Some Open Problems in the Design and Use of Modern Production Systems

During the past two decades, manufacturing systems have moved towards automation, integration and modularity. These trends will certainly continue in the future due to the constraints of the market and to evolution of the resources and worker requirements. As a consequence, design and use of manufacturing systems are increasingly expensive. Numerous methods and tools have been developed to face up to this situation, but some complementary aids could be provided for designers and manufacturing engineers. The goal of this paper is to present important open problems whose solutions could certainly improve significantly the design and use of the modern production system

Single Machine Scheduling with Discrete Earliness and Tardiness

This paper considers the problem of scheduling a given set of jobs on a single machine in order to minimize the total weighted earliness and tardiness costs. The scheduling horizon is divided into elementary periods; jobs have due-dates at the end of these periods. All jobs are assumed initially available. Jobs have unique (weighted) early and tardy staircase penalty functions. No preemption of jobs is permitted. and idle time may be inserted. We prove that this problem is NP-complete. Some results relating to job priorities and completion times in an optimal solution are presented. A Mixed Integer Linear Programming (MILP) formulation of this problem is developed. A branch-and-bound scheme that solves the above problem optimally is also presented. Heuristics, derived from simple priority rules, provide an initial upperbound to the search. We develop two lower bound procedures for the remaining jobs to be scheduled at any partial solution state. Numerical results relating to the performance of the branch-and- bound scheme are also presented

An Efficient Heuristic in Manufacturing Cell Formation for Group Technology Applications.

In this paper, the problem of finding a good decomposition of the manufacturing system into manufacturing cells, that can be assigned to part families is addressed. A simple twofold heuristic algorithm capable of minimizing the inter-cell material movement, and addressing industrial applications of realistic dimensions is presented. The first step of the proposed heuristic is a bottom-up aggregation procedure to minimize the "Normalized InterClass Traffic". The second step is a procedure to attempt further improvement, in which the significance of a machine to a cell is validated

Event Graphs for Modeling and Evaluating Modern Production Systems

Very few Mathematical Tools are available to study the dynamics of discrete manufacturing systems. Petri Nets, and in particular a special type of Petri Nets called Timed Event Graphs, seem to be of special interest for studying discrete manufacturing systems. In this paper, we define Timed Event Graphs and emphasize the properties which are of interest for out purpose. Modeling job-shop systems as well as assembly systems using event graphs is then explained. The model obtained is a strongly connected event graph whose properties are presented in the first part of the paper. These properties are used to derive the properties of the manufacturing system. In particular, it can be shown that the productivity of the manufacturing system is defined by the cycle time of the critical circuit in its event graph model. Blocking conditions of the system are also studied.Finally, we show how to use the previous results to maximize the productivity with a minimal in-process inventory when the sequences of product types are fixed at the entrance of each machine

Manufacturing Cell Design Using Simulated Annealing: an Industrial Application

In this paper, we give a brief summary of simulated annealing procedures used to solve combinatorial optimization problems. We then present the manufacturing cell design problem which consists of designing cells of limited size in order to minimize inter- cell traffic. We show how to use a SA approach to obtain a good, if not optimum, solution to this problem. Finally, we apply this approach to an industrial problem and compare the results to the ones obtained using the so-called twofold heuristic algorithm

Hierarchical Production Planning for Complex Manufacturing

A hierarchical approach to production planning for complex manufacturing systems is presented. A single facility comprising of a number of work-centers that produce multiple part types is considered. The planning horizon includes a sequence of time periods, and the demand for all part types is assumed to be known. The production planning problem consists of minimizing the holding costs for all part types as well as the work-in- process, and the backlogging cost for the end items. We present a two- level hierarchy that is based on aggregating parts to part families, work-centers to manufacturing cells and time periods to aggregate time periods. The solution at the aggregate level is imposed as a constraint to the detailed level problem which employs a decomposition based on manufacturing cells. This architecture uses a rolling horizon strategy to perform the production management function. We have employed perturbation analysis techniques to adjust certain parameters of the optimization problems at the detailed level to reach a near- optimal detailed production plan

Multiple Routings and Capacity Consideration in Group Technology Applications.

This paper addresses the problem of manufacturing cell formation, given multiple part routings, and multiple functionally similar work-centers. The suggested choice of part routings favors the decomposition of the manufacturing system into manufacturing cells in a way that minimizes part traffic, along with satisfying the part demand and work-center capacity constraints. The proposed heuristic, iteratively solves two independent problems: (i) routing selection, and (ii) cell formation. The common objective is to minimize the inter-cell traffic in the system. The first problem is formulated as a linear-programming problem, while the latter is approached by an existing bottom-up aggregation procedure, known as Inter-Cell Traffic Minimization Method (ICTMM), enhanced appropriately. Applications of the proposed system include: (i) the design of a manufacturing facility with respect to machine layout, (ii) selection of part routings for changing product mixes, and (iii) assignment of new parts to part families, given the initial layout

Temporal Aggregation in Production Planning

In this paper, the problem of temporal aggregation in production planning is addressed. A single facility with multiple part types is considered. The planning horizon consists of a sequence of elementary time periods, and the demand for all part types is assumed to be known over these periods. The production planning problem consists of minimizing the holding and backlogging cost for all part types. Due to usual errors in demand forecasting, and due to the large size of the linear programming problem commonly encountered in such problems, there is a need for aggregating the production variables over the time horizon (typically, for weekly to monthly) to result in a hierarchical structure. We consider a two-level hierarchy composing a sub- problem at each level, and we propose an iterative technique which solves these sub-problems in sequence. A posteriori bounds are developed, which are useful in evaluating the performance of the iterative algorithm. Quick lover and upper bounds of the original problem are also developed. Finally, numerical results for numerous test cases are presented