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This paper studies a facility location model in which two-dimensional Euclidean space represents the layout of a shop oor. The demand is generated by ÿxed rectangular-shaped user sites and served by a single supply facility. It is assumed that (i) communication between the supply point and a demand facility occurs at an input=output (I=O) point on the demand facility itself, (ii) the facilities themselves pose barriers to travel and (iii) distance measurement is as per the L 1 -metric. The objective is to determine optimal locations of the supply facility as well as I=O points on the demand facilities, in order to minimize total transportation costs. Several, increasingly more complex, versions of the model are formulated and polynomial time algorithms are developed to ÿnd the optimal locations in each case. Scope and purposeIn a facility layout setting, often a new central supply facility such as a parts supply center or tool crib needs to be located to serve the existing demand facilities (e.g., workstations or maintenance areas). The demand facilities are physical entities that occupy space, that cannot be traveled through, and that receive material from the central facility, through a perimeter I=O (input=output or drop-o =pick-up) point. This paper addresses the joint problem of locating the central facility and determining the I=O point on each demand facility to minimize the total material transportation cost. Di erent versions of this problem are considered. The solution methods draw from and extend results of location theory for a class of restricted location problems. For practitioners, simple results and polynomial time algorithms are developed for solving these facility (re) design problems. ?

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