An Abstract Representation And Analysis of Production Lines With Inter-Stage Storage
This thesis presents a novel methodology to represent a production system with inter-stage storages and variable cycle times. The 'abstract representation', which employs no approximation and is not based on probability, involves: (1) completely representing a system with stages and storages by elements only, each of which contains one stage and some storages, (2) measuring each element independently by supplying a predefined probing rate of job flow across an element and (3) formulating the instantaneous relationships between the independent measurements and system parameters.
This 'abstract representation' is then illustrated by three different problems. The first problem involves on-line system monitoring which requires locating the origins of production loss in a system in real-time. The 'abstract representation' is used to derive the instantaneous relationships between the causes and effects of system production loss among the elements to address this problem.
After the instantaneous relationships between the causes and effects of production loss are derived, a natural extension of this is to apply these relationships to address the problems concerning system performance improvements. Therefore, this thesis will address the second and third problems which are system production control and storage allocation.
The objectives of production control as defined in (Ryzin et al. 93) are to control the system so that one job will be produced in one unit time and to minimize the inventory in the (infinite) inter-stage storage. In this thesis, an algorithm will be derived to address the problem of production control. This algorithm is based on the instantaneous relationships between the causes and effects of production loss and will be designed to theoretically accommodate systems of any size with arbitrary cycle time behaviours. The storage capacities of the system are finite and can have any value. Therefore, the minimization of inventory being carried in an infinite storage is not pan of the objective of the production control algorithm in this thesis. This production control algorithm will calculate the maximum allowable cycle time for each stage for each cycle, so that if these maximum allowable cycle times are met by the stages, the goal of production control can be achieved. Furthermore, the maximum allowable cycle times calculated by the production control algorithm in this thesis will be bounded below so that the maximum cycle time values should fall within an acceptable range.
The goal of storage allocation in a system is to find the amount of storage space between the stages which yields the maximum system efficiency for a certain type of cycle time distribution while satisfying a set of pre-defined constraints. In this thesis, a preliminary study will be undertaken for this problem with the constraint being that the total available storage space is fixed. This preliminary study tries to show that the approximated long term relationships between the causes and effects of production loss can be helpful in providing insights which help solve the problem of storage allocation.