Showing papers in "Annals of Operations Research in 1985"

Local search in routing problems with time windows

Abstract: We develop local search algorithms for routing problems with time windows. The presented algorithms are based on thek-interchange concept. The presence of time windows introduces feasibility constraints, the checking of which normally requires O(N) time. Our method reduces this checking effort to O(1) time. We also consider the problem of finding initial solutions. A complexity result is given and an insertion heuristic is described.

Design, planning, scheduling, and control problems of flexible manufacturing systems

Abstract: The design and use of flexible manufacturing systems (FMSs) involve some intricate operations research problems.FMS design problems include, for example, determining the appropriate number of machine tools of each type, the capacity of the material handling system, and the size of buffers.FMS planning problems include the determination of which parts should be simultaneously machined, the optimal partition of machine tools into groups, allocations of pallets and fixtures to part types, and the assignment of operations and associated cutting tools among the limited-capacity tool magazines of the machine tools.FMS scheduling problems include determining the optimal input sequence of parts and an optimal sequence at each machine tool given the current part mix.FMS control problems are those concerned with, for example, monitoring the system to be sure that requirements and due dates are being met and that unreliability problems are taken care of. This paper defines and describes these FMS problems in detail for OR/MS researchers to work on.

A petri net approach to the modelling and analysis of flexible manufacturing systems

Abstract: In this paper we present an approach for modelling and analyzing flexible manufacturing systems (FMSs) using Petri nets. In this approach, we first build a Petri net model (PNM) of the given FMS in a bottom-up fashion and then analyze important qualitative aspects of FMS behaviour such as existence/absence of deadlocks and buffer overflows. The basis for our approach is a theorem we state and prove for computing the invariants of the union of a finite number of Petri nets when the invariants of the individual nets are known. We illustrate our approach using two typical manufacturing systems: an automated transfer line and a simple FMS.

A computational comparison of algorithms for the inventory routing problem

Abstract: The inventory routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Each day a fleet of trucks is dispatched over a set of routes to resupply a subset of the customers. In this paper, we describe and compare algorithms for this problem defined over a short planning period, e.g. one week. These algorithms define the set of customers to be serviced each day and produce routes for a fleet of vehicles to service those customers. Two algorithms are compared in detail, one which first allocates deliveries to days and then solves a vehicle routing problem and a second which treats the multi-day problem as a modified vehicle routing problem. The comparison is based on a set of real data obtained from a propane distribution firm in Pennsylvania. The solutions obtained by both procedures compare quite favorably with those in use by the firm.

The part families problem in flexible manufacturing systems

Abstract: Parts grouping into families can be performed in flexible manufacturing systems (FMSs) to simplify two classes of problems: long horizon planning and short horizon planning. In this paper the emphasis is on the part families problem applicable to the short horizon planning. Traditionally, parts grouping was based on classification and coding systems, some of which are reviewed in this paper. To overcome the drawbacks of the classical approach to parts grouping, two new methodologies are developed. The methodologies presented are very easy to implement because they take advantage of the information already stored in the CAD system. One of the basic elements of this system is the algorithm for solving the part families problem. Some of the existing clustering algorithms for solving this problem are discussed. A new clustering algorithm has been developed. The computational complexity and some of the computational results of solving the part families problem are also discussed.

An overview of evaluative models for flexible manufacturing systems

Abstract: Flexible manufacturing systems (FMSs) are a class of automated systems which can be used to improve productivity in discrete parts manufacturing. Due to the complexity of these systems, it is useful to have models that can aid in the design and operation of FMSs. We specifically differentiate here betweengenerative (or prescriptive) models, whichfind candidate decisions, andevaluative (or descriptive) models, whichevaluate a given set of decisions. We briefly cover, in a practical context, the pros and cons of these two classes of models. Then we focus on the latter class of models. Evaluative models for FMSs fall into five main classes, based on the technique used, namely: static allocation, queueing network theory, simulation, perturbation analysis, and Petri nets. Each of these approaches is briefly described, advantages and disadvantages mentioned, and references given to more detailed papers.

