Walter Ukovich

A mathematical for periodic scheduling problems

A mathematical model is proposed for scheduling activities of periodic type. First a model is proposed for scheduling periodic events with particular time constraints. This problem, which could be considered the extension to periodic phenomena of ordinary scheduling with precedence constraints, is shown to be NP-complete. An algorithm for it of implicit enumeration type is designed based on network flow results, and its average complexity is discussed. Some extensions of the model are considered. The results of this first part serve as a basis in modelling periodic activities using resources. Several cases are considered. Finally some applications are presented for which the proposed model can be a useful tool.

Minimizing Transportation and Inventory Costs for Several Products on a Single Link

This paper deals with the problem of determining the frequencies at which several products have to be shipped on a common link to minimize the sum of transportation and inventory costs. A set of feasible shipping frequencies is given. Transportation costs are supposed to be proportional to the number of journeys performed by vehicles of a given capacity. Vehicles may or may not be supposed to carry out completely all materials available, and products assigned to different frequencies may or may not share the same truck. Integer and mixed integer linear programming models are formulated for each of the resulting four situations, and their properties are investigated. In particular, we show that allowing products to be split among several shipping frequencies makes trucks traveling at high frequencies to be filled up completely. In this situation, trucks may always be loaded with products shipped at the same frequency.

A classification of DEA models when the internal structure of the Decision Making Units is considered

We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach.

A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem

Abstract This work deals with a dynamic dial-a-ride problem with time window constraints. In particular, new unplanned requests for service may arise at a vehicle stop and the driver must decide in real-time whether to accept or reject them. For this problem, we have developed a two-phase insertion algorithm based on route perturbations: the first phase, which is run off-line when the vehicle moves between two successive stops, aims at creating a feasible neighborhood of the current route; while the second phase, which is run in real-time every time a new request occurs, inserts, when possible, the delivery stop of the new customer in the current route.

On-line fault detection in discrete event systems by Petri nets and integer linear programming ☆

The paper addresses the fault detection problem for discrete event systems in a Petri Net (PN) framework. Assuming that the structure of the PN model and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown. The proposed diagnoser works on-line: it waits for the firing of an observable transition and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults. The results characterize the properties that the PN modelling the system fault behaviour has to fulfill in order to reduce the on-line computational effort.

Dynamic routing-and-inventory problems: a review

The paper presents a review of the available literature on a class of problems denoted as dynamic routing-and-inventory (DRAl) problems. They are characterized by the simultaneous relevance of routing and of inventory issues in a dynamic environment, within the framework of distribution logistics. A classification scheme is first proposed for these problems. Then the results obtained in this area are summarized. Finally, the papers available in the literature are clustered and discussed according to the proposed scheme.

DEA-LIKE MODELS FOR THE EFFICIENCY EVALUATION OF HIERARCHICALLY STRUCTURED UNITS

Abstract The knowledge of the internal structure of decision making units (DMUs) gives further insights with respect to the “black box” perspective when considering data envelopment analysis models. We present one-level and two-level hierarchical structures of the DMUs under evaluation. Each unit is composed of consecutive stages of parallel subunits all with constant returns to scale. In particular, the maximization of the relative efficiency of a DMU is studied. For the two-stage situation, different degrees of coordination among the subunits of the hierarchical levels are discussed. When some form of coordination has to be guaranteed, we introduce balancing constraints and we compare two different models. In both cases, we prove that the maximum relative efficiency of a DMU is assessed by comparing it with all the existing subunits.

Minimization of logistic costs with given frequencies

We study the problem of shipping products from one origin to several destinations, when a given set of possible shipping frequencies is available. The objective of the problem is the minimization of the transportation and inventory costs. We present different heuristic algorithms and test them on a set of randomly generated problem instances. The heuristics are based upon the idea of solving, in a first phase, single link problems, and of locally improving the solution in subsequent phases.

A Network Design Problem for a Distribution System with Uncertain Demands

A class of production--distribution planning problems with nonstochastic uncertain demands is modeled as a dynamic game between two players who control flows on a network with node and arc capacity constraints. Simple conditions are derived for determining which player wins the game. These conditions are then used to design a minimum cost network with the property that its feasible control strategies are allowed to meet the demand without violating the capacity constraints.

Linear programming approach to the control of discrete-time periodic systems with uncertain inputs

The problem is considered of finding a control strategy for a linear discrete-time periodic system with state and control bounds in the presence of unknown disturbances that are only known to belong to a given compact set. This kind of problem arises in practice in resource distribution systems where the demand has typically a periodic behavior, but cannot be estimated a priori without an uncertainty margin. An infinite-horizon keeping problem is formulated, which consists in confining the state within its constraint set using the allowable control, whatever the allowed disturbances may be. To face this problem, the concepts of periodically invariant set and sequence are introduced. They are used to formulate a solution strategy that solves the keeping problem. For the case of polyhedral state, control, and disturbance constraints, a computationally feasible procedure is proposed. In particular, it is shown that periodically invariant sequences may be computed off-line, and then they may be used to synthesize on-line a control strategy. Finally, an optimization criterion for the control law is discussed.