Inventory Control in Shop Floors, Production Networks and Supply Chains Using System Dynamics

The use of appropriate inventory control policies is a must in production systems. Production systems are characterised by structural and dynamic complexity. Material and information delays can occur, which may lead to inventory oscillations. In order to handle these dynamics, a system dynamics approach is used. It encompasses inventory control policies on the flow shop, the production network and supply chain level. For the shop floor level a pheromone-based decision policy is presented, which provides a flexible and autonomous control strategy. For the production network continuous and periodic inventory policies are combined. For the supply chain an adaptive order-up-to policy is developed by weighting the work in progress and the inventory. This paper presents an integrated view on inventory control in shop floors, production networks and supply chains in order to overcome the lack of flexibility that arises from long time delays of the strategic supply chain level by offering autonomous control on the operational shop floor level. 1 Inventory Control It is important to keep inventory costs low; otherwise production will be less profitable. Inventory control is about the minimization of the average cost per time period while satisfying the incoming demand. Research on inventory control started at the beginning of last century boosted by the growth of manufacturers’ activities. For the shop floor a pheromone-based autonomous control policy is proposed in section 2.1. Autonomous control means a decentralized routing of the autonomous parts themselves. Therefore there are no standard inventory policies here to apply. Thus, policies that enact the parts to decide autonomously, instantaneously and with local and present information only, which alternative to choose, are developed. Since costs of raw materials and finished goods stocks are not considered on the shop floor level, the only inventory costs arise from the buffer levels in this case. In a production network manufacturers integrate and coordinate the general net production plan according to their individual production planning to satisfy customer demand. Former studies proposed the application of order release control methods and decentralized control loops [Wie02]. In section 2.2 continuous and periodic control methods are applied to a model of a production network in order to find a policy that reduces inventory costs. Inventory costs for the production net are occasioned by products on hold and backlogs of items ordered and not yet available. The production planning and inventory control (PIC) on the supply chain level 1 Department of Planning and Control of Production Systems, University of Bremen, Hochschulring 20, 28359 Bremen, Germany Published In: Konferenzband zur 12. ASIM Fachtagung "Simulation in Produktion und Logistik", SCS Publishing House e.V, Erlangen, pp. 273-282 is challenged by highly complex products, dynamic production changes and uncertain market demand. The PIC has to optimise the inventory under the trade-off between capacity variation, buffer inventory and lead time. In order to optimise buffer inventory and lead time the order-up-to policy (OUT) is quite sufficient because it reacts fast to changes in demand. However, this policy generates high fluctuations in the production. In section 2.3 a decision rule addresses this problem by accounting for the adjustment time of the stocks as well as the fluctuating inventory and fluctuating production costs. 2 Inventory Control with System Dynamics The system dynamics models of a shop floor, production network and supply chain will be presented. The three partial models are built and simulated with the continuous system dynamics methodology, which demonstrates the ability to describe the corresponding environments as long as the emphasis is not on the individual products and aggregation is allowed. Furthermore, the continuous perspective yields negligible errors in variables ́ values. The method enables the modelling of dynamic and uncertain systems due to its inclusion of feedbacks, nonlinearities and shifting loop dominance. 2.1 Shop Floor For the inventory control on the shop floor level a pheromone-based autonomous control policy is proposed. Autonomous control means a decentralized routing of the autonomous parts themselves. Therefore there are no standard inventory policies to apply. Rather policies enact the parts to decide autonomously, instantaneously and with local and present information only, which alternative to choose. First intuitive approaches are to set up a policy like ‘go to the buffer of the machine with the shortest processing time’ (we call it conventional control) or ‘go to the machine with the lowest buffer level’ [Sch05a] etc. Here, a different policy is presented: The parts' decisions are based on backward propagated information about the throughput times of finished parts for different routes. Routes with shorter throughput times attract parts to use these routes again. This process can be compared to ants leaving pheromones on their way to communicate with following ants. In a simulation, the performance of the pheromone concept will be compared to a conventionally controlled system with respect to inventory. The considered shop floor is a matrix-like flow-line manufacturing system producing k different products