An Arborescent Network Formulation and Dual Ascent Based Procedure for the Two-Stage Multi-Item Dynamic Demand Lotsize Problem

Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single-source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed-charge network (ARBNET) programming model and dual ascent based branch-and-bound procedure for the two-stage multi-item dynamic demand lotsize problem. Computational results show that the new approach is significantly more efficient than earlier solution strategies. The largest set of problems that could be solved using dynamic programming contained 4 end items and 12 time periods, and required 475.38 CPU seconds per problem. The dual ascent algorithms averaged .06 CPU seconds for this problem set, and problems with 30 end items and 24 time periods were solved in 85.65 CPU seconds. Similar results verify the superiority of the new approach for handling backlogged demand. An additional advantage of the algorithm is the availability of a feasible solution, with a known worst-case optimality gap, throughout the problem-solving process.     

Decision Support System of Truck Routing and Refueling: A Dual‐Objective Approach

The variable‐route vehicle‐refueling problem (VRVRP) is a variant of the network‐flow problem which seeks, for a vehicle traveling from origin s to destination d, both the route and the refueling policy (sequence of fuel stations to use between s and d) that jointly minimize the fuel cost of operating the vehicle. Commercial‐grade decision support systems that solve the VRVRP are widely used by motor carriers, but they provide heuristic solutions only. Exact methods are available from the academic side, but because they focus on minimizing costs, they tend to cut fuel costs in exchange for increased vehicle miles (which can increase fuel consumptions and pollutants emission). We propose a new approach to the VRVRP that allows carriers to jointly seek the two possibly conflicting goals; minimizing fuel cost and vehicle miles. Computational testing shows that our approach (i) outperforms the commercial software products in both goals, and (ii) finds solutions that require significantly less vehicle miles than those given by the exact method proposed in the academic literature, without incurring unacceptable increases in fuel cost.     

Multiproduct,Multicriteria Model for Supplier Selection with Product Life‐Cycle Considerations

In industrial purchasing contexts firms often procure a set of products from the same suppliers to benefit from economies of scale and scope. These products are often at different stages of their respective product life cycles (PLCs). Firms consider multiple criteria in purchasing such products, and the relative importance of these criteria varies depending on the PLC stage of a given product. Therefore, a firm should select suppliers and choose sourcing arrangements such that product requirements across multiple criteria are satisfied over time. The extant models in sourcing literature for evaluating and selecting suppliers for a portfolio of products have not considered this important and practical issue faced by firms. This article proposes a mathematical model that effectively addresses this issue and contributes to the sourcing literature by demonstrating an approach for optimally selecting suppliers and supplier bids given the relative importance of multiple criteria across multiple products over their PLC. The application of the model on a hypothetical data set illustrates the strategic and tactical significance of such considerations.     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.     

Lot‐sizing Decisions Under Limited‐time Price Reduction*

We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.     

Robust Resource Allocation Decisions in Resource‐Constrained Projects*

The well‐known deterministic resource‐constrained project scheduling problem involves the determination of a predictive schedule (baseline schedule or pre‐schedule) of the project activities that satisfies the finish–start precedence relations and the renewable resource constraints under the objective of minimizing the project duration. This baseline schedule serves as a baseline for the execution of the project. During execution, however, the project can be subject to several types of disruptions that may disturb the baseline schedule. Management must then rely on a reactive scheduling procedure for revising or reoptimizing the baseline schedule. The objective of our research is to develop procedures for allocating resources to the activities of a given baseline schedule in order to maximize its stability in the presence of activity duration variability. We propose three integer programming–based heuristics and one constructive procedure for resource allocation. We derive lower bounds for schedule stability and report on computational results obtained on a set of benchmark problems.     

Concepts,Theory, and Techniques DISTRIBUTED COMPUTER SYSTEM DESIGN: A MULTICRITERIA DECISION-MAKING METHODOLOGY*

The design of distributed computer systems (DCSs) requires compromise among several conflicting objectives. For instance, high system availability conflicts with low cost which in turn conflicts with quick response time. This paper presents an approach, based on multi-criteria decision-making techniques, to arrive at a good design in this multiobjective environment. An interactive procedure is developed to support the decision making of system designers. Starting from an initial solution, the procedure presents a sequence of non-dominated vectors to designers, allowing them to explore systematically alternative possibilities on the path to a final design. The model user has control over trade-offs among different design objectives. This paper focuses on the details of the mathematical model used to provide decision support. Accordingly, a formulation of DCS design as a multicriteria decision problem is developed. The exchange search heuristic used to generate nondominated solutions also is presented. We argue that multicriteria models provide a more realistic formulation of the DCS design problem than the single-criterion models used widely in the literature. While obtaining a clear definition of design objectives (single or multiple) is an important activity, by explicitly acknowledging the trade-offs among multiple objectives in the design process, our methodology is more likely to produce a better overall design than methods addressing a single criterion in isolation.     

