Batch Production
CASE STUDY
Mario Fayez Wadea | 3 industral Engineering | 1 MAy
The CBAF factory under consideration has various concurrent production lines that
generate multiple products for the process industry on a make-to-stock basis. The
stochastic demand, setup delays, batch processing, and finite buffer capacity all
complicate planning. The key contribution is the creation of a three-stage technique that
integrates production and inventory decisions and can be used to evaluate and optimise a
variety of batch production/inventory systems. We were able to uncover considerable
potential for improving current practise by incorporating this methodology into a decision
support tool.
CBAF 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
CBAF 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.
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Demand for the products is highly uncertain, but at the same time it 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 CBAF. 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 require-ments 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 mea-sures, 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 (si, nQi) 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 si, a replenishment
order of amount nQi, n = 1, 2, . . ., is placed such that the inventory level is again between si
and si + Qi. The inventory position is defined as the physical inventory plus the stock on
order minus the backorders. The quantity Qi is called the batch size, while the amount nQi
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
PAGE 2
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 batchproduction/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 CBAF 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 (si, nQi) inventory policy is analyzed by (approximate)
stockpoints
production
lines
demand
processes
replenishment
processes
waiting lines
Figure 1: The model.
Procedure
Input / output
Computation
replenishment
process
Demandprocess
Computation
reorder levels
Performance measures
Computation
sojourn times
Figure 2: Schematic view of procedure.
renewal techniques of [3], whereas the sequencing strategies at the production lines are
represented by PG/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 (si,nQi) inventory policies, into
replenishment processes. Throughout this first step the reorders levels are kept
PAGE 3
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 (si,nQi) 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
Product
1
2
8
9
10
11
12
13
14
15
16
Replenishment order characteristics for building A
Mean quantity SD quantity Mean interarrival SD interarrival
(batches)
(batches)
(hours)
(hours)
1.03
0.18
0.45
1.00
0.06
19.67
1.04
0.21
3.52
1.02
0.14
0.32
1.00
0.03
1.61
1.12
0.36
2.04
1.01
0.12
2.93
1.03
0.16
10.53
1.00
0.07
12.62
1.01
0.09
2.72
1.00
0.07
3.44
Replenishment order characteristics for building B
0.64
13.22
2.90
0.55
1.28
1.51
2.28
16.73
7.77
1.68
2.26
PAGE 4
Product
Mean quantity
(batches)
SD quantity
(batches)
Mean interarrival
(hours)
SD interarrival
(hours)
3
4
5
6
7
2.00
4.65
1.20
2.25
3.05
0.00
0.16
0.50
0.03
0.00
2.84
1.24
3.98
6.72
2.35
1.94
1.23
3.04
4.04
1.55
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 CBAF. 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 (si, nQi) 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
PAGE 5
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
(batches)
OptStock
(batches)
Diff.
(%)
Reality
OptStock
Diff.
(%)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Total
6.00
0.69
5.08
9.13
2.82
1.16
5.86
2.30
7.28
3.33
3.52
3.61
1.74
1.86
1.67
1.17
6.50
0.87
5.51
8.90
2.86
2.04
4.22
3.12
8.53
3.61
3.92
3.78
2.40
1.84
1.67
1.17
+8.3
+25.7
+8.1
-2.5
+1.7
+75.0
-28.0
+28.4
+17.2
+8.6
+11.5
+4.7
+37.6
-1.0
0.0
0.0
+7.6
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
0.99-1.00
1.00
0.96
1.00
0.98
0.99
0.99
1.00
1.00
0.99
1.00
1.00
1.00
0.99
1.00
1.00
0.99
0.99
0.0
-3.0
0.0
-1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-0.3
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Table 4: Comparison practice and OptStock.
Product
Optimal
(batches)
Current
(batches)
Diff.
(%)
1
2
3
4
4.38
1.03
1.49
8.29
6.50
0.87
5.51
8.90
5
6
7
2.37
1.75
2.19
2.86
2.04
4.22
8
9
10
1.58
6.15
1.09
3.12
8.53
3.61
11
12
13
1.76
1.16
2.21
3.92
3.78
2.40
14
15
1.01
0.89
1.84
1.67
16
0.96
1.17
-32.6
+18.2
-72.9
6.9
-17.2
-14.3
48.0
-49.5
-27.9
69.8
-55.2
-69.3
8.0
-45.2
46.7
-18.2
Table 5:
Mean stock level for the optimal and the current setting.
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Conclusion. We have developed a three-stage methodology integrating production
and inventory decisions for the evaluation and optimization of batchproduction/inventory systems. The methodology is embedded in a decision support tool
OptStock, which has been applied to a plant of CBAF. By doing so, we identified major
opportunities for improvement of current practice. Encouraged by this first positive
application CBAF 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
CBAF with totally different logistics characteristics. Finally, in the current version of
OptStock the (si, nQi) 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 (si, Si) 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.
PAGE 8
References
[1] Ka¨mpf, M., Ko¨chel, 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.
175-184).
[2] Kok, A.G. de, (1987). Production-Inventory Systems: Algorithms and Approximations
(CWI, Amsterdam).
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