The Optimum Upper Screening Limit and Optimum Mean Fill Level to Maximize Expected Net Profit in the Canning Problem for Finite Continuous Distributions

Abstract

The “canning problem” occurs when a process has a minimum specification such that any product produced below that minimum incurs a scrap/rework cost and any product over the minimum incurs a “give-away” cost. The objective of the canning problem is to determine the target mean for production that minimizes both of these costs. An upper screening limit can also be determined; above which give-away cost is so high that reworking the product maximizes net profit. Examples of the canning problem are found in the food industry (filling jars or cans) and in the metal industry (thickness.)

In this dissertation, continuous, finite range space distributions are considered, specifically the Uniform and Triangular distributions. For the Uniform distribution, an optimum upper screening limit and an optimum value for the mean fill level is found using three net profit models. Each model assumes a fixed selling price and a linear cost to produce, but costs differ as follows: ? Model 1 uses fixed rework/scrap and reprocessing costs ? Model 2 has linear rework/scrap and reprocessing costs, and ? Model 3 has fixed rework/scrap and reprocessing costs but adds an additional, higher cost associated with a limited capacity of the container. A discussion is included relating the selection of an optimum set point for the mean to process capability. For the Triangular distribution, an optimum upper screening limit and an optimum value for the mean fill level is found for both the symmetrical and skewed cases using a net profit model that has fixed rework/scrap and reprocessing costs.