Integrated Procurement Planning in Multi‐division Firms

For large multi‐division firms, coordinating procurement policies across multiple divisions to leverage volume discounts from suppliers based on firm‐wide purchasing power can yield millions of dollars of savings in procurement costs. Coordinated procurement entails deciding which suppliers to use to meet each division's purchasing needs and sourcing preferences so as to minimize overall purchasing, logistics, and operational costs. Motivated by this tactical procurement planning problem facing a large industrial products manufacturer, we propose an integrated optimization model that simultaneously considers both firm‐wide volume discounts and divisional ordering and inventory costs. To effectively solve this large‐scale integer program, we develop and apply a tailored solution approach that exploits the problem structure to generate tight bounds. We identify several classes of valid inequalities to strengthen the linear programming relaxation, establish polyhedral properties of these inequalities, and develop both a cutting‐plane method and a sequential rounding heuristic procedure. Extensive computational tests for realistic problems demonstrate that our integrated sourcing model and solution method are effective and can provide significant economic benefits. The integrated approach yields average savings of 7.5% in total procurement costs compared to autonomous divisional policies, and our algorithm generates near‐optimal solutions (within 0.75% of optimality) within reasonable computational time.     

Coordinated Capacitated Lot‐Sizing Problem with Dynamic Demand: A Lagrangian Heuristic

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed‐integer programming formulation and Lagrangian relaxation solution procedure for the single‐family coordinated capacitated lot‐sizing problem with dynamic demand. The problem extends both the multi‐item capacitated dynamic demand lot‐sizing problem and the uncapacitated coordinated dynamic demand lot‐sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual‐based heuristic over linear programming‐based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.     

Dynamic Pricing and Lead‐Time Policies for Make‐to‐Order Systems*

Make‐to‐order firms use different approaches for managing their lead‐times and pricing in the face of changing market conditions. A particular firm's approach may be largely dictated by environmental constraints. For example, it makes little sense to carefully manage lead‐time if its effect on demand is muted, as it can be in situations where leadtime is difficult for the market to gauge or requires investment to estimate. Similarly, it can be impractical to change capacity and price. However, environmental constraints are likely to become less of an issue in the future with the expanding e‐business infrastructure, and this trend raises questions into how to manage effectively the marketing mix of price and lead‐time in a more “friction‐free” setting. We study a simple model of a make‐to‐order firm, and we examine policies for adjusting price and capacity in response to periodic and unpredictable shifts in how the market values price and lead‐time. Our analysis suggests that maintaining a fixed capacity while using lead‐time and/or price to absorb changes in the market will be most attractive when stability in throughput and profit are highly valued, but in volatile markets, this stability comes at a cost of low profits. From a pure profit maximization perspective, it is best to strive for a short and consistent lead‐times by adjusting both capacity and price in response to market changes.     

Point‐of‐Use Hybrid Inventory Policy for Hospitals

Modern point‐of‐use technology at hospitals has enabled new replenishment policies for medical supplies. One of these new policies, which we call the hybrid policy, is currently in use at a large U.S. Midwest hospital. The hybrid policy combines a low‐cost periodic replenishment epoch with a high‐cost continuous replenishment option to avoid costly stockouts. We study this new hybrid policy under deterministic and stochastic demand. We develop a parameter search engine using simulation to optimize the long‐run average cost per unit time and, via a computational study, we provide insights on the benefits (reduction in cost, inventory, and number of replenishments) that hospitals may obtain by using the hybrid policy instead of the commonly used periodic policies. We also use the optimal hybrid policy parameters from the deterministic analysis to propose approximate expressions for the stochastic hybrid policy parameters that can be easily used by hospital management.      

Project‐Level Reuse Factors: Drivers for Variation within Software Development Environments*

Systematic reuse can dramatically improve software development productivity and quality even though a software reuse methodology may require substantial investments. Some projects may fail to achieve the targeted amounts of reuse within organizations that are overall successful in employing reuse. To explain such variation, this research explores the effects of project‐level factors in the success of software reuse. A model that relates project factors to project reuse success is developed using an information‐rich case study approach. The results are based on the insights obtained in a nominal group technique session, triangulated with structured interviews and comparative case studies. Success factors identified by the study relate to client influence, project culture, project attributes, and developer reuse experience. An organization that can successfully identify the factors affecting potential software reuse will be able to better target investments for the improvement of its reuse methodology and thus positively affect its software development productivity and quality.     

Point‐of‐Dispensing Location and Capacity Optimization via a Decision Support System

Dispensing of mass prophylaxis can be critical to public health during emergency situations and involves complex decisions that must be made in a short period of time. This study presents a model and solution approach for optimizing point‐of‐dispensing (POD) location and capacity decisions. This approach is part of a decision support system designed to help officials prepare for and respond to public health emergencies. The model selects PODs from a candidate set and suggests how to staff each POD so that average travel and waiting times are minimized. A genetic algorithm (GA) quickly solves the problem based on travel and queuing approximations (QAs) and it has the ability to relax soft constraints when the dispensing goals cannot be met. We show that the proposed approach returns solutions comparable with other systems and it is able to evaluate alternative courses of action when the resources are not sufficient to meet the performance targets.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

A Clustering Algorithm for Computer-Assisted Process Organization

Amathematical programming clustering model that forms groups based on total group membership interactions is extended to include precedence relationships, group size limits, and group time limits. The extended clustering model is most appropriate for structured design of information systems as described by the computer-assisted process organization (CAPO), which requires certain ordering and may have limits on development and production capacity. An efficient algorithm for optimizing the CAPO criteria along with computational results is presented. The results show that the method is viable for the CAPO problems reported in the literature.     