Algorithmic aspects of the substitution decomposition in optimization over relations, set systems and Boolean functions

Abstract: In the last years, decomposition techniques have seen an increasing application to the solution of problems from operations research and combinatorial optimization, in particular in network theory and graph theory. This paper gives a broad treatment of a particular aspect of this approach, viz. the design of algorithms to compute the decomposition possibilities for a large class of discrete structures. The decomposition considered is thesubstitution decomposition (also known as modular decomposition, disjunctive decomposition, X-join or ordinal sum). Under rather general assumptions on the type of structure considered, these (possibly exponentially many) decomposition possibilities can be appropriately represented in acomposition tree of polynomial size. The task of determining this tree is shown to be polynomially equivalent to the seemingly weaker task of determining the closed hull of a given set w.r.t. a closure operation associated with the substitution decomposition. Based on this reduction, we show that for arbitrary relations the composition tree can be constructed in polynomial time. For clutters and monotonic Boolean functions, this task of constructing the closed hull is shown to be Turing-reducible to the problem of determining the circuits of the independence system associated with the clutter or the prime implicants of the Boolean function. This leads to polynomial algorithms for special clutters or monotonic Boolean functions. However, these results seem not to be extendable to the general case, as we derive exponential lower bounds for oracle decomposition algorithms for arbitrary set systems and Boolean functions.

LP-Based Combinatorial Problem Solving

Abstract: A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman problem, another the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.

A large scale machine loading problem in flexible assembly

Abstract: Flexible manufacturing is characterized by versatile work stations with minimum change over times and a versatile material handling system. The loading problem in flexible manufacturing is to assign tools, material, operations and jobs to work stations in order to minimize the total number of job-to-work station assignments. In this paper, we describe a special case of the general loading problem applied to flexible assembly and develop a discrete optimization model. We then discuss approaches for obtaining good heuristic solutions and present results for a large scale study.

Scheduling of project networks

Abstract: The paper deals with the network optimization problem of minimizing regular project cost subject to an arbitrary precedence relation on the sets of activities and to arbitrarily many resource constraints. The treatment is done via a purely structural approach that considerably extends the disjunctive graph concept. It is based on so-called feasible posets and includes a quite deep and useful representation theorem. This theorem permits many insights concerning the analytical behaviour of the optimal value function, the description and counting of all essentially different optimization problems, the nature of Graham anomalies, connections with the on-line stochastic generalizations, and several others. In addition, it also allows the design of a quite powerful class of branch-and-bound algorithms for such problems, which is based on an iterative construction of feasible posets. Using so-called distance matrices, this approach permits the restriction of the exponential part of the algorithm to the often comparatively small set of ‘resource and cost essential’ jobs. The paper reports on computational experience with this algorithm for examples from the building industry and includes a rough comparison with the integer programming approach by Talbot and Patterson.

Modeling a class of state-dependent routing in flexible manufacturing systems

Abstract: We develop a closed queueing network model for flexible manufacturing systems (FMSs), where parts routing follows a probabilistic shortest-queue (PSQ) scheme, i.e. parts are routed to the shortest queue (or the most empty station) with the highest probability. We allow limited local buffer at each work station. We prove that with the PSQ routing, the Markovian queue-length process satisfies time reversibility and has a product-form equilibrium distribution. An algorithm is developed to compute the solutions to the model. The model can be used as a performance evaluation tool to study FMSs.

K best solutions to combinatorial optimization problems

Abstract: We review the Lawler-Murty [24,20] procedure for finding theK best solutions to combinatorial optimization problems. Then we introduce an alternative algorithm which is based on a binary search tree procedure. We apply both algorithms to the problems of finding theK best bases in a matroid, perfect matchings, and best cuts in a network.

