International Journal of Production Research, 2016 Vol. 54, No. 3, 680–695, http://dx.doi.org/10.1080/00207543.2015.1030470 A mixed-integer programming approach to the parallel replacement problem under technological change ˙ I. Esra Büyüktahtakın a ∗ and Joseph C. Hartman b a Department of Industrial and Manufacturing Engineering, Wichita State University, Wichita, KS, USA; b College of Engineering, University of Massachusetts, Lowell, MA, USA (Received 25 October 2014; accepted 5 February 2015) The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed- integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances. Keywords: parallel equipment replacement; technological change; mixed-integer programming; optimization; cutting planes; US Postal Service (USPS) fleet management case 1. Introduction The parallel replacement problem under economies of scale (PRES) determines the minimum cost replacement policy for a group of economically interdependent and homogenous assets that operate in parallel and are subject to fixed and variable purchase costs. In this paper, we study the mixed-integer programming (MIP) formulation of PRES under technological change (PRES-T) by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. Increased capacity with the new technology leads to more efficient assets compared to older ones, and thus results in non-homogeneity among the assets owned. At the beginning of each decision-making period, the replacement decision is whether to keep an asset or to replace it with a new one. The assets are economically interdependent because budget constraints limit the number of new assets that can be purchased in each period (Karabakal, Lohmann, and Bean 1994), demand constraints require a number of assets in service each period in order to guarantee enough capacity to satisfy demand (Hartman 2000), or fixed replacement costs in the objective function necessitate collective replacement actions (Jones, Zydiak, and Hopp 1991). The parallel replacement problem has many applications in manufacturing and service industries, where the management of capital assets is vital to the efficiency and profitability of operations. These capital assets include drilling machines required to produce parts, trailers that carry goods or computers that store and process data. As assets are utilised overtime, they may become worn and deteriorate, resulting in increased operating and maintenance (O&M) costs and reduced capacity. For example, a drilling or cutting tool may deteriorate with time and require additional maintenance to perform its service and operations ( Akturk and Gurel 2007). Assets may also become obsolete, because technological improvements make it possible for newer assets to operate more efficiently, such that O&M costs are lower and capacity is higher than current assets. This is commonly observed in technological assets, such as computers or mobile communications equipment. Both the deterioration of the asset currently owned (defender) and technological advances of possible replacement assets (challengers) motivate the replacement of assets. The rate of technological improvements is one of the determinants of the rate of growth in productivity, which is the increase in the output of goods and services per hour worked (Mansfield, Mettler, and Packard 1980). Bartel, Ichniowski, and Shaw (2007) support this fact by showing that new technological investments improve the efficiency of all stages of the production process by reducing set-up times, runtimes, and inspection times with respect to computer numerically controlled machines. In this study, we incorporate technological improvements as increased capacity (number of products or services per unit time) of assets into the mathematical model. ∗ Corresponding author. Email: esra.b@wichita.edu © 2015 Taylor & Francis