A procedure for the evaluation of the characteristics of cost, time and recycle elements in flow processes

Abstract

Flow processes are characterized by a set of actions (operations) related to an appropriately defined unit and a set of paths (arcs) along which the units may travel form one operation to another. Recycle elements in such processes make the evaluation of cost and time values difficult. These recycle effects are assessed though procedures presented in this research paper. These values are then used to determine how the cost and time parameters are affected and how the buffers between operations are affected in processes for homogenous and nonhomogeneous units. The concept of a maximal flow process is presented. A procedure to adjust the standard cost values, as calculated by current methods for the assumption of 100 percent yield of good units, is developed. The use of cost modelling -- flow process analysis with respect to cost -- procedures allow the assessment of standard costs at each operation, but adjusts these costs relative to the recycle effects of the process. Determining the composition of all loops (operation sequences with one repletion) and paths (no repetitions) in a network is accomplished using a finite step, iterative, search algorithm. The general structure of the loops and paths in the order they are identified is presented. Appendix A discusses the maximum number of loops and paths that will exist in any n-operation process. The structure of the loops and paths are used in the evaluation of the recycle effects on through-put. This procedure uses the non-zero flow proportions and the loop and path structure to form the equivalent of the first column in the inverse of the coefficient matrix, in the linear equations describing the flow process. Matrices are not used, but elements of the inverse of the coefficient matrix can be evaluated. Cost mean and variance estimates are obtained using the through-put evaluations. Using the capacity indicator, the production requirement, the flow proportions and the through-put at each operation, the levels of buffers between adjacent operations are assessed for blocking, idle and variable operation performance characteristics. Capacities are assessed to provide process balance under the given assumptions, when the process is a network of queuing systems. The mean and variance of the buffer queues are assessed using these capacities. Cost, time and buffer characteristics of process for non-homogenous units are assessed using a travel ticket concept. This approach was simulated, using GPSS, for a 5 operation maximal process with two types of units. Examples of all procedures are given.