SEQUENTIAL DECISION PROCEDURES FOR BATCHING AND BALANCING IN FMSs

Abstract: Batching and balancing constitute two of the several scheduling and resource allocation problems important over different time scales in FMS operations. The time scale for batching and balancing is of the order of days to weeks — which puts it between long-term planning and part selection, of the order of months to years, and real-time part entry and dispatching, of the order of minutes. All these scheduling and resource allocation problems have been addressed at the Charles Stark Draper Laboratoty by a common methodology. We have used a sequential decision algorithm, each decision based on optimization of a probabilistic performance criterion designed to trade off whatever and however many competing attributes may be important in the particular problem. This paper discusses the common methodology, and its application to FMS batching and balancing in particular. Our computer program BATCH/BAL which implements the algorithms given here has been the starting point for all the other sequential decision programs subsequently developed at our laboratory.

Interactive decision software and computer graphics for architectural and space planning

Abstract: We describe the development and successful implementation of a decision support system now being used by several leading firms in the architecture and space planning industries. The system, which we call SPDS (spatial programming design system) has the following characteristics: (i) user-friendly convenience features permitting architects and space planners to operate the system without being experienced programmers; (ii) interactive capabilities allowing the user to control and to manipulate relevant parameters, orchestrating conditions to which his or her intuition provides valuable input; (iii) informative and understandable graphics, providing visual displays of interconnections that the computer itself treats in a more abstract methematical form; (iv) convenient ways to change configurations, and to carry out ‘what if’ analyses calling on the system’s decision support capabilities; (v) a collection of new methods, invisible to the user, capable of generating good solutions to the mathematical programming problems that underlie each major design component. These new methods succeed in generating high quality solutions to a collection of complex discrete, highly nonlinear problems. While these problems could only be solved in hours, or not at all, with previously existing software, the new methods obtain answers in seconds to minutes on a minicomputer. Major users, including Dalton, Dalton, Newport, and Marshal Erdwin, report numerous advantages of the system over traditional architectural design methods.

Analysis of flexible manufacturing systems with priority scheduling: PMVA

Abstract: A new methodology for performance analysis of flexible manufacturing systems (FMSs) with priority scheduling is presented. The analytic model developed extends the mean value analysis of closed networks of queues with multiple product types, various non-preemptive priority service disciplines, and with parallel machine stations. Performance measures derived include the expected throughput per product and per station, utilization of machines and transporters, queuing times and queue length measures for various configurations. Extensive numerical calculations have shown that the algorithm used for solving the problem converges rapidly and retains numerical stability for large models. The paper also illustrates the application of the model to a system with a mixture of FCFS and HOL disciplines which gives insights into various priority assignment policies in FMSs. Special attention was given to the problem of scheduling the robot carriers (transporters).

The shortest augmenting path method for solving assignment problems — Motivation and computational experience

Abstract: In this paper we discuss the shortest augmenting path method for solving assignment problems in the following respect: we introduce this basic concept using matching theory we present several efficient labeling techniques for constructing shortest augmenting paths we show the relationship of this approach to several classical assignment algorithms we present extensive computational experience for complete problems, and we show how postoptimal analysis can be performed using this approach and naturally leads to a new, highly efficient hybrid approach for solving large-scale dense assignment problems

Experimental investigation of real-time scheduling in flexible manufacturing systems

Abstract: This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.

Economic justification of modern computer-based factory automation equipment: A status report

Abstract: This paper provides a status report on the economic justification of modern computer-based factory automation equipment. Such equipment, although offering improved productivity and flexibility, is nevertheless oftentimes difficult to justify using traditional discounted cash flow evaluation methodologies. In this paper, we first establish and explain four different categories into which most of the literature on this subject generally falls. We then present the results of interviews with executives in manufacturing companies that have experienced varying degrees of success in justifying automation. During these interviews, we sought to determine how the automation was justified as well as the difficulties encountered. Finally, we consolidate the information obtained from our examination of the literature and our interviews, and we synthesize a set of options available to todays manager attempting to justify the introduction of automation systems. We present these options in terms of immediate, near-term and long-term managerial alternatives.

