Wilbert E. Wilhelm

Scheduling and lot sizing with sequence-dependent setup: A literature review

This paper reviews the literature related to the class of scheduling problems that involve sequence-dependent setup times (costs), an important consideration in many practical applications. It focuses on papers published within the last decade, addressing a variety of machine configurations including single machine, parallel machine, flow shop, and job shop systems and reviews the optimization and heuristic solution methods used for each category. Since lot sizing is so intimately related to scheduling, this paper reviews work that integrates these issues in relationship to each configuration. This paper provides a perspective of this line of research, gives conclusions, and discusses fertile research opportunities posed by this class of scheduling problems.

Strategic, tactical and operational decisions in multi-national logistics networks: A review and discussion of modelling issues

The rapidly developing worldwide marketplace is leading to the geographical dispersion of production, assembly and distribution operations. This paper deals with three aspects of international logistics networks: strategic, tactical and operational. The strategic level designs the logistics network, including prescribing facility locations, production technologies and plant capacities. The tactical level prescribes material flow management policies, including production levels at all plants, assembly policy, inventory levels, and lot sizes. The operational level schedules operations to assure in-time delivery of final products to customers. This paper reviews the literature that deals with strategic, tactical and operational levels and discusses relevant modelling issues.

Clique-detection models in computational biochemistry and genomics

Abstract Many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models. In particular, a number have been formulated as clique-detection models. The proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graph-theoretic aspects of the solution approaches. Each subsequent section describes a particular type of problem, gives an example to show how the graph model can be derived, summarizes recent progress, and discusses challenges associated with solving the associated graph-theoretic models. Clique-detection models include prescribing (a) a maximal clique, (b) a maximum clique, (c) a maximum weighted clique, or (d) all maximal cliques in a graph. The particular types of biochemistry and genomics problems that can be represented by a clique-detection model include integration of genome mapping data, nonoverlapping local alignments, matching and comparing molecular structures, and protein docking.

A mathematical model to design a lignocellulosic biofuel supply chain system with a case study based on a region in Central Texas.

This study formulates a model to maximize the profit of a lignocellulosic biofuel supply chain ranging from feedstock suppliers to biofuel customers. The model deals with a time-staged, multi-commodity, production/distribution system, prescribing facility locations and capacities, technologies, and material flows. A case study based on a region in Central Texas demonstrates application of the proposed model to design the most profitable biofuel supply chain under each of several scenarios. A sensitivity analysis identifies that ethanol (ETOH) price is the most significant factor in the economic viability of a lignocellulosic biofuel supply chain.

A Technical Review of Column Generation in Integer Programming

This paper provides a technical review of topics relevant to applying column generation methods to solve integer programs but emphasizes formulation issues as a means of achieving its goal, which is to bridge the gap between methodological development and application. Type I, II and III column generation approaches are described in detail and each is demonstrated by a set of prototypical formulations that provide a historical perspective of milestone contributions. Technical issues, including formulation, context, algorithm design and implementation are also related. Formulation issues encompass the restricted master problem (RMP) and subproblem (SP) structure, symmetry, complexity and the Integrality Property. Context issues comprise theoretical principles, dealing with binary or general integer variables and generating rows as well as columns. Algorithm design issues include branching strategies, SP solution strategies and problem-specific techniques. Implementation issues include determining an initial basic feasible solution, managing a pool of generated columns, optimizing the RMP at each iteration, and handling degeneracy and tailing off.

A Column-Generation Approach for the Assembly System Design Problem with Tool Changes

This assembly system design problem (ASDP) is to prescribe the minimum-cost assignment of machines, tooling, and tasks to stations, observing task precedence relationships and cycle time requirements. The ASDP with tool changes (ASDPTCs) also prescribes the optimal sequence of operations at each station, including tool changes, which are important, for example, in robotic assembly. A unique solution approach decomposes the model into a master problem, which is a minimum-cost network-flow problem that can be solved as a linear program, and subproblems, which are constrained, shortest-path problems that generate station configurations. Subproblems are solved on state-operation networks, which extend earlier formulations to incorporate tooling considerations. This paper presents a specialized algorithm to solve the subproblems. Computational tests benchmark the approach on several classes of problems, and the results are promising. In particular, tests demonstrate the importance of using engineering judgment to manage problem complexity by controlling the size of state-operation networks

Kitting process in a stochastic assembly system

In small-lot, multi-product, multi-level assembly systems, kitting (or accumulating) components required for assembly plays a crucial role in determining system performance, especially when the system operates in a stochastic environment. This paper analyzes the kitting process of a stochastic assembly system, treating it as an assembly-like queue. If components arrive according to Poisson processes, we show that the output stream departing the kitting operation is a Markov renewal process. The distribution of time between kit completions is also derived. Under the special condition of identical component arrival streams having the same Poisson parameter, we show that the output stream of kits approximates a Poisson process with parameter equal to that of the input stream. This approximately decouples assembly from kitting, allowing the assembly operation to be analyzed separately.

Prescribing the Content and Timing of Product Upgrades

Demand for a family of high-technology products such as notebook computers erodes over time as competitors introduce new products that incorporate improved technologies. A manufacturer may compensate for this by applying the model formulated in this paper to prescribe the content and timing of upgrades to maximize total profit over the life cycle of the product family. The model deals with economies of scale that might be achieved by the upgrading process. It provides decision support by integrating decisions of relevant organizations in the enterprise: marketing (e.g., marketing strategy, pricing), product design engineering, process design engineering, and supply chain management (e.g., suppliers, production, outsourcing, inventory, backorders, and distribution). The paper presents a branch-and-price solution approach that employs an effective, new method for solving associated subproblems. Computations evaluate the efficacy of the solution approach and examples demonstrate contexts in which managers might apply the model to advantage.

A cutting plane approach for the single-product assembly system design problem

This paper evaluates a new branch-and-cut approach, establishing a computational benchmark for the single-product, assembly system design (SPASD) problem. Our approach, which includes a heuristic, preprocessing, and two cutgenerating methods, outperformed OSL in solving a set of 102 instances of the SPASD problem. The approach is robust; test problems show that it can be applied to variations of the generic SPASD problem that we encountered in industry.

Analysis of a single-stage, single-product, stochastic, MRP-controlled assembly system

This paper models a single-stage, single-product, stochastic assembly system, operating according to an Materials Requirements Planning controlled (MRP) ordering philosophy. It deals explicitly with the underlying stochastic process that describes the end-product inventory position, enabling production lead times to be treated as independent and generally distributed random variables. The inventory position process is identified as a Markov renewal process, and this structure is exploited to determine system performance measures such as average inventory level, average backorder level, and the probability distribution of the end-product inventory position. An example, which demonstrates the type of analysis possible, focuses on quantifying the effect of kitting on the availability of end-products.