Genrikh Levin

MIP approach to balancing transfer lines with blocks of parallel operations

A novel line balancing problem is considered. It differs from assembly line balancing problems in that the operations of each workstation are partitioned into blocks of simultaneously executed (parallel) operations. The blocks of each workstation are executed sequentially. For the line design stage considered in this paper, the compatibility (inclusion and exclusion) constraints for grouping operations into blocks and workstations as well as precedence constraints are known. The goal is to minimize a weighted sum of the number of workstations and the number of blocks while achieving a desired cycle time and satisfying all the constraints. The developed exact and heuristic methods are based on a mixed-integer programming approach. Experimental results are reported.

A special case of transfer lines balancing by graph approach

A balancing problem for paced production lines with workstations in series and blocks of parallel operations at the workstations is considered. Operations of each workstation are partitioned into blocks. All operations of the same block are performed simultaneously by one spindle head. All blocks of the same workstation are also executed simultaneously. The relations of the necessity of executing some operations at the same workstation, the possibility of combining the blocks at the same workstation as well as precedence constraints are given. The operation time of the workstation is the maximal value among operation times of its blocks. The line cycle time is the maximal workstation time. The problem is to choose blocks from a given set and allocate them to workstations in such a way that (i) all the operations are assigned, (ii) the above constraints are satisfied, (iii) a given cycle time is not exceeded, and (iv) the line cost is minimal. A method for solving the problem is based on its transformation to a constrained shortest path problem.

A heuristic approach for transfer lines balancing

The paper deals with optimal balancing transfer lines where the operations in each workstation are grouped into blocks. All operations of the same block are executed simultaneously by one spindle head. Spindle heads of the same workstation are activated sequentially. The workstation time is the sum of the processing times of its blocks. The problem is to find the best assignment of operations to blocks and assignment of blocks to workstations that leads to the minimal transfer line cost (a weighted sum of blocks and workstation numbers). The solution must provide a desired productivity rate (cycle time). It must also satisfy precedence and compatibility constraints. Two heuristic algorithms based on the COMSOAL technique are proposed. Results from computer testing are reported.

Optimisation of multi-position machines and transfer lines

A new optimisation problem for design of multi-position machines and automatic transfer lines is considered. To reduce the number of pieces of equipment, machining operations are grouped into blocks. The operations of the same block are performed simultaneously by one piece of equipment (multi-spindle head). At the studied design stage, constraints related to the design of blocks and workstations, as well as precedence constraints for operations are known. The problem consists in an optimal grouping of the operations into blocks minimizing the total number of blocks and workstations while reaching a given cycle time (productivity). A constrained shortest path algorithm is developed and tested.

On problem of optimal design of transfer lines with parallel and sequential operations

A problem of optimal design for a class of automatic production systems is considered. The investigated systems are transfer lines without buffers and with parallel and sequential operations at each workstation. Manufacturing operations for a workstation are partitioned into blocks. All operations of the same block are performed simultaneously, and different blocks are executed sequentially. The relations of necessity and possibility of combining operations in one block and in one workstation as well as precedence constraints are given. Operation time of a block depends of assigned operations, while the operation time of a workstation is the sum of operation times of its blocks. The problem is to minimize the weighted total number of workstations and blocks, providing a given cycle time and satisfying the above constraints. The proposed method is based on reducing the initial problem to the shortest constraint path problem.

Integer programming models for logical layout design of modular machining lines

The preliminary design or reconfiguration of modular manufacturing lines is addressed. The modules are multi-spindle units. Each unit executes a subset of operations. The set of all available spindle units and their costs are known. The problem is to select the right spindle units and to arrange them into linear workstations. The objective is to design such a line respecting technological constraints and minimizing the investment cost. In this paper, some efficient formulations of linear integer programming (IP) models and specific techniques to reduce the calculation time are proposed. Experiments were carried out which highlight the performance of the models.

A heuristic multi-start decomposition approach for optimal design of serial machining lines

We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within each block are performed simultaneously by the same spindle head and the blocks of the same station are executed sequentially. The inclusion and exclusion constraints for combining operations into blocks and stations as well as the precedence constraints on the set of operations are given. The problem is to group the operations into blocks and stations minimizing the total line cost. A feasible solution must respect the given cycle time and all given constraints. In this paper, a heuristic multi-start decomposition approach is proposed. It utilizes a decomposition of the initial problem into several sub-problems on the basis of a heuristic solution. Then each obtained sub-problem is solved by an exact algorithm. This procedure is repeated many times, each time it starts with a new heuristic solution. Computational tests show that the proposed approach outperforms simple heuristic algorithms for large-scale problems.

Graph approach for optimal design of transfer machine with rotary table

A line balancing problem for transfer machines with rotary tables is considered. This type of machine is used in mass production. A part is sequentially machined on m working positions and is moved from one position to the next using a rotary table. The operations are grouped into blocks, where the operations of the same block are simultaneously performed by one piece of equipment with several tools (a multi-spindle head). All multi-spindle heads of a machine are simultaneously activated. Therefore, all operations of the machine are executed in parallel on m parts mounted on the rotary table. The line balancing problem consists of partitioning the set of all operations into sub-sets in order to minimize the number of working positions and the total number of spindle heads while satisfying all the constraints (precedence, compatibility for spindle heads, etc.). The method proposed in this paper is based on transforming this line balancing problem into a search for a constrained shortest path. An algorithm for simultaneously generating a graph and finding a constrained shortest path is developed. Some dominance rules for reducing the graph size are provided. An industrial example is presented in detail and experimental results on other industrial instances are reported.

Balancing large-scale machining lines with multi-spindle heads using decomposition

The paper deals with optimal logical layout design for a type of machining lines. Such lines are made of many machine-tools (workstations) located in sequence. On each workstation there are several multi-spindle heads. A spindle head does not execute one operation but a block of machining operations simultaneously. The problem studied in this paper consists of finding the best partition of the set of all operations to be executed on the line into blocks and workstations. The objective is to minimize the number of blocks and workstations. An optimal decision must satisfy a desired productivity rate (cycle time) and precedence and compatibility constraints for machining operations. A heuristic approach based on decomposition of a Mixed Integer Programming (MIP) model is developed. Two ways of forming sub-problems are proposed. One treats the obtained subsets independently. The second aggregates the solution of the previous subproblems. Results of their computational evaluation are reported.

Decomposition approach for a problem of lot-sizing and sequencing under uncertainties

The paper addresses a problem of optimal lot-sizing and sequencing of manufacturing items for production lines. The following factors are taken into account: processing times, set-up times, random machine breakdowns and rejects. The goal is to maximize the probability of a desired output for a given period. A mathematical model of the problem and an optimization approach are discussed. This approach is based on the decomposition of the initial problem in three sub-problems: an enumeration, a travelling salesman problem and a knapsack problem. An iterative optimization procedure is proposed, based on this decomposition.