Richard L. Daniels

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance

β-Robust scheduling for single-machine systems with uncertain processing times

In scheduling environments with processing time uncertainty, system performance is determined by both the sequence in which jobs are ordered and the actual processing times of jobs. For these situations, the risk of achieving substandard system performance can be an important measure of scheduling effectiveness. To hedge this risk requires an explicit consideration of both the mean and the variance of system performance associated with alternative schedules, and motivates a β-robustness objective to capture the likelihood that a schedule yields actual performance no worse than a given target level. In this paper we focus on β-robust scheduling issues in single-stage production environments with uncertain processing times. We define a general β-robust scheduling objective, formulate the β-robust scheduling problem that results when job processing times are independent random variables and the performance measure of interest is the total flow time across all jobs, establish problem complexity, and develop e...

Multiobjective flow-shop scheduling

Previous research on the scheduling of multimachine systems has generally focused on the optimization of individual performance measures. This article considers the sequencing of jobs through a multimachine flow shop, where the quality of the resulting schedule is evaluated according to the associated levels of two scheduling criteria, schedule makespan (Cmax) and maximum job tardiness (Tmax). We present constructive procedures that quantify the trade-off between Cmax and Tmax. The significance of this trade-off is that the optimal solution for any preference function involving only Cmax and Tmax must be contained among the set of efficient schedules that comprise the trade-off curve. For the special case of two-machine flow shops, we present an algorithm that identifies the exact set of efficient schedules. Heruistic procedures for approximating the efficient set are also provided for problems involving many jobs or larger flow shops. Computational results are reported for the procedures which indicate that both the number of efficient schedules and the error incurred by heuristically approximating the efficient set are quite small.

A model for warehouse order picking

Order picking in conventional warehouse environments involves determining a sequence in which to visit the unique locations where each part in the order is stored, and thus is often modeled as a traveling salesman problem. With computer tracking of inventories, parts may now be stored in multiple locations, simplifying replenishment of inventory and eliminating the need to reserve space for each item. In this environment, order picking requires choosing a subset of the locations that store an item to collect the required quantity. Thus, both the assignment of inventory to an order and the associated sequence in which the selected locations are visited affect the cost of satisfying an order. We formulate a model for simultaneously determining the assignment and sequencing decisions, and compare it to previous models for order picking. The complexity of the order picking problem is discussed, and an upper bound on the number of feasible assignments is established. Several extensions of TSP heuristics to the new problem setting and a tabu search algorithm are presented and experimentally tested.

A survey of manufacturing flexibility: Implications for e-business flexibility

Flexibility is an effective means by which an e-business can hedge against uncertainty in a swiftly changing environment. Systems, applications, and business processes--in short, the entire environment supporting e-business--must seamlessly adapt to changes without costly and time-consuming infrastructure overhauls. Decision makers therefore have a growing need for knowledge about e-business flexibility. However, flexibility remains largely an abstraction in the e-business domain, with the term often meaning different things to different people. Whereas very little systematic research has been directed towards the study of flexibility issues associated with e-business, a rich and burgeoning literature on manufacturing flexibility has accumulated over the past 25 years. In this paper we review the existing literature on manufacturing flexibility, and extract from it guiding principles for creating and managing e-business flexibility.

Flow Shop Scheduling with Resource Flexibility

This paper explores the improvements in manufacturing efficiency that can be achieved by broadening the scope of production scheduling to include both the sequencing of work and the coordination of the resource inputs required to perform work. Recognizing that some resources are inherently flexible and thus can be reassigned dynamically to processing centers as needed, and that job processing times are often a function of the amount of resource dedicated to specific operations, we formulate the flexible-resource scheduling problem with the objective of simultaneously determining the permutation job sequence, resource allocation policy, and operation start times that optimize system performance. Focusing on flexible-resource scheduling in flow shop production systems, we discuss problem complexity, identify properties of and establish lower bounds for optimal schedules, develop optimal and heuristic solution approaches, and report the results of extensive computational experimentation designed to explore t...

Marketing/manufacturing trade-offs in product line management

A critical decision facing firms across industries is the selection of a mix of products to offer in the marketplace. Both in practice and in the academic literature, the product line design problem has typically been considered from a marketing perspective, with a focus on how alternative sets of products interact and compete in the marketplace. The operational implications of product line decisions have been largely ignored, even while the importance and complexity of interactions among products in the manufacturing environment increase with broadening product lines. Furthermore, consideration of manufacturing synergies among products in product line design is increasingly beneficial given efforts in many industries to improve co-ordination of manufacturing activities across products. In this work we examine the benefits of integrating marketing implications of product mix with more detailed manufacturing cost implications. Traditional product line models are extended to capture both individual product costs and relevant cost interactions among products. The relevant marketing and manufacturing elements are considered in a mathematical programming formulation that identifies a profit maximizing mix of products. The resulting normative model of the product line design problem is used to generate insights into important cross-functional issues in product line management. Specifically, we examine the impact of alternative manufacturing environment characteristics on the composition of the optimal product line.

Technical Note—Single Machine Scheduling with Controllable Processing Times and Number of Jobs Tardy

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A multi-objective approach to resource allocation in single machine scheduling

Abstract Most shop scheduling research has treated job processing times as fixed parameters. However, schedulers typically exercise processing time control through the application of limited resources, e.g., overtime or the dedication of additional manpower or equipment. An effect of the judicious assignment of resource is to improve specified measures of system performance over the level attainable prior to resource allocation. This paper presents two extensions to the joint sequencing/resource allocation scheduling model for single-stage production initially proposed by Van Wassenhove and Baker. First, the impact of specified limits on individual job tardiness on optimal sequencing and single resource allocation is discussed. Next, the existence of multiple resources available for processing time control is considered. Constructive procedures are developed to identify the job sequence and resource distribution that minimize the total amount of available resource required to satisfy imposed limits on maximum and individual job tardiness. The value of T max is then varied parametrically to highlight the trade-off between the total amount of available resource and T max . The managerial significance of the resulting trade-off curve is that it provides the complete set of possibly optimal schedules for any objective function that involves only these schedule attributes.

Integrating product mix and technology adoption decisions: a portfolio approach for evaluating advanced technologies in the automobile industry

Abstract Interactions with managers in the automobile industry indicate that efforts to bring potentially profitable new technologies into production are often frustrated by the traditional unit cost-based approach that is used for evaluating new technologies. Opportunities for timely introduction of valuable or even preemptive technologies can be missed because unit cost comparisons, typically applied to a limited set of vehicle configurations with volumes based on current demand figures, invariably favor incumbent over new technologies. In this research, we develop a more complete technology adoption decision model that integrates product mix and technology adoption decisions. Specifically, we recognize that product mix and volume are important variables in determining the cost effectiveness of new technologies, and include in the model customer demand projections that reflect market trends (e.g. growing demand for increasingly sophisticated features and functions in vehicles). Anticipated experience benefits are then applied to the appropriate production volumes to more accurately predict the profit impact of adopting new technologies. The introduction of automotive multiplexing, a technology that is characteristic of current technological advances in the industry, provides a context for considering insights that can be derived from the decision model. Our interaction with a global Tier I automotive systems supplier allowed us to obtain representative cost data and other information relevant to the technology adoption decision.