Annals of Operations Research 107, 15–32, 2001  2002 Kluwer Academic Publishers. Manufactured in The Netherlands. Set-Up Coordination between Two Stages of a Supply Chain A. AGNETIS and P. DETTI Dipartimento di Ingegneria dell’Informazione Università di Siena, Siena, Italy {agnetis, detti}@dii.unisi.it C. MELONI and D. PACCIARELLI {meloni, pacciarelli}@dia.uniroma3.it Dipartimento di Informatica e Automazione, Università Roma Tre, Roma, Italy Abstract. In the material flow of a plant, parts are processed in batches, each having two distinct attributes, say shape and color. In one department, a set-up occurs every time the shape of the new batch is different from the previous one. In a downstream department, there is a set-up when the color of the new batch is different from the previous one. Since a unique sequence of batches must be established, the problem con- sists in finding such a common sequence optimizing an overall utility index. Here we consider two indices, namely the total number of set-ups and the maximum number of set-ups between the two departments. Both problems are shown to be NP-hard. An efficient heuristic approach is presented for the first index which allows to solve a set of real-life instances and performs satisfactorily on a large sample of experimental data. Keywords: scheduling, coordination, supply chain 1. Introduction This paper addresses a problem arising in the coordination between two consecutive stages of a supply chain. Although supply chains are a hot topic in logistics and op- erations management research, the scheduling of supply chains has not received quite the same attention so far, as pointed out in the recent comprehensive review by Thomas and Griffin [7]. At the operational level, a number of interesting coordination problems exist which have not yet been effectively modeled. These problems concern the way in which two consecutive stages should organize their internal work, taking into account the requirements of the other stage. The models considered in this paper arise from an application in a real industrial context, namely a plant in which a large number of different slabs of wood are cut, painted and assembled to build kitchen furniture. In different departments of the plant, items are grouped according to different attributes. In the cutting department, parts are grouped according to their shape and material, in the subsequent painting department parts are grouped according to their color, and finally the assembly of the furniture is organized on the basis of kitchen models. In this paper we analyze coordination issues between the first two stages, and therefore we are only interested in two attributes, which for simplicity we call shape and color.