The In the paper, we investigate two single processor problems, which deal with the process of negotiation between a producer and a customer about delivery time of ﬁnal products. This process is modelled by a due interval, which is a generalization of well known classical due date and describes a time interval, in which a job should be ﬁnished. In this paper we consider two diffierent mathematical models of due intervals. In both considered problems we should ﬁnd such a schedule of jobs and such a determination of due intervals to each job, that the generalized cost function is minimized. The cost function is the maximum of the following three weighted parts: the maximum tardiness, the maximum earliness and the maximum due interval size. For the ﬁrst problem we proved several properties of its optimal solution and next we show the mirror image property for both of considered problems, which helps us to provide an optimal solution for the second problem.
Mathematical programming, constraint programming and computational intelligence techniques, presented in the literature in the field of operations research and production management, are generally inadequate for planning real-life production process. These methods are in fact dedicated to solving the standard problems such as shop floor scheduling or lot-sizing, or their simple combinations such as scheduling with batching. Whereas many real-world production planning problems require the simultaneous solution of several problems (in addition to task scheduling and lot-sizing, the problems such as cutting, workforce scheduling, packing and transport issues), including the problems that are difficult to structure. The article presents examples and classification of production planning and scheduling systems in the foundry industry described in the literature, and also outlines the possible development directions of models and algorithms used in such systems.
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.
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. 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 a mathematical programming model that formally defines the optimization problem and its relaxed version that is based on the conception of rolling-horizon planning
This paper reports a new multi-item planning and scheduling problem in a job-shop production system with the consideration of energy consumption. A mixed integer linear programming is proposed to integrate planning and scheduling with the consideration of energy aspect. In this study a new operational constraint is considered in the tactical level because of the huge interest given to energy consumption and its strong link existing with production system. To evaluate the performance of this model, computational experiments are presented, and numerical results are given using the software CPLEX and then discussed.
The paper concerns the two-machine non-preemptive flow shop scheduling problem with a total late work criterion and a common due date (F2|dj = d|Y ). The late work performance measure estimates the quality of a solution with regard to the duration of late parts of activities performed in the system, not taking into account the quantity of this delay. In the paper, a few theorems are formulated and proven, describing features of an optimal solution for the problem mentioned, which is NP-hard. These theorems can be used in exact exponential algorithms (as dominance relations reducing the number of solutions enumerated explicitly), as well as in heuristic and metaheuristic methods (supporting the construction of sub-optimal schedules of a good quality).
The paper refers to planning deliveries of food products (especially those available in certain seasons) to the recipients: supermarket networks. The paper presents two approaches to solving problems of simultaneous selection of suppliers and transportation modes and construction of product flow schedules with these transportation modes. Linear mathematical models have been built for the presented solution approaches. The cost criterion has been taken into consideration in them. The following costs have been taken into account: purchase of products by individual recipients, transport services, storing of products supplied before the planned deadlines and penalties for delays in supply of products. Two solution approaches (used for transportation planning and selection of suppliers and selection of transportation modes) have been compared. The monolithic approach calls for simultaneous solutions for the problems of supplier selection and selection of transportation modes. In the alternative (hierarchical) solution approach, suppliers are selected first, and then transportation companies and their relevant transportation modes are selected. The results of computational experiments are used for comparison of the hierarchical and monolithic solution approaches.
In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data simulating actual production parameters in one of the medium size foundry.
A novel approach for treating the uncertainty about the real levels of finished products during production planning and scheduling process is presented in the paper. Interval arithmetic is used to describe uncertainty concerning the production that was planned to cover potential defective products, but meets customer’s quality requirement and can be delivered as fully valuable products. Interval lot sizing and scheduling model to solve this problem is proposed, then a dedicated version of genetic algorithm that is able to deal with interval arithmetic is used to solve the test problems taken from a real-world example described in the literature. The achieved results are compared with a standard approach in which no uncertainty about real production of valuable castings is considered. It has been shown that interval arithmetic can be a valuable method for modeling uncertainty, and proposed approach can provide more accurate information to the planners allowing them to take more tailored decisions.
The problem considered in the paper is motivated by production planning in a foundry equipped with a furnace and a casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. 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. However, contrary to the classic approach, we assumed the fuzzy nature of the demand set for a given day. The paper describes a genetic algorithm adapted to take into account the fuzzy parameters of simultaneous grouping and scheduling tasks and presents the results achieved by the algorithm for example test problem.
The paper presents a novel Iterated Local Search (ILS) algorithm to solve multi-item multi-family capacitated lot-sizing problem with setup costs independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to clients. We extended existing models by introducing minimal utilization of furnace capacity during preparing melted alloy. We developed simple and fast ILS algorithm with problem-specific operators that are responsible for the local search procedure. The computational experiments on ten instances of the problem showed that the presence of minimum furnace utilization constraint has great impact on economic and technological conditions of castings production. For all test instances the proposed heuristic is able to provide the results that are comparable to state-of-the art commercial solver.
The problem of sequencing jobs on a single machine to minimize total cost (earliness and tardiness) is nowadays not just important due to traditional concerns but also due to its importance in the context of Collaborative Networked Organizations and Virtual Enterprises, where precision about promptly responses to customers’ requests, along with other important requirements, assume a crucial role. In order to provide a contribution in this direction, in this paper the authors contribute with an applied constructive heuristics that tries to find appropriate solutions for single machine scheduling problems under different processing times and due dates, and without preemption allowed. In this paper, two different approaches for single-machine scheduling problems, based on external and internal performance measures are applied to the problem and a comparative analysis is performed. Computational results are presented for the problem under Just-in-Time and agile conditions on which each job has a due date, and the objective is to minimize the sum of holding costs for jobs completed before their due date and tardiness costs for jobs completed after their due date. Additional computational tests were developed based on different customer and enterprise oriented performance criteria, although preference is given to customer-oriented measures, namely the total number of tardy jobs and the maximum tardiness.