Determining the Minimum Sum of Production Order Delays in a Two-Machine System

Abstract

One of the main tasks in the planning of production processes is to satisfy the needs of the customers in terms of quantity, quality and time. The issue of the timely execution of production orders is becoming increasingly important. Based on the conducted studies it can be concluded that the size of the delay depends on the adopted scheduling of orders. This paper focuses on the problem of implementing a scheduling of production orders that will allow to avoid delays, and in the event such a scheduling is not possible, for minimizing the sum of delays of all the orders. A new algorithm has been proposed that allows to determine of the optimal sequence of production orders with the minimum sum of delays. The considerations have been limited to the issue of a two-machine system in which the orders are carried out in a flow.

Minimization of Delay Costs in the Realization of Production Orders in Two-Machine System

“…This method is a generalisation of two methods: a method of scheduling of the production orders with the minimal sum of the delay costs in a one-machine system [2] and a method of scheduling of the production orders with the minimal sum of the delay time in a two-machine system [5].…”

“…While all c(i) = 0 i k(i) = 1, i = 1, …, n, then the problem comes down to determining the sequence that would give the minimum sum of the delay time, then p(i) means the lack of the time reserve (see [5]). Moreover, when all t 2 (i) = 0, the problem is reduced to onemachine problem (see [2]).…”

“…The designed algorithm uses the method of branch and bounds and is a particular generalisation of the algorithm enabling for the determination of the sequence of the production orders with the minimal sum of delays that was described in the research [5]. In order to illustrate the proposed algorithm in a proper manner, chapter 4 contains graphical trees of solutions.…”