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

effective criterion for increasing efficiency in the face of here is to minimize the cost. Businesses must evaluate
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intensifying competition conditions. It is known that in- various situations during their operations and make deci-
ventory management in multi-echelon supply chains is sions that consider these. It is important to determine the
much more challenging than in single-stock-point systems correct production quantities to keep up with the fast flow
in business practices and their modeling environments. 10 in the sector. With this study, the model determining the
However, inventory problems involving non-static stochas- quantities that will optimize the efficiency of the company
tic demand and fixed ordering costs present mathematical producing clamps is intended to serve as an example for
difficulties. 11 industries with different production constraints and to be
adaptable.
This study aims to conduct inventory planning under sto-
chastic demand. Stochastic programming generally encom- The study is compiled under four main sections. After
passes mathematical programming models that can make mentioning the importance and general information cov-
decisions under uncertainty. 12 Essentially, stochastic pro- ered in the study in the first section, the second section
gramming is an approach that combines decision-making includes and examines existing studies in the literature
models with mathematical programming because it can in detail. Studies based on stochastic modeling and the
incorporate uncertainty into the mathematical model. 13, 14 sample average approximation approach are detailed. The
Furthermore, this paper presents a case study calculating third section addresses the details of the problem, mathe-
optimal production quantities to meet variable demand matical models, and problem-solving using business data.
forecasts for the production planning of clamp products The methods and techniques used are discussed, and the
used in industrial pipe systems. The products manufac- results are presented. The fourth section discusses the
tured in the company are stored in inventory, and de- benefits of the study and the results obtained from solving
mands are met from these stocks. The production facility the mathematical modeling of the problem.
and storage capacities limit the quantity of products pro-
duced in a production facility and the amount held in
inventory. 15 Thus, in this study, we aim to determine the
best production quantities for the coming year based on 2. Literature review
the annual sales data of a factory producing industrial-
type pipe clamps and to minimize costs. Considering The concept of production is a research topic addressed
the uncertainties arising from demand’s stochastic (ran- across various disciplines, encompassing a broad spectrum
dom) nature, it aims to calculate the optimal production of literature. Identifying the factors influencing produc-
quantities under different scenarios. Here, the scenario tion and utilizing resources effectively within these factors
fundamentally assumes demand uncertainty and supports have always directed studies on productivity, accurate pro-
the randomness relationship. The origin of the scenario duction quantities, and cost optimization. Mathematical
can be based on a known discrete probability distribution, modeling has greatly supported managers and businesses in
limited sample information, some types of approximation, decision-making for production planning problems.Recent
or probabilistic prior analyses based on expert opinion. 16 studies have observed that optimization problems increas-
Parameters affected by scenarios were identified, and the ingly take into account the activities of multiple functions
model was ensured to produce accurate results. Uncer- during the optimization process. To optimize the objec-
tainties in the production plan have been considered using tives of a business, all relevant units can be evaluated
relevant variables. The results obtained vary depending from an integrated perspective. Kucukkoc 20 addressed a
on the scenarios, aiming to create the most accurate pro- machine scheduling problem by optimizing carbon emis-
duction plan with this method. sions in production and transportation. He developed a
mixed-integer linear programming model that considers
both economic and environmental sustainability. Ersoy
The stochastic modeling in this study aims to optimize
et al. 21 employed a mathematical model to determine the
scenario-based applications of the stochastic approach in
stable equilibrium point of a system composed of fiber op-
production planning. One of the application tools is the
tic cables. Through simulation analyses, they derived the
Sample Average Approximation (SAA). In the literature,
necessary general formulas using this equilibrium point as
it is a methodology used to solve approximate problems
multiple times to obtain increasingly accurate solutions. 17 a reference.
Repetition enables the calculation of the optimal objec-
tive function value and also the assessment of the solution. However, as uncertainty has become an important as-
The SAA methodology was preferred in the study to ob- pect of modern times, production planning problems must
tain the most optimal solution by simulating the stochastic reflect the impact of randomness. Stochastic modeling in-
demand quantities. In the first stage, with the determined corporates randomness into problems and is a supportive
production quantities, the approach allows for the correct solution method. 19, 22
production quantity to be determined by assuming the im-
pact of uncertainty in other months. It can present the op- Simulation modeling under stochastic demand is a frame-
timal production plan with the appropriate scenario value work conducted to understand and address stochastic (ran-
obtained from different scenario outputs. Thus, decision- dom) demand situations in processes such as inventory
makers can use efficient plans from stochastic models to management, inventory control, or production planning
manage uncertainty. 18, 19 It is intended to set an example within a business. This type of modeling is used to under-
for studies where the error margin can be minimized using stand how uncertain demand situations can interact and
statistical approaches to generate the parameters used in to determine which strategies an organization can apply
scenarios. to manage this uncertainty. Meeting the required inven-
A real case study is presented, considering the working tory amount is crucial for businesses. However, periods of
capacity of a company producing clamp pipes. The aim non-stationary demand can be encountered. Periods where
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