Protective stocks in multi-stage production systems

Uncertainty in MRP systems does exist in several forms, variability in demand from period to period, uncertainty in the supply from stage to stage due to the variability in the yields from each production batch, and uncertainty in the lead times. The goals of the paper are to develop theoretical models for determining optimal decisions in this uncertain environment, to develop a computationally tractable heuristic and to examine how safety stock and safety time can arise. Finally, our methodology is compared with MRP practice.     

Flexibility of production ordering systems

The flexibility of production ordering systems as medium range production control systems are studied. The changes affecting flexibility, production ordering systems as responses to changes, and the performance measures of flexibility are clarified. On the basis of this framework, mathematical models of production system and production ordering systems are developed to evaluate their flexibility. Two types of changes are considered: demand fluctuation and downtime fluctuation due to machine breakdown, and two models for ‘push-type’ and ‘pull-type’ production ordering systems are investigated. By simulating the models, the amplifications of production quantities and inventory levels as flexibility measures for each type of production ordering system are analysed and the flexibility compared.     

Production scheduling and sequencing for multi-stage production systems

Summary This paper focuses on multistage, multiproduct dynamic production systems. Up to now little work has been done on such realistic problems, the reasons being that multiproduct models are subject to capacity considerations and to the general sequencing problem. Optimal and heuristic solution methods are presented for this combined sequencing/scheduling problem. Our computational experience indicates that the proposed heuristic is efficient and differs marginally from the optimal solution.

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Zusammenfassung In diesem Beitrag werden mehrstufige Mehrprodukt-Produktionssysteme mit dynamischem Zeitablauf betrachtet. Da die entsprechenden Modelle es erfordern, gleichzeitig Seriengröße und -folge zu bestimmen derart, daß ein zulässiger Produktionsplan erhalten wird, hat man sich bisher wenig mit solchen realistischen Problemen beschäftigt. Optimale und heuristische Lösungsverfahren für dieses kombinierte Entscheidungsproblem werden vorgestellt. Die Rechenerfahrungen deuten darauf hin, daß das vorgeschlagene heuristische Lösungsverfahren effektiv ist und die erreichten Lösungen sich von einer Optimallösung nur wenig unterscheiden.

     

Setting safety stocks in multi-stage inventory systems under rolling horizon mathematical programming models

This paper considers the problem of determining safety stocks in multi-item multi-stage inventory systems that face demand uncertainties. Safety stocks are necessary to make the supply chain, which is driven by forecasts of customer orders, responsive to (demand) uncertainties and to achieve predefined target service levels. Although there exists a large body of literature on determining safety stock levels, this literature does not provide an effective methodology that can address complex multi-constrained supply chains. In this paper, the problem of determining safety stocks is addressed by a simulation based approach, where the simulation studies are based on solving the supply chain planning problem (formulated as a mathematical programming model) in a rolling horizon setting. To demonstrate the utility of the proposed approach, an application of the approach at Organon, a worldwide operating biopharmaceutical company, will be discussed.     

Economic acceptance sampling plans in complex multi-stage production systems

Specification of economic acceptance sampling schemes in complex multi-stage production systems is considered. The analysis is based on approximations of the distribution of lot fractions defective at all production stations of the system. A heuristic algorithm is developed that combines individual optimal solutions to subproblems corresponding to the production stations, to arrive at a near-optimal solution for the original problem. Numerical examples illustrate the application of the method to serial and non-serial manufacturing-assembly processes.     

Balancing production level variations and inventory variations in complex production systems

In this study we analyse the behaviour of production levels and stocks in an integrally controlled multi-product multi-phase production system, We show that certain types of variations in the master production schedule (MPS) may lead to large short-term variations in production. To reduce the costs of these variations we introduce production smoothing, and we derive a modification of well-known integral production decision rules to realize smoothed production behaviour. By means of a small scale example we demonstrate the quantitative effects of our production smoothing rule on the variations in stocks and production levels. Finally, we present the general structure of a cost model that can be used to determine appropriate values for the smoothing parameters, given a specific production structure, a given capacity structure, and a given variability of the MPS. We discuss various possibilities to arrive at these values.     

On control strategies in a multi-stage production system

A multi-stage production system is composed of a set of stations, each station performing a given task, and a set of vehicles, each vehicle moving between two successive stations. A station can choose a buffer or a kanban mechanism for controlling the work-in-process (WIP) in the station. A vehicle can choose a push or a pull policy for carrying parts from its upstream station to its downstream station. A control strategy is formed by combining the WIP mechanisms adopted in all stations and the carrying policies employed by all vehicles. The production system is modelled as a queuing system. Some structural properties of performance measures are characterized. We develop a decomposition approach for large systems, which performs very well. We determine the optimal numbers of buffers or kanbans at all stations in the design period, and the optimal control strategy during operation. Many numerical computations are given for evaluating the efficiencies of the decomposition approach and optimization methods, and further providing some intuitions and insights.     

