The research demonstrates how mathematical optimization can determine the most profitable production mix under limited raw materials and operational capacity. By applying Linear Programming through POM-QM for Windows software, the team found that producing 62.5 packs of chocolate-flavored banana chips and 50 packs of balado (spicy) flavor per day generates a maximum net daily profit of IDR 833,121.25.
From Intuition to Data-Based Decisions
Micro, Small, and Medium Enterprises (MSMEs) play a critical role in regional economic stability. However, many small businesses still rely on intuition when deciding production volumes. This approach often leads to overproduction, wasted raw materials, or underproduction that results in lost sales opportunities.
“Aku Pisang,” a banana chips producer in Aceh Jaya, faced similar challenges. Each 100-gram pack requires:
- 250 grams of raw bananas
- 25 ml of cooking oil
- Flavor powder (0.08 kg for chocolate or 0.04 kg for balado)
Additionally, one 3 kg LPG cylinder can produce approximately 300 packs. Differences in ingredient costs create different profit margins:
- Chocolate variant: IDR 8,383.30 net profit per pack
- Balado variant: IDR 6,183.30 net profit per pack
These constraints and cost variations make production planning complex without systematic analysis.
The Optimization Model
The research team built a Linear Programming model with two decision variables:
- X1: Number of chocolate packs produced
- X2: Number of balado packs produced
The model included several operational constraints:
- Maximum 5 kg of chocolate flavor powder per day
- Maximum 2 kg of balado powder per day
- 480 minutes of labor time per day
- 115 packs maximum production capacity per day
Using the Simplex method in POM-QM software, the optimal production point was identified at:
- 62.5 chocolate packs
- 50 balado packs
This combination fully utilizes critical resources while maximizing profit.
Flavor Powder Identified as the Critical Constraint
The analysis revealed that flavor powder is the binding constraint. All available powder is fully used in the optimal solution, while labor time and production capacity still show unused capacity.
This means increasing labor hours or purchasing new equipment would not raise profit unless the supply of flavor powder increases. In optimization terms, flavor powder has a positive “shadow price,” indicating that every additional unit of seasoning directly increases profit.
The study found:
- Each additional unit of chocolate powder could increase profit by IDR 2,500
- Each additional unit of balado powder could increase profit by IDR 3,750
Meanwhile, additional labor or machine capacity has zero marginal impact as long as seasoning remains limited.
According to Agustiar, mathematical modeling provides clarity that intuition cannot. Data-driven decisions allow MSME owners to identify which resource truly drives profitability.
Practical Implications for MSMEs
The findings highlight that production optimization does not require large capital investments. Instead, it requires better allocation of existing resources.
Key implications include:
- MSMEs can increase profit without expanding workforce or facilities.
- Business owners should prioritize securing critical raw materials with high marginal value.
- Regional policymakers can introduce data-based decision tools in MSME development programs.
- Simple optimization software can significantly improve operational planning accuracy.
In Aceh Jaya, supply instability of auxiliary materials often disrupts small-scale food industries. This research confirms that managing supporting ingredient supply chains can be more important than increasing labor capacity.
A Replicable Model for Other Small Industries
The Linear Programming approach used in this study can be replicated in other food processing sectors, such as cassava chips, bakery businesses, or agricultural product processing. Any enterprise with multiple products and limited resources can benefit from this method.
Future research may apply Integer Programming to ensure whole-number production outputs or incorporate marketing costs and demand uncertainty into the model.
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