Joseph B. Mazzola

Resource-Constrained Assignment Scheduling

Many resource-constrained assignment scheduling problems can be modeled as 0-1 assignment problems with side constraints APSC. Unlike the well-known assignment problem of linear programming, APSC is NP-complete. In this paper we define a branch-and-bound algorithm for solving APSC to optimality. The algorithm employs a depth-first, polychotomous branching strategy in conjunction with a bounding procedure that utilizes subgradient optimization. We also define a heuristic procedure for obtaining approximate solutions to APSC. The heuristic uses subgradient optimization to guide the search for a good solution as well as to provide a bound on solution quality. We present computational experience with both procedures, applied to over 400 test problems. The algorithm is demonstrated to be effective across three different classes of resource-constrained assignment scheduling problems. The heuristic generates solutions for these problems that are, on average, within 0.8% of optimality.

Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type

This paper presents exact and heuristic solution procedures for a multiproduct capacitated facility location (MPCFL) problem in which the demand for a number of different product families must be supplied from a set of facility sites, and each site offers a choice of facility types exhibiting different capacities. MPCFL generalizes both the uncapacitated (or simple) facility location (UFL) problem and the pure-integer capacitated facility location problem. We define a branch-and-bound algorithm for MPCFL that utilizes bounds formed by a Lagrangian relaxation of MPCFL which decomposes the problem into UFL subproblems and easily solvable 0-1 knapsack subproblems. The UFL subproblems are solved by the dual-based procedure of Erlenkotter. We also present a subgradient optimization-Lagrangian relaxation-based heuristic for MPCFL. Computational experience with the algorithm and heuristic are reported. The MPCFL heuristic is seen to be extremely effective, generating solutions to the test problems that are on average within 2% of optimality, and the branch-and-bound algorithm is successful in solving all of the test problems to optimality.

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...

The Stochastic Learning Curve: Optimal Production in the Presence of Learning-Curve Uncertainty

Theoretical analyses incorporating production learning are typically deterministic: costs are posited to decrease in a known, deterministic fashion as cumulative production increases. This paper introduces a stochastic 1earning:curve model that incorporates random variation in the decreasing cost function. We first consider a discrete-time, infinite-horizon, dynamic programming formulation of monopolistic production planning when costs follow a learning curve. This basic formulation is then extended to allow for random variation in the learning process. We also explore properties of the resulting optimal policies. For example, in some of the stochastic models we analyze optimal production is shown to exceed myopic production, echoing a key result from the deterministic learning-curve literature. In other of the stochastic models, however, this result does not hold, underscoring the need for extended analysis in the stochastic setting. We also provide new insights in the deterministic setting: for example,...

Production planning of a flexible manufacturing system in a material requirements planning environment

Early flexible manufacturing system (FMS) production planning models exhibited a variety of planning objectives; typically, these objectives were independent of the overall production environment. More recently, some researchers have proposed hierarchical production planning and scheduling models for FMS. In this article, we examine production planning of FMS in a material requirements planning (MRP) environment. We propose a hierarchical structure that integrates FMS production planning into a closed-loop MRP system. This structure gives rise to the FMS/MRP rough-cut capacity planning (FMRCP) problem, the FMS/MRP grouping and loading (FMGL) problem, and the FMS/MRP detailed scheduling problem.We examine the FMRCP and FMGL problems in detail and present mathematical programming models for each of these problems. In particular, the FMRCP problem is modeled as a generalized assignment problem (GAP), and a GAP-based heuristic procedure is defined for the problem. We define a two-phase heuristic for the FMGL problem and present computational experience with both heuristics. The FMRCP heuristic is shown to solve problems that exhibit a dependent-demand relation within the FMS and with FMS capacity utilization as high as 99 percent. The FMGL heuristic requires very little CPU time and obtains solutions to the test problems that are on average within 1.5 percent of a theoretical lower bound.This FMS/MRP production planning framework, together with the resulting models, constitutes an important step in the integration of FMS technology with MRP production planning. The hierarchical planning mechanism directly provides for system-level MRP planning priorities to induce appropriate production planning and control objectives on the FMS while simultaneously allowing for necessary feedback from the FMS. Moreover, by demonstrating the tractability of the FMRCP and FMGL problems, this research establishes the necessary groundwork upon which to explore systemwide issues pertaining to the coordination of the hierarchical structure.

