به حداکثر رساندن میزان بازدهی سرمایه مورد استفاده در بازسازی ظرفیت حمل و نقل  Maximizing the rate of return on the capital employed in shipping capacity renewal

1. Introduction Among the most crucial decisions for a shipping company, the composition of the fleet of ships determines, to a great extent, the competitiveness of the company. Finding the best adaption of the fleet to volatile market conditions is the main scope of the Maritime Fleet Renewal Problem (MFRP), which consists of deciding how many and which types of ships to add to the fleet and which available ships to dispose of (see, e.g., [3,30,31]). The MFRP can be considered a special version of the Capacity Expansion Problem (CEP) or of the Machine Replacement Problem (MRP). CEPs seek the best addition to available capacity in order to meet increasing demand, while MRPs seek the best substitution of available machines, induced by factors such as obsolescence [29], deterioration, and ageing. In CEPs and MRPs the terms “capacity” and “machine” generically refer to equipment of various types, such as, cables, pumps, computers, and vehicles [33], with differences in, for example, economic life, cost magnitude, and relevance for the core business. CEPs and MRPs have received considerable attention by the operations research community, producing a plethora of models at increasing level of realism, and adapting to various operating configurations. For example, Fong and Srinivasan [12] consider multi-period capacity expansion and location, Li and Tirupati [22] focus on the trade-off between specialized and flexible capacity in multi-product production systems, Cormier and Gunn [10] consider warehouse capacity expansion under inventory constraints, Kimms [19] combines capacity expansion with production planning and lot sizing, van Ackere et al. [40] study the short-term problem of adjusting the capacity in reaction to the behavior of customers waiting in queues, while Ahmed et al. [2] and Bean et al. [4] study CEPs under uncertainty. The main issues faced in CEPs are related to expansion size, time, and location [24] and the option of replacing machines is typically ignored [33]. As far as MRPs are concerned, Sethi and Chand [37] consider the replacement of single machines with only one replacement alternative, while Chand and Sethi [6] allow the possibility of replacing available machines by any from a set of available alternatives. Goldstein et al. [14], Nair and Hopp [29], Hopp and Nair [16], and Adkins and Paxson [1] consider replacement decisions triggered by technological breakthroughs. Typically, MRPs do not consider the possibility of changes in the demand for equipment. Capacity expansions and replacements are however naturally tied decisions (see, e.g., [34,33,35,7]).