Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Applying Machine Based Decomposition in 2-Machine Flow Shops

The Shifting Bottleneck (SB) heuristic is among the most successful approximation methods for solving the Job Shop problem. It is essentially a machine based decomposition procedure where a series of One Machine Sequencing Problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the Flow Shop problems (Jain and Meeran 2002). In particular, we show that for the 2-machine Flow Shop problem, the SB heurisitc will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the Flow Shop. An optimal machine based decomposition procedure is formulated for the 2-machine Flow Shop, the time complexity of which is worse than that of the celebrated Johnsons Rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex Job Shops can also be suitably modified to optimally solve the simpler Flow Shops.

On the representation of the One Machine Sequencing Problem in the Shifting Bottleneck Heuristic

The Shilling Bottleneck heuristic decomposes the Job Shop problem into a series of One Machine Sequencing Problems (OMSPs) with release and due dates, precedence constraints and the minimization of maximum lateness objective. It is well known that delayed precedence constraints may exist between two operations to be performed on the same machine. We identify a new type of precedence constraint that may exist in an OMSP between the predecessor of an operation and the successor of another. The premise that an OMSP captures the sequencing relationships on other machines in the release and due date information is not valid when such precedence constraints exist. A modification of the OMSP representation is proposed based on a generalized lateness objective defined on a due window. The implications of such a representation for the OMSP solution procedure have been explored.

Applying machine based decomposition in 2-machine Flow Shops

The Shifting Bottleneck (SB) heuristic is among the most successful approximation methods for solving the Job Shop problem. It is essentially a machine based decomposition procedure where a series of One Machine Sequencing Problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the Flow Shop problems (Jain and Meeran 2002). In particular, we show that for the 2-machine Flow Shop problem, the SB heurisitc will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the Flow Shop. An optimal machine based decomposition procedure is formulated for the 2-machine Flow Shop, the time complexity of which is worse than that of the celebrated Johnson’s Rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex Job Shops can also be suitably modified to optimally solve the simpler Flow Shops