This paper deals with the decision making for resource sharing and scheduling for a class of computer-integrated manufacturing cells. Each such cell is characterized by a set of resources and it can be used for the cyclic production of several products. The production (processing) of each product requires a set of operations with sequence constraints among them. Each operation can be performed using alternative modes. Each mode defines the subset of resources needed for the operation and the timing of their use. Resource setup times are sequence-dependent. The problem is to choose the best mode for each operation and, accordingly, to allocate and schedule resources in order to minimize make-span time. A general (feasible) mixed 0-1 LP model is proposed. A customized Branch and Bound type solution algorithm is presented, which fathoms only feasible solutions and finds all optimum solutions.