Minimizing quality control costs for laboratory instruments using information delays

This paper proposes the use of a cost-based statistical process control system for monitoring the quality of an unreliable analytical machine. In this environment the accuracy of the process cannot be determined by inspecting the output, but must be verified by analyzing standards of known values. The results demonstrate that a significant cost savings can be obtained if analytical results are placed in a “buffer” and their release delayed until the accuracy of the test can be assured. Results suggest the approach not only dramatically improves the quality of results reported but also significantly reduces the expected total cost of testing. © 1996 John Wiley & Sons, Inc.     

Algorithms for the constrained maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph (MCG) problem is to find a connected subgraph with R vertices that maximizes the sum of the weights. The MCG problem is strongly NP-complete, and we study a special case of it: the constrained MCG (CMCG) problem, which is the MCG problem with a constraint of having a predetermined vertex included in the solution. We first show that the Steiner tree problem is a special case of the CMCG problem. Then we present three optimization algorithms for the CMCG problem. The first two algorithms deal with special graphs (tree and layered graphs) and employ different dynamic programming techniques, solving the CMCG problem in polynomial times. The third one deals with a general graph and uses a variant of the Balas additive method with an imbedded connectivity test and a pruning method. We also present a heuristic algorithm for the CMCG problem with a general graph and its bound analysis. We combine the two algorithms, heuristic and optimization, and present a practical solution method to the CMCG problem. Computational results are reported and future research issues are discussed. © 1996 John Wiley & Sons, Inc.     

The maximum collection problem with time-dependent rewards

We consider a routing problem where the objective is to maximize the sum of the rewards collected at the nodes visited. Node rewards are decreasing linear functions of time. Time is spent when traveling between pairs of nodes, and while visiting the nodes. We propose a penalty-based greedy (heuristic) algorithm and a branch-and-bound (optimal) algorithm for this problem. The heuristic is very effective in obtaining good solutions. We can solve problems with up to 20 nodes optimally on a microcomputer using the branch-and-bound algorithm. We report our computational experience with this problem. © 1996 John Wiley & Sons, Inc.     

Note: A local-search heuristic for large set-covering problems

In this note we describe a local-search heuristic (LSH) for large non-unicost set-covering problems (SCPs). The new heuristic is based on the simulated annealing algorithm and uses an improvement routine designed to provide low-cost solutions within a reasonable amount of CPU time. The solution costs associated with the LSH compared very favorably to the best previously published solution costs for 20 large SCPs taken from the literature. In particular, the LSH yielded new benchmark solutions for 17 of the 20 test problems. We also report that, for SCPs where column cost is correlated with column coverage, the new heuristic provides solution costs competitive with previously published results for comparable problems. © 1995 John Wiley & Sons, Inc.     

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.     

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.     

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.