A survey of the perturbation analysis of discrete event dynamic systems

Abstract: This paper introduces an analysis and optimization technique for discrete event dynamic systems, such as flexible manufacturing systems (FMSs), and other discrete part production processes. It can also be used for enhancement of the simulation results of, or the monitoring of the operations of such systems in real time. Extensive references are given where readers may pursue futher details.

A technique for on-line sensitivity analysis of flexible manufacturing systems

Abstract: The recent perturbation analysis approach to discrete event systems is applied to flexible manufacturing systems (FMS). While analytic (queueing) models are useful in preliminary design of such systems, they are not accurate enough at the detailed design/operation stage. Thus, experimentation on detailed simulations or on the actual system has been the way to optimize system performance. Perturbation analysis allows us to derive the sensitivity of system performance, with respect to several design/operating parameters, by observing a single experiment (and without having to actually alter the parameters — often a costly operation). Thus, observation of one experiment can give accurate directions for the improvement of several parameter values. Here we give a simulation example illustrating how perturbation analysis could be used on-line on an FMS to improve its performance, including reducing its operating cost. Experimental results are also presented validating the estimates obtained from this technique.

A GPSS/H model for a hypothetical flexible manufacturing system

Abstract: A GPSS/H model is presented for a hypothetical flexible manufacturing system The FMS consists of six machines composed of three machine types, manufactures three types of parts, and uses automatic guided vehicles (AGVs) to transport inprocess parts between appropriate machines and wait spaces in the system Three logical modules have been designed for the model, with copies of these modules then being appropriately distributed and interfaced throughout the model and tailored to achieve overall representation of the specific FMS The same technique can be used by others to build analogous or extended GPSS/H models for other specific FMSs in which AGVs are used as transporters Simulations can then be performed with such models to research FMS design and control alternatives

Real-time production scheduling of an automated cardline

Abstract: In this paper, we describe a flow model of an automated-printed circuit card assembly line at the International Business Machines Corporation (IBM) plant at Tucson, Arizona. We use a simulation based on this model as a test bed to discuss the performance of a hierarchical scheduling policy described in [3]. We compare this with other policies for loading parts into a flexible manufacturing system. We demonstrate that the hierarchical strategy is effective in meeting production requirements (both total volume and balance among part types) while limiting average work-in-process (WIP). This is a consequence of the feedback nature of the policy. Hedging (i.e. building up buffer stock) compensates for machine failures, thus resulting in high production percentages. The work-in-process (WIP) is low, as the policy reduces internal queues by respecting the capacity constraints of the system at every instant.

Algorithms for part and machine selection in flexible manufacturing systems

Abstract: Deciding whether FMS technology is viable for a given application, and if so, what machines should comprise the FMS and what parts should be produced on it, can be a difficult task. Manual methods suffice only for situations where a small number of FMS-type machines are to be considered and less than a few dozen candidate parts are to be chosen from. When both machines and parts are to be selected from a larger number of candidates, manual methods become cumbersome and time consuming, and computer-based decision aids become a necessity. This paper gives an overview of the required decision process, and then focuses on those stages for which computer-based decision aids can be used effectively. Particular decision aids are described, and case studies are cited to illustrate their motivation and use.

Steady state scheduling of a flexible manufacturing system with periodic releasing and flow time constraints

Abstract: This paper deals with the dynamic behaviour of an FMS when parts are released periodically. The minimal release period is induced by the most critical machine or fixture pallet type. Moreover, with a fixed period, the limited number of available pallets induces a maximal flow time for every part type. Thus, the objective of this paper is to determine a part release strategy and an activity schedule on every machine which allows to control every part flow time for steady state. An analysis method for this objective is presented in this paper. Its purpose is to obtain releasing and scheduling conditions ensuring a workshop steady state compatible with the considered constraints, especially part flow times. This method is based on the resolution of conflicts between activities processed on a common machine. This resolution uses limit times associated with each activity and it can modify these limit times. These modifications in turn can induce modifications for other activity limit times due to part routing, steady-state periodicity, and part flow time constraints. Thus, an iterative procedure has been defined. It refines steady-state feasibility conditions through limit times and sequencing conditions of activities processed on a common machine. The method is illustrated with two examples.