Flow Shop Scheduling with Partial Resource Flexibility

Resource flexibility refers to the ability to dynamically reallocate units of resource from one stage of a production process to another in response to shifting bottlenecks. Recent research has demonstrated that substantial improvements in operational performance can be realized in both serial- and parallel-machine production environments through the effective utilization of resource flexibility. In these contexts the resource was assumed to exhibit complete flexibility. This research explores the extent to which the operational benefits associated with resource flexibility can be achieved in a flow shop environment using a partially flexible resource. Focusing on labor flexibility, we propose corresponding metrics for partial flexibility and formulate a model for flow shop scheduling with partial resource flexibility. On the basis of computational experiments, we explore properties pertaining to the relative amounts as well as the allocation of partial resource flexibility as it is distributed across the workforce. The conclusions drawn from this research provide significant insight into the management of flow shops with a workforce that is crosstrained to achieve partial flexibility. Moreover, we extend the principles developed by Jordan and Graves (1995) for partially flexible manufacturing plants to the flow shop scheduling environment, and we link these principles in a novel way to recent research on self-buffering flow lines.

A tabu-search heuristic for the flexible-resource flow shop scheduling problem

This paper presents a tabu-search heuristic for the flexible-resource flow shop scheduling (FRFS) problem [7]. The FRFS problem generalizes the classic flow shop scheduling problem by allowing job-operation processing times to depend on the amount of resource assigned to an operation; the objective is to determine simultaneously the job sequence, resource-allocation policy, and operation start times that optimize system performance. The tabu-search heuristic (TSH) employs a nested-search strategy based on a decomposition of the FRFS problem into these three components. We discuss computational experience with the THS procedure on more than 1600 test problems. The results show that TSH is effective in obtaining near-optimal solutions to the FRFS test problems. In particular, TSH generates optimal solutions for more than 70% of the test problems for which optimal solutions are known; overall, these solutions are within 0.3% of optimality on the average, and within 2.5% of optimality in the worst case.

Multiproduct production planning in the presence of work-force learning

This paper explores the multiproduct production planning problem in the presence of work-force learning (MPPL). In this setting the work-force productivity reflects a learning-curve effect which can either increase or decrease (learn or forget) as a function of previous production volume. This research advances the understanding of MPPL along a number of dimensions. We formulate MPPL as a nonlinear mixed-integer programming problem and establish problem complexity, demonstrating that it is strongly NP-hard. We also discuss some important economic properties of production planning in the presence of learning. We then define a branch-and-bound algorithm for MPPL, as well as a tabu-search heuristic (TSH). In addition, we consider a previously defined heuristic for MPPL and demonstrate that its performance can be arbitrarily bad. Computational experiments on a large set of test problems were performed to assess the performance of the algorithm and the TSH procedure, and also to study the behavior of MPPL problems. The results of the experiments indicate that despite the underlying problem complexity, the algorithm is able to solve reasonably large problems, thus providing a basis for evaluating the heuristic solution quality. The TSH consistently obtains high-quality solutions to the test problems, suggesting that the tabu-search methodology offers an effective approach to complex production planning problems. MPPL problem difficulty is seen to vary with the number of periods in the planning horizon, the relative degree of labor intensity, and the relative demand behavior of products.

Algorithms and heuristics for variable-yield lot sizing

Abstract : We consider the multiperiod lot-sizing problem in which the production yield (the proportion of usable goods) is variable according to a known probability distribution. A dynamic programming algorithm for an arbitrary sequence of demand requirements is presented. We review two economic order quantity (EOQ) models for the stationary demand continuous-time problem and derive an EOQ model when the production yield follows a binomial distribution and backlogging of demand is permitted. Heuristics based on the EOQ model are discussed, and a computational evaluation of these heuristics is presented. The heuristics consistently produced near optimal lot-sizing policies for problems with stationary and cyclic demands. (Author)

An algorithm for the bottleneck generalized assignment problem

Abstract We discuss a bottleneck (or minimax) version of the generalized assignment problem, known as the task bottleneck generalized assignment problem (TBGAP). TBGAP involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. The objective is to minimize the maximum of the costs of the assignments that are made. We present an algorithm for solving TBGAP. The TBGAP algorithm is illustrated by an example and computational experience is reported. The algorithm is seen to be effective in solving TBGAP problems to optimality.