A characterization of associativity

A necessary and sufficient condition for associativity of a function is given, in terms of a particular relation being a function. The concept of an associative function is generalized to the concept of a function being asssociative relative to a sequence and a characterization of such relative associativity is also given. These two characteristics are applied to the problem of proving the associativity, or relative associativity, of a function

The nondeterministic divide

The nondeterministic divide partitions a vector into two non-empty slices by allowing the point of division to be chosen nondeterministically. Support for high-level divide-and-conquer programming provided by the nondeterministic divide is investigated. A diva algorithm is a recursive divide-and-conquer sequential algorithm on one or more vectors of the same range, whose division point for a new pair of recursive calls is chosen nondeterministically before any computation is performed and whose recursive calls are made immediately after the choice of division point; also, access to vector components is only permitted during activations in which the vector parameters have unit length. The notion of diva algorithm is formulated precisely as a diva call, a restricted call on a sequential procedure. Diva calls are proven to be intimately related to associativity. Numerous applications of diva calls are given and strategies are described for translating a diva call into code for a variety of parallel computers. Thus diva algorithms separate logical correctness concerns from implementation concerns

Considerations for Rapidly Converging Genetic Algorithms Designed for Application to Problems with Expensive Evaluation Functions

A genetic algorithm is a technique designed to search large problem spaces using the Darwinian concepts of evolution. Solution representations are treated as living organisms. The procedure attempts to evolve increasingly superior solutions. As in natural genetics, however, there is no guarantee that the optimum organism will be produced. One of the problems in producing optimal organisms in a genetic algorithm is the difficulty of premature convergence. Premature convergence occurs when the organisms converge in similarity to a pattern which is sub-optimal, but insufficient genetic material is present to continue the search beyond this sub-optimal level, called a local maximum. The prevention of premature convergence of the organisms is crucial to the success of most genetic algorithms. In order to prevent such convergence, numerous operators have been developed and refined. All such operators, however, rely on the property of the underlying problem that the evaluation of individuals is a computationally inexpensive process. In this paper, the design of genetic algorithms which intentionally converge rapidly is addressed. The design considerations are outlined, and the concept is applied to an NP-Complete problem, known as a Crozzle, which does not have an inexpensive evaluation function. This property would normally make the Crozzle unsuitable for processing by a genetic algorithm. It is shown that a rapidly converging genetic algorithm can successfully reduce the effective complexity of the problem

SIMULATION AND OPTIMIZATION OF A CROSSDOCKING OPERATION IN A JUST-IN-TIME ENVIRONMENT

In an ideal Just-in-Time (JIT) production environment, parts should be delivered to the workstationsat the exact time they are needed and in the exact quantity required. In reality, formost components/subassemblies this is neither practical nor economical. In this study, thematerial flow of the crossdocking operation at the Toyota Motor Manufacturing plant inGeorgetown, KY (TMMK) is simulated and analyzed.At the Georgetown plant between 80 and 120 trucks are unloaded every day, with approximately1300 different parts being handled in the crossdocking area. The crossdocking areaconsists of 12 lanes, each lane corresponding to one section of the assembly line. Whereassome pallets contain parts designated for only one lane, other parts are delivered in such smallquantities that they arrive as mixed pallets. These pallets have to be sorted/crossdocked intothe proper lanes before they can be delivered to the workstations at the assembly line. Thisprocedure is both time consuming and costly.In this study, the present layout of the crossdocking area at Toyota and a layout proposed byToyota are compared via simulation with three newly designed layouts. The simulation modelswill test the influence of two different volumes of incoming quantities, the actual volumeas it is now and one of 50% reduced volume. The models will also examine the effects ofcrossdocking on the performance of the system, simulating three different percentage levelsof pallets that have to be crossdocked.The objectives of the initial study are twofold. First, simulations of the current system,based on data provided by Toyota, will give insight into the dynamic behavior and the materialflow of the existing arrangement. These simulations will simultaneously serve to validateour modeling techniques. The second objective is to reduce the travel distances in the crossdockingarea; this will reduce the workload of the team members and decrease the lead timefrom unloading of the truck to delivery to the assembly line. In the second phase of theproject, the design will be further optimized. Starting with the best layouts from the simulationresults, the lanes will be rearranged using a genetic algorithm to allow the lanes withthe most crossdocking traffic to be closest together.The different crossdocking quantities and percentages of crossdocking pallets in the simulationsallow a generalization of the study and the development of guidelines for layouts ofother types of crossdocking operations. The simulation and optimization can be used as abasis for further studies of material flow in JIT and/or crossdocking environments

A Multiple Objective Formulation and Algorithm for the Layout Design of Food Processing Facilities.

A multiple objective formulation, which incorporates robustness and constraint enforcement as design criteria, is utilized to model the layout of food processing facilities. These facilities are subject to the compliance with guidelines dictated by public health agencies, changes in product mix, and variation in production levels due to seasonality, which render existing layout design algorithms unsuitable for their design. The solution of the robust multiple objective formulation is implemented using a construction heuristic algorithm, MORCH, and an improvement heuristics, MOLAD. The MORCH/MOLAD hybrid algorithm performs comparably to well known heuristic algorithms where materials handling cost is used as the only design criterion. Also, the MORCH/MOLAD solutions are more robust than those of robust heuristic algorithms. Moreover, through the use of a qualitative constraint matrix, the hybrid algorithm generates layouts that conform to guidelines imposed by U.S. regulatory agencies without significantly penalizing materials handling cost. As a qualitative constraint matrix in conjunction with materials handling cost are present in the model, a multicriteria decision making aid that deals with qualitative and quantitative factors, the Analytic Hierarchy Process, is used to select the most suitable layout and to guide the generation of and search for good alternative layout solutions by the hybrid algorithm

SIMAID: a rapid development methodology for the design of acyclic, bufferless, multi-process and mixed model agile production facilities for spaceframe vehicles

The facility layout problem (FL) is a non-linear, NP-complete problem whose complexity is derived from the vast solution space generated by multiple variables and interdependent factors. For reconfigurable, agile facilities the problem is compounded by parallelism (simultaneity of operations) and scheduling issues. Previous work has either concentrated on conventional (linear or branched) facility layout design, or has not considered the issues of agile, reconfigurable facilities and scheduling. This work is the first comprehensive methodology incorporating the design and scheduling of parallel cellular facilities for the purpose of easy and rapid reconfiguration in the increasingly demanding world of agile manufacturing. A novel three-stage algorithm is described for the design of acyclic (asynchronous), bufferless, parallel, multi-process and mixed-model production facilities for spaceframe-based vehicles. Data input begins with vehicle part processing and volume requirements from multiple models and includes time, budget and space constraints. The algorithm consists of a powerful combination of a guided cell formation stage, iterative solution improvement searches and design stage scheduling. The improvement iterations utilise a modified (rules-based) Tabu search applied to a constant-flow group technology, while the design stage scheduling is done by the use of genetic algorithms. The objective-based solution optimisation direction is not random but guided, based on measurement criteria from simulation. The end product is the selection and graphic presentation of the best solution out of a database of feasible ones. The case is presented in the form of an executable program and three real world industrial examples are included. The results provide evidence that good solutions can be found to this new type and size of heavily constrained problem within a reasonable amount of time