Computational procedures for stochastic multi-echelon production systems

This paper is concerned with the numerical evaluation of multi-echelon production systems. Each stage requires a fixed predetermined leadtime; furthermore, we assume a stochastic, stationary end-time demand process. In a previous paper, we have developed an analytical framework for determining optimal control policies for such systems under an average cost criterion.\ud \ud The current paper is based on this analytical theory but discusses computational aspects, in particular for serial and assembly systems. A hierarchical (exact) decomposition of these systems can be obtained by considering echelon stocks and by transforming penalty and holding costs accordingly. The one-dimensional problems arising after this decomposition however involve incomplete convolutions of distribution functions, which are only recursively defined. We develop numerical procedures for analysing these incomplete convolutions; these procedures are based on approximations of distribution functions by mixtures of Erlang distributions. Combining the analytically obtained (exact) decomposition results with these numerical procedures enables us to quickly determine optimal order-up-to levels for all stages. Moreover, expressions for the customer service level of such a multi-stage are obtained, yielding the possibility to determine policies which minimize average inventory holding costs, given a service level constraint

Performance analysis of a decoupling stock in a make-to-order system

In a Make-to-Order system, products are only manufactured when orders are placed. As this may lead to overly long delivery times, a stock of semi-finished products can be installed to reduce production time: the so-called decoupling stock. As performance of the decoupling stock is critical to the overall performance and cost of the production system, we propose and analyse a Markovian model of the decoupling stock. In particular, we focus on a queueing model with two buffers, thereby accounting for both the decoupling stock as well as for possible backlog of orders. By means of numerical examples, we then quantify the impact of production inefficiency on delivery times and overall cost

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

Customized Pull Systems for Single-Product Flow Lines

Traditionally pull production systems are managed through classic control systems such as Kanban, Conwip, or Base stock, but this paper proposes ‘customized’ pull control. Customization means that a given production line is managed through a pull control system that in principle connects each stage of that line with each preceding stage; optimization of the corresponding simulation model, however, shows which of these potential control loops are actually implemented. This novel approach may result in one of the classic systems, but it may also be another type: (1) the total line may be decomposed into several segments, each with its own classic control system (e.g., segment 1 with Kanban, segment 2 with Conwip); (2) the total line or segments may combine different classic systems; (3) the line may be controlled through a new type of system. These different pull systems are found when applying the new approach to a set of twelve production lines. These lines are configured through the application of a statistical (Plackett-Burman) design with ten factors that characterize production lines (such as line length, demand variability, and machine breakdowns).Pull production / inventory;sampling;optimization;evolutionary algorithm

Multi-job production systems: definition, problems, and product-mix performance portrait of serial lines

This paper pursues two goals: (a) Define a class of widely used in practice flexible manufacturing systems, referred to as Multi-Job Production (MJP) and formulate industrially motivated problems related to their performance. (b) Provide initial results concerning some of these problems pertaining to analysis of the throughput and bottlenecks of MJP serial lines as functions of the product-mix. In MJP systems, all job-types are processed by the same sequence of manufacturing operations, but with different processing time at some or all machines. To analyse MJP with unreliable machines, we introduce the work-based model of production systems, which is insensitive to whether single- or multi-job manufacturing takes place. Based on this model, we investigate the performance of MJP lines as a function of the product-mix. We show, in particular, that for the so-called conflicting jobs there exists a range of product-mixes, wherein the throughput of MJP is larger than that of any constituent job-type manufactured in a single-job regime. To characterise the global behaviour of MJP lines, we introduce the Product-Mix Performance Portrait, which represents the system properties for all product-mixes and which can be used for operations management. Finally, we report the results of an application at an automotive assembly plant