Les R. Foulds

Optimal bin location and sequencing in printed circuit board assembly

Abstract A particular problem concerning the efficient production of printed circuit boards in the electronics industry is addressed. It concerns the location of feeder bins which contain parts to be inserted in the boards. We address the question of identifying the optimal bin locations in order to determine the best insertion sequence of the parts. The location problem is formulated as a number of one-facility location models. The sequencing problem is formulated as a traveling salesman problem. Techniques are presented for these problems which accomodate a variety of distance norms and take into account the possibility of only certain feasible regions for the location of the bins.

A positive linear discrete-time model of capacity planning and its controllability properties

One of the most important concepts in production planning is that of the establishment of an overall or aggregate production plan. In this paper, the problem of establishing an aggregate production plan for a manufacturing plant is considered. A new dynamic discrete-time model of capacity planning utilizing concepts arising in positive linear systems (PLS) theory is proposed and its controllability property is analyzed. Controllability is a fundamental property of the system with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control) but also in feedback control problems. Some new open problems regarding controllability of stationary and nonstationary PLS with linear constraints are posed in the paper. An optimal control problem for capacity planning is formulated and discussed.

FleetManager: a microcomputer-based decision support system for vehicle routing

Abstract We report on a decision support system (DSS) that recommends solutions to a particular version of the vehicle routing problem occurring in the New Zealand dairy industry. FleetManager is a DSS developed for use by New Zealand milk tanker schedulers and is designed to aid them in creating or improving milk tanker routes using their experience and preferences. The DSS uses multiple, resizable, overlapping windows to assist schedulers in their tasks. Users can also interact with the system through a graphical interface which displays a road map of the area and the location of the milk processing plants and milk suppliers. FleetManager also contains the option of automatically creating vehicle routes, which can be modified by the users. The system can be used to analyze a wide variety of “What-if?” scenarios with potential cost impacts.

Scheduling contractors' farm-to-farm crop harvesting operations

The harvesting of renewable resources from an operations scheduling viewpoint is introduced, and a harvesting scenario arising in the agricultural context involving a commercial contracting enterprise that travels from farm-to-farm harvesting crops is discussed. This paper is an extension of previous work by two of the authors from the one-farm to the multi-farm case. In both cases, the duration of each operation is dependent upon the combination of constrained resources allocated to it, equipment and worker allocation is restricted, and minimum or maximum time lags on the start and completion of operations may be imposed. The present case incorporates harvesting at more than one farm and thus the sequence in which the farms are visited and the inter-farm travel times must be taken into account. We report on a harvesting scheduling model and solution procedures designed specifically for large-scale versions of the multi-farm case. The computational times experienced in solving general instances of the model of small-to-medium practical size by a commercial integer programming package are encouraging. Greedy and tabu search heuristics, which are capable of solving problems of relatively large dimensions in reasonable computational time are also included. The authors believe that the model and the solution techniques developed represent a useful addition to the farm crop contractors tool kit.

SlotManager: a microcomputer-based decision support system for university timetabling

Abstract A user-friendly, menu-driven decision support system that can be used to construct university timetables is described. The system is written in Microsoft Access, within the Microsoft Windows environment, for an MS-DOS personal computer. A case study is reported, involving the successful use of the system in the environment that motivated its development, namely course timetabling at a New Zealand university. The system provides a useful addition to the university timetablers toolkit and an interesting application of the DSS approach in an important area.

The sustainable cell formation problem: manufacturing cell creation with machine modification costs

An approach for manufacturing cell formation with machine modification is presented. In cell formation it is often important in practice to be able to reassign parts to additional machine types in order to create better cell configurations. This involves extending the set of parts that certain individual machines can process. Such extensions may be cheaper than simply purchasing additional machines. Thus, there is the possibility of machine modification to reduce inter-cell travel. The cost of such modifications must be balanced by the consequent reduction in inter-cell travel cost. The extended machine cell formation problem to be described involves the specification of which individual machines should be modified to enable them to process additional part types, part-machine assignment, and the grouping of individual machines for cell formation. The objective is to minimize the sum of the machine modification costs and the inter-cell travel. We call this the sustainable cell formation problem (SCFP). As far as the authors are aware, there have not been any solution procedures for this important problem reported in the open literature. It is our purpose to fill this gap by presenting a mixed integer programming model of the SCFP. We also propose and analyze greedy and tabu search heuristics for the design of large-scale systems related to the SCFP. Computational experience with the solution procedures indicates that they are likely to be useful additions to the production engineers toolkit.

Integer programming approaches tofacilities layout models with forbidden areas

The facilities layout problem is concerned with a given number of facilities of some system which are to be laid out in a plane region, such as a factory floor or a flat building site. The aim of the classical facilities layout problem is to produce a plan drawn to scale which shows the relative positions of the facilities to be laid out in order to optimise some measure of the performance of the system. We assume that the region P, in which the facilities are to be laid out, is a rectangle and that each of the facilities to be laid out in it is to be a connected subregion of given area, of arbitrary shape, except that all facility boundaries are straight-line segments that are parallel to the perimeter of P. In many practical layout scenarios there are regions in which it is forbidden to locate facilities. This sometimes occurs when a factory is to be redesigned and certain existing facilities are to remain where they are. In other scenarios, the forbidden regions represent areas which cannot contain any facilities at all, e.g., for security, transport, technical, or other reasons. We devise integer programming models for the facilities layout problem with forbidden areas, and report on computational experience in solving them.

The impact and benefits of a DSS: the case of FleetManager

Abstract A DSS used for vehicle routing at the Westland Co-operative Dairy Company Ltd., New Zealand, is providing a spectrum of benefits and business values. Labor hours, required by the schedulers, have been significantly reduced; the schedules they develop are more efficient, the number of truck drivers has been reduced even though the volume of the traffic is increasing, and the Transport Office has a greater flexibility and higher morale. The system includes powerful tools to plan schedules, choose plans, generate alternative plans, and assess alternative plans with respect to the given criteria. The system also allows the scheduler to create routes automatically, minimize the total distance traveled, and manually modify routes created by a model. It also has several classic characteristics that are too seldom actually realized: it leverages the judgment of the DSS user; it has evolved over time through an iterative development process and is being adapted for use in another company. Taken together, these benefits and attributes make the system a rare example of a successful DSS that can provide guidance for the development of other systems in the important problem domain of vehicle routing.

A variation of the generalized assignment problem arising in the New Zealand dairy industry

Within the New Zealand dairy industry, milk is collected from farms by road tanker vehicles and delivered to the factories of a dairy company for processing. Before the tankers can be scheduled to pick up the milk, each company must decide to which factory the output of each of its client farms is to be sent. We present a mathematical model of this allocation problem and solution procedures for it. The model is a variation on the generalized assignment problem. The problem is NP-hard, which reinforces the search for efficient heuristics for it. We present heuristics which yield solutions close to optimality in a reasonable amount of computing time for problems of the size commonly encountered in the dairy industry.

An exact algorithm for a milk tanker scheduling and sequencing problem

In rural areas, milk tankers collect milk from farms for processing at a central base.Collection runs are assigned to tankers, each tanker performing a series of runs. After eachrun, the tankers need to be emptied by pumps, which are limited in number. A schedulingsystem has been devised to allocate runs to tankers, despatch the tankers and determinewhen the tanker may be emptied on its return in order to minimise the total time taken(makespan) for all runs to be completed. The joint problem of scheduling and sequencing isposed as a linear integer programming (IP) problem with additional nonlinear constraints.The problem is then solved by embedding an IP algorithm within an overall branch andbound approach. The results of testing this algorithm will be discussed and compared to aproposed heuristic approach.