Case study of a batch-production/inventory system E.M.M. Winands 1, A.G. de Kok 2 and C. Timpe 3

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1 Case study of a batch-production/inventory system E.M.M. Winands 1, A.G. de Kok 2 and C. Timpe 3 The plant of BASF under consideration consists of multiple parallel production lines, which produce multiple products in a make-to-stock fashion for process industry. Complicating factors for planning are the stochastic demand, setup times, batch processing and finite buffer capacities. The main contribution is the development of a three-stage methodology integrating production and inventory decisions, which can be used for the evaluation and optimization of a wide range of batch-production/inventory systems. Implementation of this methodology in a decision support tool enabled us to identify major opportunities for improvement of current practice. BASF is the worlds leading chemical company. It has customers in over 170 countries and supplies about 8,000 products to almost all industries. While the chemical, technical and business processes for the different products can be quite diverse, there are, from the viewpoint of inventory planning and production scheduling, some key aspects that occur frequently and that are also relevant in this case: 1) Changeover / sequencing: Process plant productivity is very sensitive to product transitions, and properly sequencing these transitions is extremely important to improving yields and reducing changeovers. Cleanups must be taken into account, and product wheels and changeover matrices provide critical planning criteria when planning product mix and sequencing. 2) Tanks / Silos: Inventory and work-in-process material is often stored in tanks or silos. Planning for production in tanks and silos must not only address the time required for the operation, but the volume of the material. The inflow from one operation and the outflow from the next dictate when the tank is available, and upstream and downstream operations have to be scheduled synchronously to ensure that the tank does not overflow. The present case study - which is an abbreviated version of [6] - analyzes a plant of BASF that has two buildings (A and B). In each of the two buildings two production lines are available for production. Most products can be produced on the two lines in building A, whereas for only a small number of products production is possible in building B. The planning of the plant is critically impacted by the fact that production in all production lines has to take place in fixed batch sizes (implying that production of partial batches is impossible). There exists one major difference between the lay-outs of the production lines in the two buildings. The production lines in building B start as two parallel lines, but share a single resource at end of the production process (so-called post-processing). Between the production of two different products, this resource has to be cleaned and, thus, setup times are incurred. However, in building A we distinguish two parallel lines during the complete production process. Products are produced in a make-to-stock fashion. A complicating factor is the limited stock space for the individual products, i.e., a dedicated tank is assigned to each individual product. At the moment a replenishment order is placed, one should be sure that there is sufficient space in the tank. Otherwise, the complete line is blocked and costly production capacity is wasted. Demand for the products is highly uncertain, but at the same time it is 1 Department of Mathematics, VU University, The Netherlands, Corresponding author: 2 Department of Technology Management, Eindhoven University of Technology, The Netherlands 3 GVC/S Scientific Computing, BASF SE, Germany 1

2 requested to deliver at short notice. It may be desirable to batch current and future demand for a product to avoid small production runs and high frequency of setups. When several batches for a product are combined in one production run, this is called a campaign. Raw material for the production is always available. Finally, since the shelf life of the products is relatively long, they can be considered as non-perishable goods. For each customer order a due date is set, which results from an agreement between the customer and BASF. Demand that cannot be delivered before or on this due date is backlogged until the product becomes available after production. We use the fraction of demand satisfied before or on the agreed due date to quantify the performance of the plant, where only complete deliveries are allowed. In the present project, we obtain the inventory requirements such that given quality-of-service levels can be met. Though we focus on the fraction of demand delivered on time, our analysis can be readily extended to other performance measures, mutatis mutandis. Lastly, we note that the vast production literature includes several problems related to the present case study, yet the one that comes closest is the SELSP which assumes a single production line though (see [5], for a survey). Planning methodology. The planning methodology is done on a daily basis and consists of two parts. Firstly, replenishment orders are placed by the planner according to an (s i,nq i ) inventory policy, which controls the inventory level for each individual product i = 1,2,...,N as follows. When the inventory position of a product falls below the reorder level s i, a replenishment order of amount nq i, n = 1,2,..., is placed such that the inventory level is again between s i and s i + Q i. The inventory position is defined as the physical inventory plus the stock on order minus the backorders. The quantity Q i is called the batch size, while the amount nq i is referred to as the campaign size. Secondly, the production people assign these replenishment orders to the production lines and determine the sequence of production. These allocation and sequencing decisions are based on experience and future expectations. The above planning methodology has been studied before in the open literature both by simulation [1] and by approximate analytical models deploying restrictive assumptions [7] (such as Poisson replenishment processes and a single production line). These challenges motivated us to look for an analytical method to compute the performance of the system without making these restrictive assumptions while integrating production and inventory decisions into a single model. Main contribution. The main contribution of the present research is the development of a fast, accurate and easy-to-implement algorithm for the evaluation and optimization of batch-production/inventory systems. This algorithm is based on compound renewal customer demand processes, which permits us to model both general interarrival and demand processes with any probability distribution function. Furthermore, the algorithm is applicable in the situation of multiple parallel identical production lines and is able to compute a wide range of performance measures. The implemented algorithm is the main building block of the deliverable of the present study, i.e., the decision support tool named OptStock. OptStock has been applied to the BASF plant analyzed in the present case study, which enabled us to make recommendations on the required inventory levels and tank capacities. Model. We propose an integrated batch-production/inventory model (see Figure 1), which consists of three stages. Firstly, the (s i,nq i ) inventory policy is analyzed by (approximate) 2