Selection of a pull production control system in multi-stage production processes

In this paper, we conduct an analytical comparison of three pull production control systems: Kanban, CONWIP and Base-stock in multi-stage production processes. First, we compare the three control systems in a multi-stage serial production process. Then, we compare them in multi-stage assembly production processes, and present guidelines that allow us to select the best system. As a result, we show which structural parameters decide the superiority of one control scheme to the others, and how they are related. A key for superiority is a configuration of parameters, such as processing times and number of cards employed in the system. We show that there is no general superiority amongst the analysed concepts. Finally, we verify the effect of variability on the system performance, and generalise the analytical results of deterministic cases by conducting numerical experiments.     

Economic batch quantity in a multi-stage production system

A mathematical model has been developed in this paper for determining the total annual variable cost for a product which requires processing on a number of production stages. The demand for the product is assumed uniform over time and it is manufactured in equal lot sizes. In order to minimize the manufacturing cycle time of o production lot, the movement of the items between production stages is in sub-batches of equal sizes, As a result of manufacturing a production lot in sub-batches, the following additional costs are incurred: (1) additional cost of stock holding for process inventory; (2) cost of transporting sub-batches; (3) cost of multiple set-ups. A simple method is then adopted for minimizing the total annual variable cost of the multistage production system. An example has been solved to illustrate the method.     

Batch sizing with controllable production rates in a multi-stage production system

In this paper, a comprehensive model is presented for cell formation and layout design in cellular manufacturing systems (CMS). The proposed model incorporates an extensive coverage of important operational features and especially layout design aspects to determine optimal cell configuration and Intra and Inter-cell layout in CMS. Hence, proposed integrated approach attempts to design intra and inter-cell layout and material handling flow path structure simultaneously. We examine the great potential benefits of providing these features consist of routing flexibility, operation sequence, machine capacity, considering number of cells as a decision variable, un-equal dimension of machines, free machines and cells orientation, and considering pickup and drop off station for each cell. In order to show the effects and important of integrated design in the CMS, two approaches, sequentially and integrated, have been investigated and demonstrate the integrated approach improve the quality of obtained solution. The proposed model is a mixed integer non-linear programme. Linearisation procedures are proposed to transfer it into a linearised mixed integer programming formulation. Computational results are presented with the linearised formulation. We presented several enhancements in terms of valid inequalities and extensions to the proposed model in order to improve its computational performance. Finally, concluding remarks are provided.     

Location and sequencing of imperfect inspection operations in serial multi-stage production systems

An integrated approach to the problem of allocation of inspection effort in multistage production systems is presented. The problem addresses multiple inspection operations, different disposition policies and inspection, production and repair errors. Quality and cost transfer functions are developed to model production operations and different types of inspection operations in a unified manner and to facilitate the recursive computations required to evaluate alternative system configurations. We formulate the combined inspection location and sequencing problem as a nonlinear mathematical programming problem and solve it with a branch and bound technique, using a heuristic to generate a feasible solution and upper bound. These developments are illustrated with a numerical example.     

The role of inventory banks in flow-line production systems

Many production managers of flow-line systems, such as in the steel and metal processing industries, observe the high levels of in-process inventories. They feel that it should be possible to reduce these inventories; however, before doing so it is necessary for them to understand their function. Although the general rule that inventories exist because of imbalance in supply and demand at a point within the system is true, it is necessary to show more precisely how such an imbalance might arise in single-product systems due to variability in processing times at the stations, or interruptions in production due to breakdown and subsequent repair of stations. Quantitative results have been obtained which indicate how such factors as the number, location and capacity of inventory bank, affect the system production rate. These results enable system designers and operators to check whether their systems could be improved.     

Server assignment for multi-stage production systems with finite buffers

We consider a multi-stage production system with finite buffers under the so-called repetitive-service blocking mechanism, modelled by a tandem queueing system with blocking. The objective is to find to which stage each server should be assigned in order to maximize the throughput. For this server assignment problem we first derive a throughput upper bound which is found to be very close to the exact one to be used as a substitute measure. Based on this measure we show that the rules of placing the worst servers from the outermost stages by Yamazaki et al. ( 1989) for the case of no buffers, are effective for the case with buffers of equal size. For the general case with buffers of different sizes, we propose an algorithm based on the observation that our throughput upper bound can be increased fastest by placing the fastest servers around the smallest buffered stage. Effectiveness of this algorithm as well as the proposed rules are well demonstrated by the extensive computational experiments conducted with a number of test examples ranging up to five stages.     