Experiments with an interactive paired comparison simplex method for molp problems

Abstract: In this paper, an interactive paired comparison simplex based method formultiple objective linear programming (MOLP) problems is developed and compared to other interactive MOLP methods. The decision maker (DM)’s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for ‘utility efficiency’ for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of ‘strength of preference ’ is developed for the assessment of the DM’s unknown utility function where he can express his preference for a pair of extreme points as ‘strong ’, ‘weak ’, or ‘almost indifferent ’. The problem of ‘inconsistency of the DM’ is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed.

Capital budgeting and optimal timing of investments in flexible manufacturing systems

Abstract: This paper investigates the financial-economic decision process for investments in flexible manufacturing systems (FMS). Contrary to popular belief, we show that conventional capital budgeting techniques can be used to make such investment decisions. First, we identify theoverall impact of installing an FMS and present guidelines for a cash flow forecasting model. We then present ways in which to incorporate uncertainty in these cash flows within a risk-adjusted discount rate. These expected cash flows and the discount rate are used in calculating the net present value (NPV). Once the capital budgeting analysis is completed, a critical issue facing the firm is the optimal timing of the installation. We reinterpret the general results on optimal timing of investments within the special context of an FMS project. Finally, we illustrate the above technique via a stylized example.

An integrated FMS design procedure

Abstract: This paper considers the problem of the design of an FMS system. An integrated design procedure is outlined, which involves three stages — planning, design and implementation. Within each stage the design decisions to be made are discussed, together with the techniques and skills required to complete each design stage. At each stage, reference is made to the views of other designers and researchers. Finally, the procedure is illustrated through a case study of a miniature FMS designed and installed at the Cranfield Institute of Technology.

Modeling flexible manufacturing systems with MAP/1

Abstract: There are many techniques available for performance modeling of flexible manufacturing systems, including computer simulation and queuing models. This paper presents MAP/1, a simulation-basedmodeling andanalysisprogram developed specifically for manufacturing systems. We begin with a short description of the MAP/1 program. This is followed by a discussion of special features available to support the modeling of flexible manufacturing systems. An example model illustrating these features is then presented.

Economic evaluation for the optimal introduction of flexible manufacturing technology under rivalry

Abstract: Unless procedures for the economic evaluation of flexible manufacturing technology are revamped, much of U.S. industry could repeat the experience of American automobile and steel companies from the recent past. The dynamic character of flexible manufacturing technology in terms of associated developments in microelectronics, a trend toward equipment modularity, and the increasing diversity of relevant markets make flexible manufacturing especially vulnerable to the weaknesses of conventional procedures for the justification of capital expenditures. Building on the work of V. Smith, M.I. Kamien and N.L. Schwartz, this paper presents optimization models from which economically reasonable plans can be derived for the implementation of flexible manufacturing technology. Although the assumptions of these models are not focused on the situation of a specific plant, model implications and the overall perspectives here on the economic evaluation of flexible system options should provide general guidance for manufacturing planners.

A problem expanding parametric programming method for solving the job shop scheduling problem

Abstract: A new zero-one integer programming model for the job shop scheduling problem with minimum makespan criterion is presented. The algorithm consists of two parts: (a) a branch and bound parametric linear programming code for solving the job shop problem with fixed completion time; (b) a problem expanding algorithm for finding the optimal completion time. Computational experience for problems having up to thirty-six operations is presented. The largest problem solved was limited by memory space, not computation time. Efforts are under way to improve the efficiency of the algorithm and to reduce its memory requirements.