In this work, a multiagent network flow problem is addressed, aiming at characterizing the properties of stable flows and allowing their computation. Two types of agents are considered:transportation‐agents, that carry a flow of products on a given network and another agent, either aproduceror acustomer, who is willing to ship (receive, respectively), products. Every transportation‐agent controls a set of arcs, each having a capacity that can be increased up to a certain point at a given cost. The other agent (i.e., the customer/producer) is interested in maximizing the flow transshipped through the network. To this aim, we assume it offers the transportation‐agents a reward that is proportional to the realized flow value. This particular multiagent framework is referred to as a Multiagent network expansion game. We characterize and find particular stable strategies (i.e., Nash equilibria) that are of interest for this game. We particularly focus on the problem of finding a Nash Equilibrium and a sharing policy that maximize the value of the total flow. We prove that this problem is NP‐hard in the strong sense and show how such a strategy can be characterized considering paths in specific auxiliary graphs. We also provide a mixed integer linear programming formulation to solve the problem. Computational experiments are provided to prove the effectiveness of our approach and derive some insights for practitioners. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 94–109 2017

In this paper, we study an integrated production an outbound delivery scheduling problem with a predefined sequence. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to multiple customers. A single vehicle with limited capacity is used for the delivery. Each job has a processing time and a specific customer location. Starting from the manufacturer location, the vehicle delivers a set of jobs which constitute a batch by taking into account the transportation times. Since the production sequence and delivery sequence are fixed and identical, the problem consists in deciding the composition of batches. We prove that for any regular sum-type objective function of the delivery times, the problem in NP-hard in the ordinary sense and can be solved in pseudopolynomial time. A dynamic programming algorithm is proposed.

We address a class of single-machine, hard scheduling problems with the objective of minimizing the maximum tardiness. The jobs can be preempted, but whenever a job is started or resumed, there is a recovery interval affecting its progress. Such a feature is motivated by certain application environments and generalizes the usual preemption concept. For three different cases of this problem, we propose a heuristic algorithm, based on the partial enumeration of feasible schedules. A packing formulation solved by means of a column generation approach is used to certify the quality of the heuristic solution. An extensive computational experience shows the effectiveness of the approach on different classes of instances and shows that real-size problems can be solved to optimality in an acceptable amount of time.

Abstract An important problem arising in the management of logistic networks is the following: given a set of activities to be performed, each requiring a set of resources, select the optimal set of resources compatible with the system capacity constraints. This problem is called Batch Selection Problem (BSP) from traditional applications to flexible manufacturing. BSP is known to be NP‐hard, and is also considered a difficult integer programming problem. In fact, polyhedral approaches to BSP suffer from the poor quality of the bound provided by the linear relaxation, even after strengthening. We devise an implicit enumeration scheme that attempts to overcome this difficulty. It is based on a formulation of BSP, which is equivalent to a stable set problem with one side constraint. This allows to exploit the upper bound, not only for pruning subproblems, but also for controlling the number and the quality of the subproblems generated. We show the effectiveness of the approach by an extensive computational experience on real‐sized randomly generated instances. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 151–159 2004

This paper deals with models for flow management problems in flexible assembly systems (FASs). The system consists of a set of machines that must perform the assembly of a number of parts, possibly of different types. Each part type requires a set of operations; the precedence relations among the operations are specified by an assembly tree. Machines are provided with limited-capacity tool magazines and a finite buffer for holding parts. Each machine can be tooled to perform only a particular subset of the operations required by the whole process. One problem is that of finding a feasible assignment of operations to machines and a feasible schedule of the subassemblies in order to minimize the completion time of all of the parts. In this paper, the problem is analysed as a case of pipelined assembly, i.e., when the FAS is characterized by a serial transportation system (flow line) and there exist a dominating path in the assembly tree. We present polynomial-time dynamic programming algorithms for solving the problem for both single-type and multi-type production.>

The authors deal with the problem of part flow management in a class of assembly systems characterized by a serial transportation system connecting the workstations. The system assembles a number of identical units, each requiring a set of operations. Each operation is performed by a workstation and each workstation can perform any operation. The problem consists of assigning the operations to the workstations to maximize some productivity index of the system. Usually, a tree-like precedence relationship exists among the operations (assembly tree). The problem is analyzed for the case in which a dominating path on the assembly tree exists. A polynomial time dynamic programming algorithm is presented for the optimal assignment of operations to workstations.>

Some optimization models for the problem of tool management in flexible manufacturing cells are presented. The cell considered consists of two machines (working centers) in charge of executing a set of part programs. The tools required by the machining operations are located in a central tool magazine and are moved to the machines by a tool handling system consisting of two shuttles and one robot. The robot picks and places the tools from/in the magazine; each shuttle exchanges the tools with the robot and with the machine. The problem is to synchronize the robot and shuttle moves in order to maximize the cell productivity (minimize the machines' idle time). Two different models are proposed for the situation in which a configuration of tools in the magazine is given and in which a budget for tool purchasing is fixed.>

The problem of part routing and scheduling in flexible manufacturing systems is considered with the goal of increasing the throughput. The flexible system considered is strongly characterized by the inclusion of assembly among the manufacturing operations to be performed on a mix of part batches. In particular, the logic structure of some basic decision problems is indicated through a set of combinatorial models. Two basic assembly problems characterized by batches of large and small size, respectively, are analyzed.>