or pseudo‐polynomiality is achieved under certain special conditions that may be of practical interest; for example, a regularity pattern in the string of due dates combined with earliness and tardiness costs that are similar for different types of products. The class of models we consider includes as special cases discrete counterparts of a number of inventory models that have been considered in the literature before, e.g., Wagner and Whitin (Manage Sci 5 (1958), 89–96) and Zangwill (Oper Res 14 (1966), 486–507; Manage Sci 15 (1969), 506–527). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.     

Israel's Northern eyes and shield: The strategic value of the Golan Heights revisited

According to common wisdom, the Golan provides Israel with an ideal platform for its warning stations as well as the best available defense line against a massive Syrian ground attack. Challenging this belief, this article compares the present situation with an alternative defined by (a) a complete Israeli withdrawal from the Golan, (b) a complete demilitarization of the evacuated territory, and (c) considerable limitations on Syrian military presence in the area between the Golan and Damascus. The article reaches two conclusions. First, that a combination of means, primarily airborne and space‐based platforms, can effectively answer Israel's northern intelligence needs. Second, the security arrangements set above, combined with recent revolutionary military technologies and its relative advantage in this domain, offer Israel an effective ‐ in some respects even a better ‐ alternative, to the present defense line.     

Scheduling parallel machines with inclusive processing set restrictions

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Factors that affect the optimal amount of central control in complex systems

Whereas much of the previous research in complex systems has focused on emergent properties resulting from self‐organization of the individual agents that make up the system, this article studies one vital role of central organization. In particular, four factors are conjectured to be key in determining the optimal amount of central control. To validate this hypothesis, these factors are represented as controllable parameters in a mathematical model. For different combinations of parameter values, the optimal amount of central control is found, either analytically or by computer simulation. The model is shown to provide results that match well with the level of control found across a broad spectrum of specific complex systems. This model also provides general guidelines as to how combinations of these factors affect the desirable level of control and specific guidelines for selecting and evaluating leaders. These results indicate that all of these factors, though not exhaustive, should be considered carefully when attempting to determine the amount of control that is best for a system. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Special Operators: A Key Ingredient for Successful Peacekeeping Operations Management

As an integral component of the Military Observer Mission Ecuador and Peru (MOMEP), 1995-99, Special Operations Forces (SOF) performed as a true confidence-building measure (CBM). They succeeded in changing the behaviour of states, helping to resolve a longstanding conflict. MOMEP consequently serves as an example of risk management and reduction measures that insure regional stability. Further, it is an example of a regional multi-national military peacekeeping effort (PKO), conducted by conventional forces from various nations with influence and guidance from SOF, that succeeded without the reliance upon the United Nations.     

Multiple subset sum with inclusive assignment set restrictions

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001