Production Scheduling for the Furnace - Casting Line System

Abstract

The problem considered in the paper is motivated by production planning in a foundry equipped with the furnace and casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The quantity of molten metal does not exceed the capacity of the furnace, the load is a particular type of metal from which the products are made in the automatic casting lines. The goal is to create the order of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and scheduling problem. The paper describes two computational intelligence algorithms for simultaneous grouping and scheduling tasks and presents the results achieved by these algorithms for example test problems.

Production Scheduling under Fuzziness for the Furnace - Casting Line System

“…In this paper, the mathematical programming model presented earlier [7] for a small foundry has been extended to more complex problem, in which demand is expressed in the form of fuzzy numbers. The model is based on a well-known lot-sizing problem extended to handle the fuzzy constraints.…”

“…In [3] we have presented three different strategies on how to represent a schedule for a foundry as a chromosome. Later [7] we have focused on the most efficient one regarding the memory complexity. In the representation that is shown in Figure 1 the vector coding the solution consists of three parts (segments in a chromosome): vectors x representing the quantity of items that are produced in a given subperiod, vectors o representing the orders' numbers of the produced items, and vector a representing alloy type that is produced in this subperiod.…”

Mathematical modeling to optimize production planning and scheduling in a small foundry with multiple alternating furnaces

“…Li et al (2017) present a mathematical profit maximization model for production planning in a market foundry with a flow shop system and limited capacity. Models with multiple furnaces, aiming to minimize setup costs, inventory, and item backlog are found in Silva and Morabito (2004) and Stawowy and Duda (2020), which consider production lines in which the furnaces can be used in parallel, i.e., simultaneously.…”

Application of Interval Arithmetic to Production Planning in a Foundry

“…Planning horizon is T=5 days with N=10 subperiods. Demand dit has been generated in a random way from the range [10,60], weight of castings wi from the range [1,30] and the setup for alloy stk from the range of [5,10]. The only change introduced to the test data is the percentage value of defective products and it was generated for each order from the range of [1%-20%].…”

“…The first three rows represent the interval for valuable items produced in subsequent subperiods, the next three rows represent the numbers identifying different orders, and the last row repents the number identifying the alloy type. The same genetic operators as in [10] were used, i.e. onepoint crossover and three types of the mutation operator: first mutation that alters the number of produced items (x vectors), second mutation that can alter the orders (o vectors) and third mutation altering the alloy type (vector a).…”