A multi-period order selection problem in flexible manufacturing systems

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roduction A ¯exible manufacturing system (FMS) can be de®ned as an automated manufacturing system consisting of computer numerically controlled machines that are interconnected by a materials handling system, all controlled by a computer system. Although FMSs are highly capital-intensive, they have been widely implemented in various types, since they can give good productivity and ¯exibility at the same time. However, this can only be obtained if decision problems for FMSs are solved (near) optimally. Among four decision problems (design, system setup, scheduling and control) in FMSs, the system setup problem (alternatively called FMS planning problem) is concerned with decisions that have to be made before the FMS can begin to produce parts.1 This problem includes subproblems of selecting subsets of part types for immediate and simultaneous production, partitioning machines of each type into machine groups, allocating operations and associated cutting tools to machines or machine groups, and allocating pallets and ®xtures to the selected part types. These problems are called the part type selection problem, the machine grouping problem, the loading problem, and the resource allocation problem, respectively. When solutions to these problems are obtained and tools are loaded onto the tool magazines according to the solutions, production can start. In general, the part type selection problem is concerned with selecting a group of parts to be simultaneously produced in the system. This problem should be Correspondence: Dr Y-D Kim, Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Yusong-gu, Daejon 305-701, Korea. E-mail: [email protected]

considered ®rst before the other subproblems, since the others can be considered only after it is solved. For the part type selection problem, most previous studies employ single-period models, in which a set of part types is selected for an immediate and simultaneous production for a single upcoming production period (a new problem has tso be solved after these selected parts are completed). Unlike these, this paper considers a multiperiod version of the problem. The multi-period order selection problem considered in this paper is the problem of determining a set of orders to be produced in each period subject to the processing time capacity and tool magazine capacity constraints with the objective of minimising earliness and tardiness costs and subcontracting costs. Here, an order is de®ned by a part type, production quantity, and due date. In this research, the terminology of the order selection problem is used instead of the part type selection problem, since there may be different orders for the same part type, that is, parts of the same part type may have different due dates. In the objective, the earliness cost implies inventory holding cost, which is incurred if an order is ®nished earlier than its due date. The tardiness cost implies a shortage penalty (for example, opportunity costs or backorder costs), which is incurred if an o