Non‐dominated Time‐Window Policies in City Distribution

Urban freight contributes significantly to pollution, noise disturbance, traffic congestion, and safety problems in city centers. In many cities, local governments have introduced policy measures, in particular time‐access restrictions, to alleviate these problems. However, setting time windows is very challenging due to the conflicting interests and objectives of the stakeholders involved. In this article, we examine whether it is possible to develop time‐window policies that enhance environmental sustainability and distribution efficiencies, while meeting the objectives of the municipalities. We develop a framework for balancing retailer (costs), municipality (satisfaction), and environmental (emissions) objectives, using data envelopment analysis, under different urban time‐window policies. The approach is illustrated by a case study of three Dutch retail organizations, with a large number of stores affected by such time windows. On the basis of an evaluation of 99 different time‐window policies, our results show that harmonizing time windows between neighboring cities leads to the best overall performance. The currently used time‐window policy appears to perform reasonably well, but can be improved on all dimensions . However, harmonizing time‐window policies may be difficult to realize in practice.     

Estimating the Effects of a Time‐Limited Earnings Subsidy for Welfare‐Leavers

In the Self Sufficiency Project (SSP) welfare demonstration, members of a randomly assigned treatment group could receive a subsidy for full‐time work. The subsidy was available for 3 years, but only to people who began working full time within 12 months of random assignment. A simple optimizing model suggests that the eligibility rules created an “establishment” incentive to find a job and leave welfare within a year of random assignment, and an “entitlement” incentive to choose work over welfare once eligibility was established. Building on this insight, we develop an econometric model of welfare participation that allows us to separate the two effects and estimate the impact of the earnings subsidy on welfare entry and exit rates among those who achieved eligibility. The combination of the two incentives explains the time profile of the experimental impacts, which peaked 15 months after random assignment and faded relatively quickly. Our findings suggest that about half of the peak impact of SSP was attributable to the establishment incentive. Despite the extra work effort generated by SSP, the program had no lasting impact on wages and little or no long‐run effect on welfare participation.     

Economic Production Lot Sizing with Periodic Costs and Overtime*

Traditional approaches for modeling economic production lot‐sizing problems assume that a single, fixed equipment setup cost is incurred each time a product is run, regardless of the quantity manufactured. This permits multiple days of production from one production setup. In this paper, we extend the model to consider additional fixed charges, such as cleanup or inspection costs, that are associated with each time period's production. This manufacturing cost structure is common in the food, chemical, and pharmaceutical industries, where process equipment must be sanitized between item changeovers and at the end of each day's production. We propose two mathematical problem formulations and optimization algorithms. The models' unique features include regular time production constraints, a fixed charge for each time period's production, and the availability of overtime production capacity. Experimental results indicate the conditions under which our algorithms' performance is superior to traditional approaches. We also test the procedures on a set of lot‐sizing problems facing a national food processor and document their potential economic benefit.     

Setting Tolerable Misstatements When Auditing Aggregated Accounts*

Generally accepted auditing standards require auditors to plan audits of clients' account balances. If accounts are to be sampled, then part of this planning must include setting the tolerable misstatement for each account or class of transactions to be sampled. Although classical sampling approaches provide certain advantages, they have not been widely used because they are viewed as complex and difficult to implement. We present a remedy to these difficulties in an efficient, easily implemented optimal solution method for the problem of setting tolerable misstatements given constraints on tolerable misstatements for individual account balances as well as the overall audit. Further, our method suggests when the materialities of certain accounts or the materiality of the overall audit are irrelevant to the problem. Several example auditing problems demonstrate both our solution approach and the settings in which our approach provides a more effective or more efficient sampling plan than that provided by monetary unit sampling.     

Time‐Staged Overtime Staffing for Services with Updated Forecasts and Availabilities

This article develops a framework for staffing in a service environment when multiple opportunities exist for prescheduling overtime prior to the start of a shift. Demand forecasts improve as the shift approaches, while the availability of workers to be scheduled for overtime decreases. First, a single‐shift model is developed and used in computational studies to evaluate the benefits of time‐staged overtime staffing, which include slightly lower costs and significant reductions in unscheduled overtime and outside agents. A multishift model is then developed to consider constraints on consecutive hours worked and minimum rest intervals between shifts. A multishift computational study shows how the benefits of time‐staged overtime staffing depend on problem characteristics when interactions between shifts are considered. The article discusses how single‐shift and multishift models relate to each other and alternative ways the models may be used in practice, including decentralized open shift management and centralized overtime scheduling.