Cyclic production for the robotic balanced no-wait flow shop Fabien Mangione (*), Nadia Brauner(**), Bernard Penz(*) (*)GILCO, ENSGI-INPG, France 46, avenue Felix Viallet 38031 Grenoble cedex 1 {Fabien.Mangione,Bernard.Penz}@gilco.inpg.fr (**)Leibniz-IMAG, IUT2 dpt GEA, France 46 av. F´ elix Viallet, 38031 Grenoble Cedex Nadia.Brauner@imag.fr Abstract. In a no-wait robotic flow-shop, the parts are transferred from a machine to another one by a robot and the time a part can remain on a machine is fixed. The objective is to maximize the throughput rate of the cell, i.e. to find optimal cyclic robot moves. In this paper, we consider identical parts in the balanced case (all processing times are equal). We present a conjecture which gives the structure of the optimal production cycle and prove it for several cases. These results confirm Agnetis conjecture which claims that, in a no-wait robotic cell, the degree of the dominant cycles can be bounded by the number of machines minus one (which simplifies the search of an optimal production cycle). Keywords: Hoist Scheduling Problem, no-wait flow shop, flow-shop scheduling, optimal cycles. 1 Introduction In surface treatment lines, products are immersed in several tanks. The tanks contain chemical baths like acids which affect the electrical or mechanical properties of the products. This kind of line is used, for instance, for galvanoplasty or circuit board assembly. The products are mounted on carriers and transported from a tank to another one by a hoist. The time a part can stay in a tank is upper and lower bounded. The lower bound indicates the minimum time for a correct treatment. The upper limit is justified by the chemical properties of the baths. For instance, a product should not remain too long in an acid bath or the quantity of precious metal deposed should not be too important in order to minimize the costs. A classical objective is to find the cyclic hoist moves which yield the maximum throughput. This problem is usually called Cyclic Hoist Scheduling Problem (CHSP). We shall restrict the problem to the production of identical parts. (Lei & Wang 1989) showed that the CHSP is NP-complete. Different methods were proposed to solve this problem: Constraint Logic Pro- gramming (Baptiste, Legeard, Manier & Varnier 1996), Genetic Algorithm (Lim 1997) or Branch and Bound Algorithm (Ng 1996). A survey on those problems was proposed by (Baptiste, Bloch & Varnier 2001). The problem with unbounded processing windows (infinite upper bound) is usually called the Robotic Cell Scheduling Problem (RCSP). It was first studied by (Sethi, Sriskandarajah, Sorger, Blazewicz & Kubiak 1992). For quality reasons, it can be better for all products to remain exactly the same time in tank T i (for all i). This constraint can be modelled by a no-wait constraint in every tank (equal lower and upper bound). For those zero-width processing window problems, (Agnetis 2000) describes a conjecture which bounds the degree of the optimal cycles and proves 1 hal-00259546, version 1 - 28 Feb 2008 Author manuscript, published in "International Conference of Industrial Engineering and Production Management - IEPM, Porto : Portugal (2003)"