3 I J? F E J I F K? J E E A I 2 H? K H A 1 F K J K J F K J + F K J = J E H A F A E I D A J, A F H? A I I F H? A I A F H? A I I A I H A F A E I D F H? A I I A I A J M = E J E C E A I + F K J = J E I K H J E A I + F K J = J E H A A H A L A I 2 A H B H =? A A = I K H A I Figure 1: The model. Figure 2: Schematic view of procedure. renewal techniques of [3], whereas the sequencing strategies at the production lines are represented by G/G/c queueing models analyzed by the recently developed and highly accurate procedure of [4]. Building on the outcomes of the first two building blocks, the logistical performance measures are computed by asymptotic results from renewal theory (see [3]). These three individual building blocks are incorporated in a single integrated batchproduction/inventory system. A high-level description of the resulting computational procedure as implemented in OptStock is shown in Figure 2. In the first step, the demand processes are translated, via the (s i,nq i ) inventory policies, into replenishment processes. Throughout this first step the reorders levels are kept unspecified. The second step aims to determine the sojourn times in the queueing model, which equal the delivery times for the inventory policy. Finally, the last step calculates the reorder level, and thus the required inventory levels as well, for given service levels. Alternatively, we can fix the latter and calculate the achieved service levels. Numerical results. The primary aim of the numerical evaluation is the validation of the extrinsic accuracy of the model, i.e., does it reflect reality, and not the intrinsic accuracy, are all approximate analytical steps allowed. The latter has been done extensively for all individual building blocks in [2, 4]. Data collection was done by analyzing production and sales data and interviewing people from various departments. The presence of setup times in building B hinders a direct implementation of OptStock a little. That is, the inventory policy is driven entirely by the individual inventory positions. The implication is that too much costly production capacity may be wasted on setups in building B due to small replenishment orders placed by the (s i,nq i ) policy. In practice, the minimum campaign size in building B is, therefore, not a single batch, but a multiple thereof (see Table 2). Throughout we adopt these practical adjusted minimum campaign size for validation purposes. Table 1 displays the moments of the sizes and the interarrival times of the replenishment orders computed by OptStock. From this table, we can draw various conclusions. Firstly, the mean replenishment order sizes are for all products approximately equal to the minimum campaign sizes. Secondly, we observe that the variability in these order quantities is low. Finally, these tables show that the replenishment processes for the individual products differ significantly in their characteristics. A related observation is that the interarrival times in general also 3

