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Significance of stochastic programming in addressing production planning under uncertain demand...

Table 3. Monte Carlo Simulation N=10, m=10
Cluster No Product Product Product Value of Test Gap
1 2 3 Objective result in
Function large
(z) sample
(Z)
1 22.986 31.976 20.897 -5.049.434 -5.019.969 -29.465
2 22.112 34.344 21.575 -4.888.018 -5.020.088 132.070
3 21.734 35.576 21.868 -5.009.936 -5.020.124 10.189
4 23.298 32.411 20.655 -5.018.321 -5.019.987 1.666
5 22.166 30.828 21.533 -4.849.015 -5.019.920 170.904
6 23.127 31.020 20.787 -4.941.427 -5.019.922 78.495
7 22.201 36.355 21.506 -5.194.353 -5.020.120 -174.232
8 23.236 30.391 20.703 -4.939.808 -5.019.891 80.083
9 23.500 34.633 20.498 -4.934.362 -5.020.092 85.730
10 21.322 31.052 22.188 -4.947.533 -5.019.921 72.388

gap value was observed to be Cluster 4, which is recom- decision support mechanisms.
mended as the solution to apply.
When planning production under various uncertainty cri-
Table 3 points up that the decision variable values for teria, managers should ensure that their decisions are
Cluster 4 are close to the average of the objective function supportive for the subsequent period. A stochastic ap-
values obtained from the large sample test, and it provides proach to production planning problems can make uncer-
the best gap value. Although the minimization problem tainty manageable for them, allowing for linear operations
allows for accepting the smallest objective function value, aligned with their goals. This approach supports cost min-
this study focused on the gap value. Therefore, the best imization and provides valuable data for various aspects
solution cluster has been determined as Cluster 4 among such as inventory management, workforce planning, and
the clusters with 10 scenarios. raw material consumption.

4. Conclusion This study provides a comprehensive overview of the sto-
chastic modeling approach used to determine production
Achieving and maintaining stable production conditions is quantities for a company manufacturing natural gas pipes.
quite challenging in today’s world. Furthermore, numerous The company can optimize its production plans under
social, economic, and societal factors can influence com- demand uncertainty for a 6-month period by evaluating
panies’ production plans. It should be acknowledged that various scenarios and calculating optimal solutions based
uncertainty is a significant part of our lives and should be on production parameters affected by this uncertainty.
incorporated into our systems. Indeed, this study demon- Notably, stochastic modeling tools such as the SAA al-
strates that incorporating randomness and uncertainty gorithm play a crucial role in managing uncertainty by
into production planning can yield positive differences for sampling existing data and have successfully managed this
companies. Using standard linear programming, optimiza- uncertainty. However, the assumptions and limitations of
tion problems are solved based on the data set available at the model may not always hold in real-world conditions;
any given time t. This can result in a production plan with for example, demand uncertainty could be more complex,
z min = −4.696.619, assuming consistent production quan- or external factors in the company’s production processes
tities over six months, which could cause significant issues may not have been adequately considered. The limitation
such as sales losses or high inventory costs in real-world of using annual sales data for the model may affect its
serial production. In contrast, by adopting a stochas- performance in different industries or with larger datasets.
tic modeling approach, which considers different demand Additionally, the limited number of scenarios used in the
quantities for different months, the production system is study may prevent the complete optimization of deci-
simulated with its constraints and parameters. This al- sion variables. Future research could explore the model’s
lows for determining optimal production quantities and performance with larger datasets and across various indus-
calculating the minimum cost at an optimal point. It has tries, assess the effectiveness of stochastic modeling with
been observed that the stochastic model provides a more real-time data, and compare different optimization meth-
advantageous solution. ods.In such problems, where stochastic parameters must
be handled, chance constraint-based models may be cre-
The minimum value of the objective function obtained ated instead of SAA. However, the disadvantage of chance
from the stochastic model is z min = −5.259.730. Com- constraint is that based on considered probability distri-
pared to the deterministic model result, this represents a bution, a nonlinear model has to be created and dealt
significant difference. The stochastic model offers a more with. Another option is simulation, which has its own
flexible, efficient, and profitable decision. Managers can or- disadvantages, such as difficulty in developing the model,
ganize their production plans to control random demands. long processing time, and not guaranteeing the optimal
The stochastic model can be revised based on various goals solution. Such studies could expand the model’s applica-
and used as an important data source in the company’s tion area and provide more comprehensive performance
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