The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

Target selection in lanchester combat: Heterogeneous forces and time-dependent attrition-rate coefficients

We develop solutions to two fire distribution problems for a homogeneous force in Lanchester combat against heterogeneous enemy forces. The combat continues over a period of time with a choice of tactics available to the homogeneous force and subject to change with time. In these idealized combat situations the lethality of each force's fire (as expressed by the Lanchester attrition-rate coefficient) depends upon time. Optimal fire distribution rules are developed through the combination of Lanchester-type equations for combat attrition and deterministic optimal control theory (Pontryagin maximum principle). Additionally, the theory of state variable inequality constraints is used to treat the nonnegativity of force levels. The synthesis of optimal fire distribution policies was facilitated by exploiting special mathematical structures in these problems.     

Finding equivalent transportation formulations for constrained transportation problems

This paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation problems by a linear transformation involving the node constraints and the extra constraints. Our results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables.     

On nash subsets and mobility chains in bimatrix games

This work is concerned with constructing, analyzing, and finding “mobility chains” for bimatrix games, sequences of equilibrium points along which it is possible for the two players to progress, one equilibrium point at a time, to an equilibrium point that is preferred by both players. The relationship between mobility chains and Nash subsets is established, and some properties of maximal Nash subsets are proved.     

Algorithms for minimizing total cost,bottleneck time and bottleneck shipment in transportation problems

We consider the transportation problem of determining nonnegative shipments from a set of m warehouses with given availabilities to a set of n markets with given requirements. Three objectives are defined for each solution: (i) total cost, TC, (ii) bottleneck time, BT (i.e., maximum transportation time for a positive shipment), and (iii) bottleneck shipment, SB (i.e., total shipment over routes with bottleneck time). An algorithm is given for determining all efficient (pareto-optimal or nondominated) (TC, BT) solution pairs. The special case of this algorithm when all the unit cost coefficients are zero is shown to be the same as the algorithms for minimizing BT. provided by Szwarc and Hammer. This algorithm for minimizing BT is shown to be computationally superior. Transportation or assignment problems with m=n=100 average about a second on the UNIVAC 1108 computer (FORTRAN V)) to the threshold algorithm for minimizing BT. The algorithm is then extended to provide not only all the efficient (TC, BT) solution pairs but also, for each such BT, all the efficient (TC, SB) solution pairs. The algorithms are based on the cost operator theory of parametric programming for the transportation problem developed by the authors.     

Determining the most vital link in a flow network

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.     

Some simple victory-prediction conditions for lanchester-type combat between two homogeneous forces with supporting fires

This paper develops new “simple” victory-prediction conditions for a linear Lanchester-type model of combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. These simple victory-prediction conditions involve only the initial conditions of battle and certain assumptions about the nature of temporal variations in the attrition-rate coefficients. They are developed for a fixed-force-ratio-breakpoint battle by studying the force-ratio equation for the linear combat model. An important consideration is shown to be required for developing such simple victory-prediction conditions: victory is not guaranteed in a fixed-force-ratio-breakpoint battle even when the force ratio is always changing to the advantage of one of the combatants. One must specify additional conditions to hold for the cumulative fire effectivenesses of the primary weapon systems in order to develop correct victory-prediction conditions. The inadequacy of previous victory-prediction results is explained by examining (for the linear combat model without the supporting fires) new “exact” victory-prediction conditions, which show that even the range of possible battle outcomes may be significantly different for variable-coefficient and constant-coefficients models.     

A comparison of waiting time approximations in series queueing systems

The determination of steady-state characteristics in systems of tandem queues has been left to computer simulation because of the lack of exact solutions in all but the simplest newtorks. In this paper, several methods developed for approximating the average waiting time in single-server queues are extended to systems of queues in series. Three methods, due to Fraker, Page, and Marchal, are compared along with results gathered through GPSS simulation. Various queueing networks with Erlangian service distributions are investigated.     

An examination of the effects of the criterion functional on optimal fire-support policies

This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantification of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the “approach to contact” of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization problem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular difficulty in one of them. For the same combat dynamics, the splitting of supporting fires between two enemy forces in any optimal policy (i.e. the optimality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an “overall” military advantage or a “local” one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fire-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.