Claudio Arbib

A three-dimensional matching model for perishable production scheduling

Abstract In the production of perishable goods, particular stress is often given to performance indicators generally less critical in such manufacturing settings as metal-cutting, or mechanical/electronic assembly. For instance, in food or biochemical productions, a prominent interest of the producer is to reduce the time from distribution to the so-called best-before end. A scheduling problem with a goal of this sort is here addressed. The decision variables considered are launching and completion times of parts in a production line with critical aspects in the initial and/or final stages. The basic problem is to find an assignment of a maximum number of products to launching and completion times, so that no two products are assigned the same launching or completion time: feasible solutions have therefore the form of three-dimensional matchings. The problem is studied under two independent respects, assuming either (i) the relative perishability of products or (ii) the feasibility of launching/completion time pairs not affected by the intermediate transformation stage. We show that the problem is NP-Complete, even under such a ranking assumption as (i), whereas is in P under assumption (ii). Polynomial-time algorithms are also proposed to solve other optimization versions of the problem (in two cases, based on the identification of a matroid structure).

Integrating process optimization and inventory planning in cutting-stock with skiving option: An optimization model and its application

Abstract We consider a two-stage flow line where the first stage produces components for the downstream assembly stage. An integer programming model which integrates decisions at both the planning and the operation level is proposed, with the aim of minimizing production, holding and transportation costs. The model is tested on instances built on the basis of a real cutting process with skiving option, i.e., with the possibility of recombining components to obtain required parts. The implementation of the proposed methodology allows the integration of two hierarchical decision levels (short-term operations vs. mid-term planning) and functional areas (production vs. purchase of materials) within a single planning model, and provides an example of how an element of an Advanced Planning System (APS) could be designed. Moreover, the use of suitable cost figures in the model allows to correctly manage the insertion of hot orders of finite parts.

Part routing in flexible assembly systems

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. >

A competitive scheduling problem and its relevance to UMTS channel assignment

This article investigates a two-user competitive scheduling problem. The problem arises in a Universal Mobile Telecommunication System (UMTS) developed within the European IST project FUTURE: given two mobile terminals, one wants to maximize the on-time data packets transmitted to one user, while guaranteeing a certain amount of on-time data packets to the other. We show that the problem is NP-hard, despite peculiar properties of data and solutions. We propose a fast lagrangian heuristic able to cope with a severe real-time requirement, and compare it to a greedy-like heuristic on a set of practical instances.

Optimal resource assignment through negotiation in a multi-agent manufacturing system

Research studies on multi-agent systems have been recently boosted by manufacturing and logistics with deep motivations like the presence of independent human deciders with individual goals, the aspiration to dominate the complexity of decision-making in large organizations, the simplicity and robustness of self-reacting distributed systems. After a survey of the multi-agent paradigm and its applications, the paper introduces the notion of hybrid holonic system to study the effect of supervision on a system whose elements negotiate and cooperate in a rule-settled environment to obtain resources for system operation. The supervisor can spur or disincentive agents by assigning/denying resources to them. A simple single-decider optimization model referred to a real application is described, and solution methodologies for optimal resource allocation fitting different scenarios (centralized, distributed, multi-agent) are discussed, identifying ranges of autonomy, quantifying rewarding and defining a negotiation protocol between the agents and the supervisor. Aim of the paper is to describe through an example a general methodology for quantitative decision-making in multi-agent organizations.

Workload balance and part-transfer minimization in flexible manufacturing systems

Problems related to the flow management of a flexible manufacturing system (FMS) are here formulated in terms of combinatorial optimization. We consider a system consisting of several multitool automated machines, each one equipped with a possibly different tool set and linked to each other by a transportation system for part moving. The system operates with a given production mix.The focused flow-management problem is that of finding the part routings allowing for an optimal machine workload balancing. The problem is formulated in terms of a particular capacity assignment problem.With the proposed approach, a balanced solution can be achieved by routing parts on a limited number of different paths. Such a balancing routing can be found in polynomial time. We also give polynomial-time and-space algorithms for choosing, among all workload-balancing routings, the ones that minimize the global amount of part transfer among all machines.

Cutting and Reuse: An Application from Automobile Component Manufacturing

This paper presents a decision support tool for solving a cutting and reuse problem arising in a European plant devoted to the production of gear belts. In this production, rectangular pieces of rubberised nylon are cut using machines employing parallel blades, so as to obtain rectangular components of identical height and (possibly) different width. A component is then used to produce a set of belts with the same girth; but, if necessary, the girth required can also be obtained by sewing together two components. The major objectives of optimisation are: trim loss minimisation, quality control, workload equalisation, setup minimisation. The problem, a particular one-dimensional cutting stock with both cutting and reuse decision variables, has been formulated in terms of integer linear programming and then efficiently solved by applying standard packages within a column generation scheme. A significant improvement of performance has been obtained in terms of both economic savings and product quality. This has convinced the management to implement the model in the plant operation.

Task assignment and subassembly scheduling in flexible assembly lines

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. >

Optimal two-machine scheduling in a flexible flow system

An approach to part-type selection and scheduling of parts in a two-machine flexible-flow line is presented. It consists of first selecting a small number of part types for simultaneous production (in suitable ratios in order to balance the workloads among the machines), and then scheduling the parts of each batch in order to minimize both completion time as well as the maximum level of in-process inventory required. The system consists of two machines, and all of the parts visit the two machines in the same order. Some advantages of the approach presented include management effectiveness and simplicity, in addition to other benefits inherent in a dynamic and flexible approach to part-type selection (such as a higher utilization of the machines, a smoother tool-changing activity, etc.).<<ETX>>

Predicting deadlock in store‐and‐forward networks

We consider the problem of predicting whether a deadlock will necessarily occur in a store-and-forward network. We define two versions of this problem, depending on whether or not the routes to be followed by packets are fixed. For networks with only one buffer per vertex, both versions of this problem are shown to be NP-complete even for simple classes of graphs (among others bipartite graphs, two terminal series-parallel [TTSP] graphs and therefore planar graphs). On the other hand, the same problems are shown to be polynomially solvable for treelike networks. In this case, two efficient algorithms for checking whether a treelike network with n vertices and p packets is bound to deadlock are proposed. The former has an O(pn) time and space complexity, whereas the latter runs in O(n log n)1 time and requires O(n) space. In the case of multibuffered networks, both versions of the problem are shown to be NP-complete even on treelike networks.