| Abstract: | In job-lot production situations the decision must be made as to the number of units to start into production. Setup cost, unit cost, expected system yield, and salvage values of unacceptable and surplus acceptable units are parameters that can be considered when making the decision. If the expected yield is 100%, then the decision is to produce exactly the number needed. If the expected yield is less than 100%, the usual case, then some allowance must be made for the items rejected. The problem of determining this allowance is the 'reject allowance problem.' The purpose of this research was the development of exact mathematical cost models for small lots of job-lot production systems that are single-stage, serial multi-stage, or multi-stage with feed-forward or feed-back loops. In addition to the development of these models, Fortran programs were written to permit computer solutions of the models for the single-stage and serial multi-stage systems. The models are based on several concepts. First, disposition of each unit is independent of the disposition of all other units, i.e. disposition of a unit follows a multinomial distribution. If the system is single-stage or serial multi-stage in nature, the distribution is binomial. If the system has feed-forward or feed-back loops, the distribution is trinomial. Second, the exact optimal number of units will be started into each stage. Third, all reruns will begin at the first stage; there is no inventory of partially completed units at any stage. Fourth, inspection is done after all units started into a stage are through that stage. Fifth, in systems with loops, all units ready for entry into any stage for rework or recycling will be rejected at the time enough units are acceptable for the next primary stage or are through the system. These models provide a basis for continued research in the area of the 'reject allowance problem.' The Fortran programs are tools that can be utilized now by industry and business. |
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