Assessment of stock size to minimize cutting stock production costs J. Erjavec n , M. Gradisar, P. Trkman University of Ljubljana, Faculty of Economics, Kardeljeva ploˇ scˇad 17, 1000 Ljubljana, Slovenia article info Article history: Received 13 May 2008 Accepted 1 October 2010 Available online 8 October 2010 Keywords: Cutting stock problem Inventory management Cost minimization Simulation abstract A method for assessing the optimal stock size for the expected order size for a single-period one- dimensional cutting stock problem is proposed. The stock size is optimal when the expected total costs of trim loss, warehousing, and non-fulfilment are minimum. The stock size is the sum of all bar lengths in the stock, and the order size is the sum of shorter bar lengths in various numbers of pieces. Using simulated test cases, a statistical estimation of optimal stock size is conducted, which in our case is approximately 50% above the expected order. The proposed method can help company choose the appropriate level of stock to minimize their total costs. & 2010 Elsevier B.V. All rights reserved. 1. Introduction The main focus of past research examining the cutting stock problem (CSP), regardless of its type, has been trim loss minimiza- tion. There have been many methods (W¨ ascher et al., 2007) for solving the CSP since the seminal paper by Gilmore and Gomory (1961), which led to either heuristic or exact solutions. The problem that most papers deal with is how to fill orders of a certain number of small pieces by cutting available large pieces in stock in such a way that trim loss is minimized. Therefore a generalized definition of the problem used in literature is as follows: available materials have various dimensions, and orders are received as the number of pieces for each order. It is obvious that the trim loss of a given order depends on the available stock. Diversity in terms of stock lengths enables lower trim loss because there are more possible cutting options (Gradisar et al., 1999). A lower trim loss effect is also achieved if the stock is significantly less than the total order, but in this case other costs such as the costs of non-fulfilment rise rapidly. Various successful methods have been developed to address the CSP (Belov and Scheithauer, 2002; Gradisar et al., 1999; Suliman, 2006), with some approaches resulting in less than 0.1% trim loss (Gradisar and Trkman, 2005). There is little room for a trim loss improvement when specific cutting stock algorithms are considered. However, reducing production costs can be one key factor to increasing competitiveness (Demeter, 2003). Therefore, in the last few years the main research focus has shifted to approaches that apply multiple criteria to optimize the CSP and that also encompass other parts of the production process. Arbib and Marinelli (2005) introduced a model that integrates short-term and mid-term planning decision levels and functional areas of production and purchasing. Other authors point out that cutting is merely one part of the cutting stock process and as such should be viewed through a broader perspective to increase a company’s competitiveness (Erjavec et al., 2009). Optimizing the cutting stock process in production is also discussed in Keskinocak et al. (2002), in which interactions between different stages of production are considered. Similarly, Suliman (2001) developed a method to determine the production schedule while minimizing trim loss. Some also note that cutting stock algorithms should be linked with other decision-support tools (Rodriguez and Vecchietti, 2008; ˇ Cizˇman and ˇ Cerneticˇ, 2004), with the input for the algorithm being selected by criteria defined by a decision-support tool enabling better overall business performance. Some solutions are also used to provide forecasts for future stock sizes (Lin, 2005). Several costs in addition to trim loss costs that primarily relate to inventory management – such as warehousing costs, unfilled order costs, insurance costs, holding costs, transportation costs, and packing costs – can be taken into consideration when mini- mizing total cutting costs (Trkman and Gradisar, 2003; Arbib and Marinelli, 2005). Cochran and Ramanujam (2006) also address the importance of lowering the overall costs of logistics directly connected to the production process and they propose a methodology for choosing a third-party logistics provider. The costs also depend on the type of stock that the company holds (Holthaus, 2003). The stock could consist of only one standard size of material, or it could have different sizes up to the point where all units in stock differ from one another. Substantial savings can be achieved by selecting a type of stock with more than only one standard size. Estimating future orders is also important when seeking to decrease costs. When orders are uncertain, the costs of stock can be decreased through better forecasts of future demand. Even if a company already has forecasts, additional improvements Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.10.001 n Corresponding author. Tel.: + 386 1 589 2400; fax: + 386 1 589 2698. E-mail addresses: jure.erjavec@ef.uni-lj.si (J. Erjavec), miro.gradisar@ef.uni-lj.si (M. Gradisar), peter.trkman@ef.uni-lj.si (P. Trkman). Int. J. Production Economics 135 (2012) 170–176