Minimizing flow time on a single machine with job classes and setup times

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.     

Heuristic scheduling of resource-constrained projects with cash flows

Resource-constrained project scheduling with cash flows occurs in many settings, ranging from research and development to commercial and residential construction. Although efforts have been made to develop efficient optimal procedures to maximize the net present value of cash flows for resource-constrained projects, the inherent intractability of the problem has led to the development of a variety of heuristic methods to aid in the development of near-optimal schedules for large projects. This research focuses on the use of insights gained from the solution of a relaxed optimization model in developing heuristic procedures to schedule projects with multiple constrained resources. It is shown that a heuristic procedure with embedded priority rules that uses information from the revised solution of a relaxed optimization model increases project net present value. The heuristic procedure and nine different embedded priority rules are tested in a variety of project environments that account for different network structures, levels of resource constrainedness, and cash-flow parameters. Extensive testing with problems ranging in size from 21 to 1000 activities shows that the new heuristic procedures dominate heuristics using information from the critical path method (CPM), and in most cases outperform heuristics from previous research. The best performing heuristic rules classify activities into priority and secondary queues according to whether they lead to immediate progress payments, thus front loading the project schedule. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 365–381, 1997     

Robustness of the normal approximation of lead-time demand in a distribution setting

Previous studies criticize the general use of the normal approximation of lead-time demand on the grounds that it can lead to serious errors in safety stock. We reexamine this issue for the distribution of fast-moving finished goods. We first determine the optimal reorder points and quantities by using the classical normal-approximation method and a theoretically correct procedure. We then evaluate the misspecification error of the normal approximation solution with respect to safety stock, logistics-system costs, total costs (logistics costs, including acquisition costs), and fill rates. The results provide evidence that the normal approximation is robust with respect to both cost and service for seven major industry groups. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 165–186, 1997     

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.     

Present practices and future plans for MIL-STD-781

MIL-STD-781 specifies reliability acceptance test procedures based on both fixed-length tests and probability ratio sequential tests. The assumption underlying MIL-STD-781 is a constant mean time between failures (MTBF) and typical practice applies MIL-STD-781 to electrical, electronic, and mechanical equipment. This article discusses some of the difficulties that have prompted the C and D revisions of MIL-STD-781. In addition, it discusses the relationship of MIL-STD-781 with MIL-STD-1635(EC) which deals with reliability growth testing. The article concludes with a discussion of needed research in reliability growth testing, in support of MIL-STD-781, and in the area of stress and its impact of MTBF.     

Some recent findings in bayesian attribute single and double sampling

This article deals with several items, including theoretical and applied results. Specific topics include (1) a discrete, economically based, attributes acceptance sampling model and its adaptations, (2) relevant costs, (3) relevant prior distributions, (4) comparison of single- and double-sampling results, and (5) reasons for marginal implementation success following excellent implementation efforts. The basic model used is one developed by Guthrie and Johns; adaptations include provisions for fixed costs as well as modifications to permit double sampling. Optimization is exact, rather than approximate. Costs incorporated into the model are for sampling inspection, lot acceptance, and lot rejection. For each of these three categories a fixed cost is included as well as two variable costs, one for each item and the other for each defective item. Discrete prior distributions for the number of defectives in a lot are used exclusively. These include the mixed binomial and Polya distributions. Single- and double-sampling results are compared. Double sampling regularly performs at only slightly lower cost per lot than single sampling. Also, some cost and prior distribution sensitivity results are presented. Comments are provided regarding actual implementation experiences in industry. Practical deficiencies with the Bayesian approach are described, and a recommendation for future research is offered.     

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.     

Minimal forecast horizon procedures for dynamic lot size models

This article presents new results which should be useful in finding production decisions while solving the dynamic lot sizing problem of Wagner–Whitin on a rolling horizon basis. In a rolling horizon environment, managers obtain decisions for the first period (or the first few periods) by looking at the forecasts for several periods. This article develops procedures to find optimal decisions for any specified number of initial periods (called planning horizon in the article) by using the forecast data for the minimum possible number of future periods. Computational results comparing these procedures with the other procedures reported in the literature are very encouraging.     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.