Open-Loop-Feedback Scheduling for Multi-stage Production Systems

The task of scheduling product orders and updating the schedule at each arrival of a new order, especially if received from an “important” client, is of crucial importance in Small-Medium Enterprises - SME. These firms, in fact, are often operating according to production-to-order with a variety of products whose amplitude depends on the industry. This note proposes a new procedure for dynamic scheduling, that means re- scheduling at the occurrence of a new job to be produced. The re-scheduling procedure is specifically developed for manufacturing SMEs, in which each job is defined: i) by a precise machining sequence that must be followed exactly; ii) by a date at which orders are released together with the necessary raw materials, and especially iii) by a delivery date that must be satisfied. Accounting for these strong constraints, from the theoretical point of view, the solution of the dynamic scheduling problem is obtained by applying the constraint programming approach, with an innovative formulation of matrix type. The manufacturing system is represented in terms of a multi-stage model, able to process a number of different products orders, each one to be manufactured according a specific “path”, i.e. a sequence of work centers. Each time a new order will arrive to the system, an upgrading of the schedule has to be done, and no assumption about the next arrival time neither the next order type and dimension can be done.As the need for a simple but robust procedure to re-scheduling is especially urgent in the field of footwear production, which contributes significantly to the export of “made in Italy”, the case study - to test the procedure - is derived from data of an FMS belonging to this sector, operating in southern Italy.