at the same time. Each of the products has to undergo m production stages. For each of these production stages there are n parallel production lines available. Therefore, the shop floor consists of mxn machines. The raw materials for each product enter the system via sources; the final products leave the system via drains. The production lines are coupled at every stage and every line is able to process every type of product within a certain stage. At each production stage a part has to make a decision to which of the lines to go to in the next stage. The service rule for the different products is first in first out. Each machine has an input buffer in front of it, containing items of the three product types. Additionally, different product lines are more suitable for certain products: it is assumed that each machine at each stage has different processing times for each product (for the topology cf. also [Sch05a, Sch05b]). In other words: A part is Published In: Konferenzband zur 12. ASIM Fachtagung "Simulation in Produktion und Logistik", SCS Publishing House e.V, Erlangen, pp. 273-282 punished when it decides to switch production lines. This punish-time can be interpreted as a setup time for each product that chooses to switch the production line. A scenario like this can be found in the food processing industry, where for example an enwrapping machine can enwrap different products in different times without any setups. This is different from scenarios where setup times are understood as a punishment only for the first part of the new type that switches production lines. A pheromone-based inventory policy is implemented analogue to the way social insects communicate with the help of pheromones. As in other pheromone concepts [Bon99, Pee99], the communication takes place indirectly by changing the environment. Social insects leave an evaporating substance called pheromone on their way and the following insects proceed along the trail with the strongest pheromone concentration. In this model the parts have to be able to access updated information about throughput time only. Thus, the pheromone-based policy differs from approaches from ant colony optimization (for example [Bon99]) since there is no self-reinforcing guided search process for optimal solutions. The pheromone concentration depends on the evaporation of the pheromone and on the time previous parts had to spend waiting in the buffer in addition to the processing time on the respective machine as well as the throughput time. This scenario is simulated with the system dynamics method because it offers the opportunity to store not only the moving average of the throughput times for each part on each buffermachine system [Arm06], but also to implement a feedback loop for the pheromone concentration according to actual data during the simulation. Clearly the fine-tuning of the evaporation constant for the pheromone is crucial. Here it was chosen in order to minimize the buffer levels. Previously proposed concepts for manufacturing control (e.g. [Pee99]) include a reinforcement of the pheromone trail when ants walk back their way to the nest. Here the parts simply disappear after the completion of the production steps. In order to handle the complexity the simulation model is reduced to 3x3 machines producing 3 different products. The arrival functions for the three product types are defined as sine functions. They are identical except for a phase shift of 1/3 period and modelled in a way that every 2:24 h a new part of every type arrives to the system. The processing times for each product are cyclic: 2 h, 2.5 h and 3 h respectively for the first, second and third best choice respectively. For simplicity the buffer levels of the first production step are considered only because the following stages act qualitatively in the same way but with an influx, which is smoothed by the processing times of the machines. Figure 1A shows the buffer levels of the three machines on the first production step in the case of conventional control. Conventional control means the centralized pre-planned policy that schedules the parts to the line with the lowest processing time. Because of the identical arrival functions (except for the phase shift), the time series of the buffer levels have the same shape. The buffer levels illustrate the oscillations of the given sinusoidal arrival functions. Within one simulation period (30 days) we can observe the three maxima at 8.73 pieces and the mean buffer level of 3 pieces with a standard deviation of 5.36 pieces. Figure 1B shows the buffer levels for the pheromone-based approach which performs very well. Obviously, this effect occurs because the parts learn to switch to other production lines in case of capacity overload even if the processing time is higher there. The maximum buffer level is reduced to 8.26 pieces and the mean buffer level is 3 Published In: Konferenzband zur 12. ASIM Fachtagung "Simulation in Produktion und Logistik", SCS Publishing House e.V, Erlangen, pp. 273-282 pieces with a standard deviation of only 3.05 pieces. To analyze the robustness of the pheromone concept, a machine failure for the second machine of the first stage is modelled with a 12-hours downtime. In the conventionally controlled system the parts pile up in the respective buffer until the machine starts to work again. A C Pheromone concept B D Pheromone concept with machine breakdown 15