4 Replenishment order characteristics for building A Product Mean quantity SD quantity Mean interarrival SD interarrival (batches) (batches) (hours) (hours) Replenishment order characteristics for building B Product Mean quantity SD quantity Mean interarrival SD interarrival (batches) (batches) (hours) (hours) Table 1: Replenishment order characteristics. deviate considerably from negative exponential distributions as typically assumed in analyses of production systems (but which is not assumption in the present research). The utilization degree reflects the percentage of the net production capacity a production line is actually producing products. The results of OptStock for the load and sojourn times in both buildings are summarized in Table 3. For the load, we have identified a very good accuracy compared to reality. A direct validation of the results for the sojourn times is not possible, due to the fact these data are not directly recorded within BASF. However, the values are checked by the planner and the production people and they coincide with their expectations of reality. Although Table 3 shows that the load differs significantly between the two buildings, it can also be seen that the sojourn times are almost identical. Table 4 shows the service levels and stock levels measured in reality and computed by OptStock for the same reorder levels. As seen from this table, the figures manifest reasonable agreement. The total amount of stock as well as the allocation of this stock to the individual products matches reality within a reasonable margin. For some smaller products, the relative difference in stock may seem to be significant, the absolute differences are, however, still acceptable. Looking more closely at the results for the stock levels, one sees that the results of OptStock are often larger than the practical values. Our feeling is that a minor limitation of the (s i,nq i ) policy shows up; this inventory policy is reactive and does not use future demand information, whereas in practice advanced demand information is available. The implication of this fact is that part of a replenishment order may never be fed into the tank, rather is directly delivered 4

5 Minimum campaign sizes Product Size (batches) Table 2: Minimum campaign sizes in building B. Building A Building B Utilization (%) Mean sojourn time (days) SD sojourn time (days) Table 3: Characteristics of buildings. to the customers obviously decreasing the average stock level over time. Table 4 shows that the service levels obtained by OptStock are almost identical to reality. Finally, we move to the optimization of the inventory requirements. Table 5 compares the inventory requirements obtained by OptStock for the optimal reorder levels when a service level of 98% is maintained to the values used in reality. It can be seen that OptStock, with the optimized parameter settings, clearly outperforms current practice in terms of inventory requirements. Average stock levels Service levels Product Reality OptStock Diff. Reality OptStock Diff. (batches) (batches) (%) (%) Total Table 4: Comparison practice and OptStock. 5

6 Product Optimal Current Diff. (batches) (batches) (%) Table 5: Mean stock level for the optimal and the current setting. Conclusion. We have developed a three-stage methodology integrating production and inventory decisions for the evaluation and optimization of batch-production/inventory systems. The methodology is embedded in a decision support tool OptStock, which has been applied to a plant of BASF. By doing so, we identified major opportunities for improvement of current practice. Encouraged by this first positive application BASF intends to apply OptStock for periodical re-setting of tactical parameters in a number of other plants inside and outside Germany. Although we took full advantage of the idiosyncrasies of the specific setting, we believe that the present case study is rather generic in nature, i.e., many firms in the process industry face the problems (stochastic demand, significant setup times, batch processing and finite buffer capacities) illustrated here. In this context, it is important to remark that the methodology of OptStock (after some adjustments) has recently proved his worth in another project at BASF with totally different logistics characteristics. Finally, in the current version of OptStock the (s i,nq i ) inventory policy is implemented. Proceeding along the lines of the present paper, one could, however, easily integrate any continuous review inventory policy such as the (s i,s i ) strategy. Acknowledgement The authors are indebted to Marcel van Vuuren for making the computer program corresponding to [4] available. Furthermore, the authors wish to thank Marko Boon for his assistance in the implementation of the decision support tool. 6

7 References [1] Kämpf, M., Köchel, P., (2004). Simulation-based sequencing and lot size optimisation for a production-and-inventory system with multiple items (Proceedings of the 13th International Working Seminar on Production Economics, Igls/Innsbruck, vol. 3, pp ). [2] Kok, A.G. de, (1987). Production-Inventory Systems: Algorithms and Approximations (CWI, Amsterdam). [3] Kok, A.G. de, (1991). Basics of inventory management: part 3 the (b, Q) model (Research report, Catholic University Brabant). [4] Vuuren, M. van, Adan, I.J.B.F., (2005). Approximating the GI/G/s queue by using aggregation and matrix analytic methods (Stochastic Models, vol. 21, no. 2-3, pp ). [5] Winands, E.M.M., Adan, I.J.B.F., Houtum, G.J. van, (2005). The stochastic economic lot scheduling problem: a survey (Invited review for European Journal of Operational Research, under revision). [6] Winands, E.M.M., Kok, A.G. de, Timpe, C., (2007). Case study of a batchproduction/inventory system (Report, BASF). [7] Zipkin, P.H., (1986). Models for design and control of stochastic multi-item batch production systems (Operations Research, vol. 34, no. 1, pp ). 7

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