Gaia Nicosia

Optimally balancing assembly lines with different workstations

In this paper, we consider the problem of assigning operations to an ordered sequence of non-identical workstations, observing precedence relationships and cycle time restrictions. The objective is to minimize the cost of the workstations. We first present a dynamic programming algorithm, and introduce several fathoming rules in order to reduce the number of states in the dynamic program. A characterization of a wide class of polynomially solvable instances is given, and computational results are reported.

A job-shop problem with one additional resource type

We consider a job-shop scheduling problem with n jobs and the constraint that at most p<n jobs can be processed simultaneously. This model arises in several manufacturing processes, where each operation has to be assisted by one human operator and there are p (versatile) operators. The problem is binary NP-hard even with n=3 and p=2. When the number of jobs is fixed, we give a pseudopolynomial dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS). We also propose an enumeration scheme based on a generalized disjunctive graph, and a dynamic programming-based heuristic algorithm. The results of an extensive computational study for the case with n=3 and p=2 are presented.

The Subset Sum game

Highlights • A game theoretic version of the Subset Sum problem is considered.• Two agents take turns to fill a shared knapsack with their items.• Natural heuristic strategies are proposed and analyzed from a worst-case perspective.

Parallel dedicated machines scheduling with chain precedence constraints

A set of n nonpreemptive tasks are to be scheduled on m parallel dedicated machines with a regular criterion. Chain precedence constraints among the tasks, deterministic processing times and processing machine of each task are given.

Scheduling three chains on two parallel machines

We consider the problem of scheduling n tasks subject to chain-precedence constraints on two identical machines with the objective of minimizing the makespan. The problem is known to be strongly NP-hard. Here, we prove that it is binary NP-hard even with three chains. Furthermore, we characterize the complexity of this case by presenting a pseudopolynomial time algorithm and a fully polynomial time approximation scheme.

A heuristic approach to batching and scheduling a single machine to minimize setup costs

Abstract In this paper we consider the problem of creating batches of parts, to be processed in a flexible manufacturing cell, and scheduling their operations. We consider the case in which the system consists of one machine and at most k parts may be present in the system at the same time. Given that each part requires a sequence of operations, and each operation requires a given tool, the objective is to minimize the total number of setups. We develop a heuristic algorithm for its solution and we present an extensive computational experience.

Minimum cost multi-product flow lines

In this paper, the problem of finding the minimum cost flow line able to produce different products is considered. This problem can be formulated as a shortest path problem on an acyclic di-graph when the machines graph associated with each product family is a chain or a comb. These graphs are relevant in production planning when dealing with pipelined assembly systems. We solve the problem using A* algorithm which can be efficiently exploited when there is a good estimate on the value of an optimal solution. Therefore, we adapt a known bound for the Shortest Common Supersequence problem to our case and show the effectiveness of the approach by presenting an extensive computational experience.

An approximate A* algorithm and its application to the SCS problem

In this paper we deal with algorithm A? and its application to the problem of finding the shortest common supersequence of a set of sequences. A? is a powerful search algorithm which may be used to carry out concurrently the construction of a network and the solution of a shortest path problem on it. We prove a general approximation property of A? which, by building a smaller network, allows us to find a solution with a given approximation ratio. This is particularly useful when dealing with large instances of some problem. We apply this approach to the solution of the shortest common supersequence problem and show its effectiveness.

Competitive subset selection with two agents

We address an optimization problem in which two agents, each with a set of weighted items, compete in order to maximize the total weight of their winning sets. The latter are built according to a sequential game consisting in a flxed number of rounds. In every round each agent submits one item for possible inclusion in its winning set. We study two natural rules to decide the winner of each round. For both rules we deal with the problem from difierent perspectives. From a centralized point of view, we investigate (i) the structure and the number of e‐cient (i.e. Pareto optimal) solutions, (ii) the complexity of flnding such solutions, (iii) the best-worst ratio, i.e. the ratio between the e‐cient solution with largest and smallest total weight, and (iv) existence of Nash equilibria. Finally, we address the problem from a single agent perspective. We consider preventive or maximin strategies, optimizing the objective of the agent in the worst case, and best response strategies, where the items submitted by the other agent are known in advance either in each round (on-line) or for the whole game (ofi-line).

Part Batching and Scheduling in a Flexible Cell to Minimize Setup Costs

In this paper we consider the problem of batching parts and scheduling their operations in flexible manufacturing cells. We consider the case in which there is only one processor and no more than k parts may be present in the system at the same time. The objective is to minimize the total number of setups, given that each part requires a sequence of operations, and each operation requires a given tool. We prove that even for k=3 the problem is NP-hard and we develop a branch-and-price scheme for its solution. Moreover, we present an extensive computational experience. Finally, we analyze some special cases and related problems.