Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work

We consider the problem of scheduling n independent and simultaneously available jobs without preemption on a single machine, where the machine has a fixed maintenance activity. The objective is to find the optimal job sequence to minimize the total amount of late work, where the late work of a job is the amount of processing of the job that is performed after its due date. We first discuss the approximability of the problem. We then develop two pseudo‐polynomial dynamic programming algorithms and a fully polynomial‐time approximation scheme for the problem. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 172–183, 2016     

The dynamic transshipment problem

We investigate the strategy of transshipments in a dynamic deterministic demand environment over a finite planning horizon. This is the first time that transshipments are examined in a dynamic or deterministic setting. We consider a system of two locations which replenish their stock from a single supplier, and where transshipments between the locations are possible. Our model includes fixed (possibly joint) and variable replenishment costs, fixed and variable transshipment costs, as well as holding costs for each location and transshipment costs between locations. The problem is to determine how much to replenish and how much to transship each period; thus this work can be viewed as a synthesis of transshipment problems in a static stochastic setting and multilocation dynamic deterministic lot sizing problems. We provide interesting structural properties of optimal policies which enhance our understanding of the important issues which motivate transshipments and allow us to develop an efficient polynomial time algorithm for obtaining the optimal strategy. By exploring the reasons for using transshipments, we enable practitioners to envision the sources of savings from using this strategy and therefore motivate them to incorporate it into their replenishment strategies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:386–408, 2001     

Lateral stock transshipments in a two‐location inventory system with fixed and joint replenishment costs

We address the problem of inventory management in a two‐location inventory system, in which the transshipments are carried out as means of emergency or alternative supply after demand has been realized. This model differs from previous ones as regards its replenishment costs structure, in which nonnegligible fixed replenishment costs and a joint replenishment cost are considered. The single period planning horizon is analyzed, with the form and several properties of the optimal replenishment and transshipment policies developed, discussed and illustrated. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 525–547, 1999     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

An optimal critical level policy for inventory systems with two demand classes

Traditional inventory systems treat all demands of a given item equally. This approach is optimal if the penalty costs of all customers are the same, but it is not optimal if the penalty costs are different for different customer classes. Then, demands of customers with high penalty costs must be filled before demands of customers with low penalty costs. A commonly used inventory policy for dealing with demands with different penalty costs is the critical level inventory policy. Under this policy demands with low penalty costs are filled as long as inventory is above a certain critical level. If the inventory reaches the critical level, only demands with high penalty costs are filled and demands with low penalty costs are backordered. In this article, we consider a critical level policy for a periodic review inventory system with two demand classes. Because traditional approaches cannot be used to find the optimal parameters of the policy, we use a multidimensional Markov chain to model the inventory system. We use a sample path approach to prove several properties of this inventory system. Although the cost function is not convex, we can build on these properties to develop an optimization approach that finds the optimal solution. We also present some numerical results. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

An algorithm for the discrete bilevel programming problem

The bilevel programming problem (BLPP) is an example of a two-stage, noncooperative game in which the first player can influence but not control the actions of the second. This article addresses the linear formulation and presents a new algorithm for solving the zero-one case. We begin by converting the leader's objective function into a parameterized constraint, and then attempt to solve the resultant problem. This produces a candidate solution that is used to find a point in the BLPP feasible reagion. Incremental improvements are sought, which ultimately lead to a global optimum. An example is presented to highlight the computations and to demonstrate some basic characteristics of the solution. Computational experience indicates that the algorithm is capable of solving problems with up to 50 variables in a reasonable amount of time.     

Some distributions arising as a consequence of errors in inspection

In this article, the authors survey and consolidate their investigations during the years 1980-1983 dealing with consequences of errors in inspection sampling models. Some indication of the current and future research is given.     

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.