フロー・ショップとそのスケジュールの解析

抄録

A definite description of the flow shop scheduling problems and their analytic results are presented here.
A job shop can be regarded as consisting of three kinds of components, i.e. the work station, the intermediate pool and the transport way. The reverse flow shop is defined as a shop having a flow direction opposite to that of the primal flow shop.
It makes our problems more practical and more flexible to introduce two more concepts; one is the initial condition and the other is the terminal condition. They represent the desired shapes at the beginning and at the end of the Gantt chart of the solution, respectively. Also, a generalized objective function is adopted, which can be used to estimate the idling cost of any set of work stations, the rate of operations in the shop, etc.
On the basis of these ideas, two types of deterministic scheduling problems (the Primal Problems) and their Reverse Problems (the same types of problems concerned with the reverse flow shop) are defined.
The authors are sure that the separation of the definition of shops from that of problems makes it possible to systemize various job shop problems and to utilize scheduling theory for system design.
The main results can be stated briefly as follows.
(1) A theorem which gives one of the principal methods to get the lower bounds of a class of functions including the objective function adopted.
(2) Four theorems concerned with the properties of the solutions and the structures of our generalized primal problems.
(3) Two theorems stating the mutuality of the solutions of the primal and the reverse problems.
These results would be very useful for the construction of the effective algorithms for the solution of the scheduling problems.