Optimal ordering and pricing policy for an inventory system with order cancellations

This paper investigates the problem of ordering and pricing over a finite time planning horizon for an inventory system with advance sales and spot sales. It is assumed that the planning horizon is divided into several sales cycles each of which is divided into an advance sales period and a spot sales period. During the advance sales period, all customers are required to make reservations for their orders and will receive them at the arrival time of the replenishment orders. In the case of the spot sales periods, all customers receive their orders at the time of the purchase. In actual practice, since customers with reservations may cancel their orders before receiving them, this paper considers this phenomenon and develops a continuous time inventory model to deal with the proposed problem. This paper maximizes the total profit over a finite time planning horizon by determining the optimal advance sales price, spot sales price, order size, and replenishment frequency. Analysis of results shows that a simple algorithm can be developed to arrive at an optimal decision.     

Robust policies for a multi-stage production/inventory problem with switching costs and uncertain demand

In this paper, we seek robust policies for a multi-stage production/inventory problem to minimise total costs, including switching, production, inventory or shortage costs. While minimising switching costs often leads to non-convexity in the model, 0–1 variables are introduced to linearise the objective function. Considering the impossibility of obtaining the exact distribution of uncertain demand, we study the production/inventory problem under worst cases to resist uncertainty. In contrast to traditional inventory problems, unexpected yields in production are considered. Robust support vector regression is developed to approximate the yields of each unit. A mixed-integer linear programming is proposed, employing the duality theory to address the min–max model. A practical case study from cold rolling is considered. Experiments on the actual steel production data are reported to illustrate the validity of the proposed approach.     

Integrated inventory valuation in multi-echelon production/distribution systems

The pressure to reduce inventory has increased as competition expands, product variety grows, and capital costs increase. This investigation addresses the problem of inventory quantification and distribution within multi-echelon supply chains under market uncertainty and management flexibility. This approach is based on an optimisation model emphasising demand uncertainty and the relevant dimensions of network design as number of echelons, lead time, service level, and cost of processing activities. Overstock quantification enables the understanding of inventory level sensitivity to market uncertainty. A comparison among production sites and storage facilities revealed that higher downstream overstock levels decrease upstream echelons of uncertainty exposition. The contribution of this study relies on management's ability to establish inventory targets for each stocking point according to risk exposure and to promote the optimisation of working capital. Overall, this investigation increases knowledge related to the treatment of demand uncertainty in flexible and integrated supply chains     

Multi-dimensional clearing functions for aggregate capacity modelling in multi-stage production systems

Nonlinear clearing functions have been proposed in the literature as metamodels to represent the behaviour of production resources that can be embedded in optimisation models for production planning. However, most clearing functions tested to date use a single-state variable to represent aggregate system workload over all products, which performs poorly when product mix affects system throughput. Clearing functions using multiple-state variables have shown promise, but require significant computational effort to fit the functions and to solve the resulting optimisation models. This paper examines the impact of aggregation in state variables on solution time and quality in multi-item multi-stage production systems with differing degrees of manufacturing flexibility. We propose multi-dimensional clearing functions using alternative aggregations of state variables, and evaluate their performance in computational experiments. We find that at low utilisation, aggregation of state variables has little effect on system performance; multi-dimensional clearing functions outperform single-dimensional ones in general; and increasing manufacturing flexibility allows the use of aggregate clearing functions with little loss of solution quality.     

Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.     

Real-time disruption management in a two-stage production and inventory system

This paper presents a general disruption management approach for a two-stage production and inventory control system. A penalty cost for deviations of the new plan from the original plan is incorporated and the concept of a disruption recovery time window is introduced. We define two classes of problems: one with fixed setup epochs and another with flexible setup epochs. With linear or quadratic penalty functions for production/ordering quantity change and fixed setup epochs, the best recovery plan is obtained by solving a quadratic mathematical programming problem. With convex penalty functions for quantity changes and flexible setup epochs, it is shown that the second stage orders have identical order quantities within each production cycle. Therefore, in a lot-for-lot system, the ordering and production quantities for both stages are the same. As a special case, we consider disruption recovery problems with short time windows spanning one or two production cycles. We also discuss solution procedures for both major and minor disruption problems and give an extension for the case of multiple retailers. Throughout the paper managerial insights are presented that indicate how a company should respond to various types of disruptions during its operations.     

Lot-sizing in a multi-stage flow line production system with energy consideration

In this paper, a single-item capacitated lot-sizing problem in a flow-shop system with energy consideration is studied. The planning horizon is defined by a set of periods where each one is characterised by a length, an allowed maximal power, an electricity price, a power price and a demand. The objective is to determine the quantities to be produced by each machine at each period while minimising the production cost in terms of electrical, inventory, set-up and power required costs. For medium- and large-scale problems, lot-sizing problems are hard to solve. Therefore, in this study, two heuristics are developed to solve this problem in a reasonable time. To evaluate the performances of these heuristics, computational experiments are presented and numerical results are discussed and analysed.