Exact algorithms for integrated facility location and production planning problems

We consider a class of facility location problems with a time dimension, which requires assigning every customer to a supply facility in each of a finite number of periods. Each facility must meet all assigned customer demand in every period at a minimum cost via its production and inventory decisions. We provide exact branch‐and‐price algorithms for this class of problems and several important variants. The corresponding pricing problem takes the form of an interesting class of production planning and order selection problems. This problem class requires selecting a set of orders that maximizes profit, defined as the revenue from selected orders minus production‐planning‐related costs incurred in fulfilling the selected orders. We provide polynomial‐time dynamic programming algorithms for this class of pricing problems, as well as for generalizations thereof. Computational testing indicates the advantage of our branch‐and‐price algorithm over various approaches that use commercial software packages. These tests also highlight the significant cost savings possible from integrating location with production and inventory decisions and demonstrate that the problem is rather insensitive to forecast errors associated with the demand streams. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Using real options analysis to value reoptimization options in the shifting bottleneck heuristic

The reoptimization procedure within the shifting bottleneck (SB) involves reevaluation of all previously scheduled toolgroup subproblems at each iteration of the SB heuristic. A real options analysis (ROA) model is developed to value the option to reoptimize in the SB heuristic, such that reoptimization only occurs when it is most likely to lead to a schedule with a lower objective function. To date, all ROA models have sought to value options financially (i.e., in terms of monetary value). The ROA model developed in this paper is completely original in that it has absolutely no monetary basis. The ROA methodologies presented are shown to greatly outperform both full and no reoptimization approaches with respect to both computation time and total weighted tardiness. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Requirements planning for modular products

The focus of this paper is on determining the requirements of different component options of a modular end‐product in an uncertain environment. We explicitly model two distinct sources of uncertainty: stochastic end‐product demand and unknown market proportions for the different product options available. Our cost minimizing model focuses on determining the optimal requirements policies for component options that meet a pre‐set service level. We show that simple common‐sense requirements policies are not generally optimal; there is a non‐linear connection between service level and component requirements that is hard to characterize without a detailed analysis. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Economic design of X¯ control charts for two manufacturing process models

Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.     

Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure

Quantity discounts are considered in the context of the single-period inventory model known as “the newsboy problem.” It is argued that the behavioral implications of the all-units discount schedule are more complex and interesting than the literature has suggested. Consideration of this behavior and the use of marginal analysis lead to a new method for solving this problem that is both conceptually simpler and more efficient than the traditional approach. This marginal-cost solution procedure is described graphically, an algorithm is presented, and an example is used to demonstrate that this solution procedure can be extended easily to handle complex discount schedules, such as some combined (simultaneously applied) purchasing and transportation cost discount schedules.     

Nature of renyi's entropy and associated divergence function

Nature of Renyi's entropy and associated divergence function is discussed in terms of concave (convex) and pseudoconcave (pseudoconvex) functions.     

Mexico: a model for success

In Mexico, a 40 year period of political stability and economic advancement, hailed for its high rates of growth in income per capita, rapid urbanization, and impressive gains in indicators of health and education, seemed to come to a halt in the early 1980s. Since the early 1970s, fertility has declined sharply in chronological association with a new population policy and the implementation of a national family planning program. If in 1940 there was no apparent reason for the Mexican state to have much interest in limiting fertility, such was no longer the case by 1970. The General Law of Population that had been passed in 1947 was laced with the expansionist ideology that dominated demographic issues for more that a century; its pro-natalism had been reinforced by health regulations prohibiting the sale and use of contraceptives and by a penal code that made abortion a crime. Between 1970 and 1981 the total fertility rate fell by about 39%. Since 1975, change in contraceptive practice accounts for the bulk of the measured fertility decline. Between 1976 and 1982 there was a 66% increase in contraceptive prevalence. The government's involvement in family planning activities helped to: 1) develop an effective contraceptive distribution system; 2) circulate extensive information, education, and communication publicizing fertility and images of the small family; and 3) mobilize health practitioners in public institutions to counsel and persuade their clients to accept and practice contraception. The emerging debate over population policy in Brazil may well prefigure debates in other Latin American countries; the recent democratization in Brazil is the vocalization of a demand from women's groups and the left for government provided family planning services. Overall, Mexico's willingness to take the long view tackle the birth rate issue head on is likely to remain an exception in Latin America.     

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.