Preliminary Draft - To be rewritten.
Equipment Costs: Equipment costs concern purchasing as well as operating and maintenance costs for machinery, tools and corresponding supplies. There exist various processing and equipment
alternatives and therefore the choice of equipment and the task assignment to stations becomes interrelated decisions.
Graves and Lamar  were among the first to consider a line balancing problem combined with equipment choice by considering non-identical workstations.
Bukchin and Tzur  optimized equipment cost respectively, for simple lines.
Nicosia et al.  also studied this problem and proposed a dynamic programming algorithm addressing resource assignments,
approximate solution approaches were used to produce solutions for FMS [Chen and Ho, 2005]. Following a multiobjective approach and making use of Pareto dominance relationships, Chen and Ho  addressed four criteria: total flow time, machine workload unbalance, greatest
machine workload and total tool cost.
Bukchin and Rabinowitch  relaxed the assumption that a common task of different models is assigned to a single station. They also attempted the mixed model line problem. However, task
duplications are penalized through duplication costs in the objective function. For solution, a branch and bound solution algorithm was developed.
Pekin and Azizoglu  generalized the work of Bukchin and Tzur  by minimizing total equipment cost and total number of workstations simultaneously. They generated the set of non-dominated solutions.
Similarly, addressing resource assignments, Corominas et al.  formulated a general
model that minimizes total cost, which includes fixed station costs and unit cost of different resource types.
Barutcuoglu and Azizoglu  investigated the same problem, however they fixed the number of stations and added the assumption that operation time and equipment cost are correlated so that the cheaper equipment never produces shorter operation time.
Kazemi et al.  extended the model of Bukchin and Rabinowitch  for U-type lines. The authors used genetic algorithms to solve the problem.
S.C. Graves and B. W. Lamar. An integer programming procedure for assembly system design problems. Operations Research, 31(3):522–545, 1983.
J. Bukchin and M. Tzur. Design of flexible assembly line to minimize equipment cost. IIE Transactions, 32(7): 585–598, 2000.
G. Nicosia, D. Pacciarelli, and A. Pacifici. Optimally balancing assembly lines with different workstations. Discrete Applied Mathematics, 118:99–113, 2002.
Y. Bukchin and I. Rabinowitch. A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs. European Journal of Operational Research, 174(1):492–508, 2006.
N. Pekin and M. Azizoglu. Bi criteria flexible assembly
line design problem with equipment decisions. International
Journal of Production Research, 46(22):6323–
A. Corominas, L. Ferrer, and R. Pastor. Assembly line
balancing: general resource-constrained case. International
Journal of Production Research, 49(12):3527–
S.M. Kazemi, R. Ghodsi, M. Rabbani, and R. Tavakkoli-Moghaddam. A novel two-stage genetic algorithm for a mixed-model U-line balancing problem with duplicated tasks. The International Journal of Advanced Manufacturing Technology, 55(9-12):1111–1122, 2011.
Transfer Line Balancing
Another optimization area that focuses on equipment selection is transfer line balancing [Belmokhtar et al., 2006, Dolgui et al., 2006c,a, 2012, Battaia and Dolgui, 2012, Borisovsky et al., 2012, Delorme
et al., 2012]. In these systems, stations can be equipped with changeable units such as spindle heads. These units that operate parallel at a station are called blocks. The problem is to figure out the optimum number of stations and block assignments so that total line investment cost is
When assembly line balancing and equipment selection problems are simultaneously treated, the resulting more complex problem is called assembly system design problem (ASDP). It
associates the equipment selection for task requirements and task assignment to the stations. In this concurrent decision, a cost-based objective such as the fixed cost of installing the equipment in the stations and the variable cost of operations depending on the station is optimized.
[Pinnoi and Wilhelm, 1997b,a, Wilhelm, 1999, Pinnoi and
Wilhelm, 1998, Gadidov and Wilhelm, 2000, Pinnoi and
Wilhelm, 2000, Wilhelm and Gadidov, 2004].
Ozdemir and Ayag  have examined a multi-criteria ASDP. They integrated the branch and bound and analytic hierarchy process (AHP) so that first, the branch and bound generates line design candidates, then, these alternatives are assessed with AHP method to choose the optimal candidate.
Reconfigurable Manufacturing Systems (RMSs)
One of the main challenges of industry is to respond to the rapid changing demands of the customers. Accordingly, reconfigurable manufacturing systems (RMSs), which give emphasis to modularity and customization of machines and processes, has been widely employed recently.
RMSs facilitate manufacturing systems that can change configuration such as altering the layout or adding machines cost effectively [Dolgui and Proth, 2010].
Integer programming models minimizing equipment and installation cost and approximate solution methods are generally used [Youssef and ElMaraghy, 2007, Essafi et al., 2010, Dou et al., 2011].
A heuristic approach based on a Greedy Randomized Adaptive Search Procedure (GRASP) has also been proposed for this problem [Essafi et al., 2012].
An other case has been studied by Hamta et al. [2011, 2013], who modeled flexible operation times in the sense that with additional costs task times can be reduced up to a limit. A linear time/cost relationship was assumed.
Reference for the main content of the paper
Oncu Hazi r, Xavier Delorme and Alexandre Dolgui, "A Survey on Cost and Pro t Oriented
Assembly Line Balancing," Preprints of the 19th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 24-29, 2014