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.     

Optimal refueling strategies for a mixed-vehicle fleet

The problem treated here involves a mixed fleet of vehicles comprising two types of vehicles: K₁ tanker-type vehicles capable of refueling themselves and other vehicles, and K₂ nontanker vehicles incapable of refueling. The two groups of vehicles have different fuel capacities as well as different fuel consumption rates. The problem is to find the tanker refueling sequence that maximizes the range attainable for the K₂ nontankers. A tanker refueling sequence is a partition of the tankers into m subsets (2 ≤ m ≤ K₁). A given sequence of the partition provides a realization of the number of tankers participating in each successive refueling operation. The problem is first formulated as a nonlinear mixed-integer program and reduced to a linear program for a fixed sequence which may be solved by a simple recursive procedure. It is proven that a “unit refueling sequence” composed of one tanker refueling at each of K₁ refueling operations is optimal. In addition, the problem of designing the “minimum fleet” (minimum number of tankers) required for a given set of K₂ nontankers to attain maximal range is resolved. Also studied are extensions to the problem with a constraint on the number of refueling operations, different nontanker recovery base geometry, and refueling on the return trip.     

Three-machine flowshop stochastic scheduling to minimize distribution of schedule length

This article studies a special case of stochastic three-machine, permutation flowshop scheduling. It is proved that a sequence where processing times on the first and third machines are in a monotone nondecreasing and nonincreasing order of the likelihood ratio, respectively, and on the second machine are equally distributed, minimizes distribution of schedule length.     

Flowshop/no-idle or no-wait scheduling to minimize the sum of completion times

This paper deals with flowshop/sum of completion times scheduling problems, working under a “no-idle” or a “no-wait” constraint, the former prescribes for the machines to work continuously without idle intervals and the latter for the jobs to be processed continuously without waiting times between consecutive machines. Under either of the constraints the problem is unary NP-Complete for two machines. We prove some properties of the optimal schedule for n/2/F, no-idle/σC_i. For n/m/P, no-idle/σC_i, and n/m/P, no-wait/σC_i, with an increasing or decreasing series of dominating machines, we prove theorems that are the basis for polynomial bounded algorithms. All theorems are demonstrated numerically.     

Probabilistic ideas in heuristic algorithms for solving some scheduling problems

Heuristic algorithms for positioning a maximal number of independent units and constructing a schedule with minimal fleet size are proposed. These algorithms consist of two stages: defining the “leading” job and finding an optimal position for it. Decisions on both stages use some special criteria which have a probabilistic interpretation. Some experimental data are given.     

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 dynamic model for component testing

We consider the component testing problem of a system where the main feature is that the component failure rates are not constant parameters, but they change in a dynamic fashion with respect to time. More precisely, each component has a piecewise-constant failure-rate function such that the lifetime distribution is exponential with a constant rate over local intervals of time within the overall mission time. There are several such intervals, and the rates change dynamically from one interval to another. We note that these lifetime distributions can also be used in a more general setting to approximate arbitrary lifetime distributions. The optimal component testing problem is formulated as a semi-infinite linear program. We present an algorithmic procedure to compute optimal test times based on the column-generation technique and illustrate it with a numerical example. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 187–197, 1997     

Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

Discretization of the continuous ambush game

This article further considers the two‐person continuous ambush game introduced by Ruckle. This article extends the work of Ruckle, Baston and Bostock, and Lee by considering the game for a general number of barriers. By supplanting optimal strategies from a discretized version of the game, we show that there always exists a value for the game, which, furthermore, can be found using linear programming techniques. Further to this, we show that the discrete ambush game considered by Garnaev has the same value as a continuous game, allowing many new results to be obtained in both games. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 515–529, 2003     

Initiatives in Africa

Since the 1st oil crisis in 1973, the economies of sub-Saharan Africa have barely kept pace with their burgeoning populations. Women in Sub-Saharan Africa give birth more often than women in any other region of the world, with an average of more than 6.5 live births each. The region's natural increase average 2.5% a year in the 1960s, 2.7% in the 1970s, and in the mid-1980s, it is 3.1% per annum--a rate that will double the regions population in 22 years. National leaders in Sub-Saharan Africa were slow to consider population policy as a key component of the social and economic development effort. The neglect of population issues is reflected in the limited scope of public or private family planning programs in the sub-continent. Donor countries and institutions play an important role in developing the information base by providing technical training to government staff, supporting research, and disseminating information to a broad spectrum of political actors. Some examples of policy reconsiderations in Nigeria, Zambia, Liberia, and Niger are given. These countries are starting to give active consideration to population policies to reduce fertility and high rates of population growth by expanding family planning services, raising the age of marriage, improving the status of women, providing family-life education, and incorporating economic incentives for smaller families into the provision of social services. The highly centralized nature of African governments dictates that the acquiescence of the governmental elite must be obtained before any policy can take hold. Overall, high population growth rates in combination with a stagnating social and economic development effort throughout the region have provided the catalyst for a new look at Sub-Saharan Africa population policy. The ability of African nations to implement policies that reduce fertility is more open to question; no African nation has as yet done so, and the socioeconomics factors contributing to high fertility remain strong.