Alan W. Neebe

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.

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.

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.

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.

Generating alternative solutions for dynamic programming-based planning problems

Abstract An approach is developed for generating alternative near-optimal solutions for dynamic programming-based planning problems. The proposed methodology improves on an existing approach in three respects. First, computational efficiencies are achieved by recomputing the optimal policy for only a subset of the total number of stages. Second, the approach can be easily structured such that there is increased variation in alternatives within the first stages. Third, the maximum allowable difference in objective function value between alternative solutions can be explicitly stated by the user. A hypothetical shortest route problem is used to illustrate the characteristics of the proposed approach. Results are also presented for a facility capacity planning problem in the municipal solid waste management area.

The Discrete-Time Sequencing Expansion Problem

We consider a sequencing expansion problem in which capacity can be added only at discrete points in time. Given is a forecast of demand in each period, and a set of expansion projects each with a given capacity and cost. The problem is to determine the sequence of expansions necessary to provide sufficient capacity to meet the demand in all periods at minimum cost. The problem is solved using Lagrangean relaxation. Computational results are given.

Procedures for solving bottleneck generalized assignment problems

We discuss bottleneck (or minimax) versions of the generalized assignment problem. The basic problem 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. Two versions of the bottleneck generalized problem (BGAP) are defined. The first of these is called the Task BGAP and has as its objective the minimization of the maximum of the costs of the assignments that are made. The second version is referred to as the Agent BGAP and has as its objective the minimization of the maximum of the total costs assigned to each agent.

Real-time task reallocation in fault-tolerant distributed computer systems

Abstract We address the issue of real-time task reallocation due to the failure of one or more processors in a software implemented fault-tolerant system. The incremental and total task reallocation problems are discussed, and a heuristic procedure for both problems is proposed. Computational experiments with the heuristic on the total task reallocation problem produce near perfect system reconfigurations. Further experiments with a slightly modified version of the heuristic show that excellent quality system reconfigurations are obtainable with minimal computational effort.