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Computers & Operations Research
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Planning production using mathematical programming: The case of a woodturning company
Rafael Pastor a,b,∗ , Jordi Altimiras b , Manuel Mateo b
Institute of Industrial and ControlEngineering (IOC), Spain Department of Management, Technical University of Catalonia, Spain
A R T I C L E
I N F O
A B S T R A C T
Available online 13 August 2008 Keywords: Production planning Mixed-integer linear programming
Herein we present a case of production planning in a woodturning company. The company wishes to plan the turning of various types of products of different radiiin a set of parallel machines (lathes) and with the following principal conditions: for each type of product there is a minimum production lot size; some lathes cannot manufacture every type of product; the production capacity of a lathe depends on the lathe itself and the type of product to be manufactured; the products are classified into families according to radius; and there is anintra-family setup time (for manufacturing different products that have the same radius) and an inter-family setup time (for consecutively manufacturing products that have different radii), which is longer; part of the production can be subcontracted; each type of product can be manufactured on different lathes and/or subcontracted; and the operators can work overtime, during which additional time they cansimultaneously operate multiple lathes. The goal is to meet the demand at minimum cost, which includes the cost of any overtime plus that of any subcontracting. The problem was modelled and solved by mixed-integer linear programming (MILP). The company considers the results to be satisfactory. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction The production planning problem is common tomany production systems, and typically implies assigning the required tasks to the available resources. Given its combinatorial nature, the planning problem—which consists in determining the number of products to be produced in a set of parallel machines—is often very difficult to solve optimally; this is especially true when additional factors such as setup times must be considered. This workdeals with the problem of production planning in a woodturning company. The function of said planning is to establish the delivery dates of orders and to produce at minimum cost. Planning is presently done manually. It is time-consuming and inefficient and, according to the company, could be improved. Moreover, the results depend on the experience of the planner. Therefore, our goal was to improveand facilitate the planning process while maintaining all the constraints on the company's production system. The purpose of the paper is to describe, model and solve optimally a problem of planning and scheduling in a real-life production
∗ Corresponding author at: IOC—Institute of Industrial and Control Engineering, Av. Diagonal 647 (Edif. ETSEIB), 11th floor, 08028 Barcelona, Spain. Tel.: +34 93 401 17 01; fax: +34 93 401 66 05. E-mail addresses: firstname.lastname@example.org (R. Pastor), email@example.com (M. Mateo).
system. The problem seeks to meet the demand for different products at the lowest cost, subject to capacity constraints, setup times, the possibility of overtime and subcontracting and some other conditions. A mixed-integer linear program (MILP) is proposed for planningand scheduling the woodturning operations; the optimal solution can be reached quite fast with standard optimisation software. The company is located in Spain and works with cylinders of wood which are turned to obtain the final product. In a given window of time (the planning horizon), the company must manufacture a specific demand quantity of each type of product. In addition to using its...