**A Goal Programming Approach For Frozen Food Production Planning**

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**HIGHLIGHTS**

  - > Lexicographic Goal Programming was used to develop models for food production planning in small and medium enterprise (SME).

  - > The result was obtained using LINGO software. 

  - > The result was compared using available and other findings were reviewed.

ABSTRACT

*This paper examines the Goal Programming (GP) approach in food production planning in order to further enhance and find better solutions. The objective of this paper is to determine the optimum level of frozen food production for small and medium enterprise (SME). Azali Frozen Food, a small and medium enterprise located in Penang was selected as it can produce a range of frozen foods throughout the country. The problem is handled through Lexicographic Goal Programming. The results are compared to the available data that was given and other findings were reviewed. The findings of this paper are expected to assist community small and medium enterprise and other decision makers involved in production planning. The developed method will also be of use for those who are interested in the model of goal programming to solve complex planning issues involving uncertain parameters.*

*Keywords: goal programming, small and medium enterprise, production planning*

# INTRODUCTION 

A small and medium enterprise (SME) is defined as a company with fewer than 150 employees (Hassan and Ayop, 2012). It is considered as a business tool, as well as a source of employment and income. It is the biggest contributor to accomplishing the fundamental goals of any national economy, as well as an innovative and competitive power (Herman, 2012). A plan for determining production goals and estimating resources is known as production planning. To achieve these objectives, production planning is required in organisation’s process in order to get optimize production. Production planning is an essential activity in any manufacturing system. It also entails allocating available resources to the required operations (Saidi-Mehrabad, Paydar and Aalaei, 2013). Furthermore, it allows to create a detailed plan for achieving production goals in a cost-effective, efficient, and timely manner. Still, it also discovered that production planning is a difficult task. For this reason, close collaboration between all units in any organisation is required (Hassan, Idris and Razman, 2013). The problem that companies frequently face when conducting production planning is optimizing more than one goal, so proper planning and a solution method to combine optimal solutions from incompatible factors are required. Georgios, Luis, and Micheal (2011).

# LITERATURE REVIEW 

According to Silva et al. (2013), GP is a multi-objective optimization technique. This technique is used by decision-makers to solve complex problems, as well as those committed to finding solutions that meet the multiple objectives (Shrivastava, Verma, and Sharman, 2013). Many recent research ideas for production planning using goal programming have been developed. Previously Setiawati & Arisya, 2018 optimized amount of three types of chocolate product in order to maximize the profit of the chocolate factory using goal programming. Kumar 2019 created pre-emptive priory weighted goal programming for a small scale industry in Hyderabad that produces five bakery products. Meanwhile for clothing production, Anggraeni et al., 2015used the goal programming method to determine how many clothing productions should be produced in order to achieve the best possible production results that are in line with the company's goals. In fact, according to (Hassan and Ayop, 2012) SME's can use the GP model to determine their production planning in order to meet the expanding demands of their markets. There is an evidence stated that small and medium enterprise require the goal programming model to calculate their profits based on the use of their labour, machinery, and raw materials (Hassan et al., 2013).

# METHODOLOGY 

**Goal Programming Approach**

GP can be used in solving multiple objectives. According to Chang & Lee, (2010) , it can be used to design the best overall optimal performance in a multi objective decision problem. The general GP as defined by Ignizio (1976) can be presented as

Minimize lexicographically

subject to

for all i and j

represents the priority level assigned to each relevant goal in rank order. For example and are nonnegative constants representing the numerical weights associated with deviational variables, and corresponding goal, . The represents the decision variables for the items while represents the decision variables coefficients.

**Steps for Formulating Goal Programming Model**

There are a few important steps in order to create a GP model. The step can be concluded as follows (Ahmad et al., 2005):

Step 1: Determine decision variables.

Step 2: Determine the aspirational levels of each objective.

Step 3: Determine the deviational variables of each objective and each of the constraint.

Step 4: Rank the goals of importance.

Step 5: Setting the achievement functions.

**Proposed Method**

The proposed method is based on pre-emptive goal programming. The aim of this study is to construct a goal programming model that can be used in a real-life production situation in a small-medium industry. The data is collected from Azali Frozen Food in Penang.  The optimization aim is to maximize its daily sale profit of RM 330 per day, minimise overtime and staff, and maximizing machine utility. The procedure for a goal programming approach for frozen food production planning is summarized as in Figure 1.

![](630d5b4e5ca3b_media/media/image12.png)

**Figure 1**: Flowchart of Goal Programming Approach for Frozen Food Production Planning

# IMPLEMENTATION

There are a few things that need to be considered before build the model depend on the steps taken in the goal programming formulation. Thus, this model is developed with three decision variables, 17 hard constraints, three goals, three aspirational levels and two priorities. All these factors need to be considered. The data were collected from person in charge at Azali Frozen Food which located in Penang.

**Table 1:** Decision Variables

| **Notation** | **Decision variable** |
| ------------ | --------------------- |
|              | Number of murtabak    |
|              | Number of samosa      |
|              | Number of cucur badak |

**Table 2**: Ingredient for Each Product

<table>
<thead>
<tr class="header">
<th><strong>Symbol</strong></th>
<th><strong>Data</strong></th>
<th><strong>Value (gram)</strong></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td></td>
<td>Quantities of flour to murtabak</td>
<td>20</td>
</tr>
<tr class="even">
<td></td>
<td>Quantities of flour to cucur badak</td>
<td>4.6</td>
</tr>
<tr class="odd">
<td></td>
<td>Quantities of onion to murtabak</td>
<td>37.5</td>
</tr>
<tr class="even">
<td></td>
<td>Quantities of onion to samosa</td>
<td>2.3</td>
</tr>
<tr class="odd">
<td></td>
<td>Quantities of eggs to murtabak</td>
<td>25</td>
</tr>
<tr class="even">
<td></td>
<td>Quantities of meat to murtabak</td>
<td>8</td>
</tr>
<tr class="odd">
<td></td>
<td>Quantities of chicken to murtabak</td>
<td>8</td>
</tr>
<tr class="even">
<td></td>
<td>Quantities of potatoes to murtabak</td>
<td>10</td>
</tr>
<tr class="odd">
<td></td>
<td>Quantities of potatoes to samosa</td>
<td>6.5</td>
</tr>
<tr class="even">
<td></td>
<td>Quantities of potatoes to cucur badak</td>
<td>8</td>
</tr>
<tr class="odd">
<td></td>
<td>Quantities of sugar to murtabak</td>
<td>5</td>
</tr>
<tr class="even">
<td></td>
<td><p>Quantities of sugar to samosa</p>
<p>Quantities of sugar to cucur badak</p>
<p>Quantities of carrot to samosa</p>
<p>Quantities of coconut to cucur badak</p>
<p>Quantities of prawn to cucur badak</p>
<p>Quantities of spice to murtabak</p>
<p>Quantities of spice to samosa</p>
<p>Quantities of spice to cucur badak</p>
<p>Quantities of spring roll pastry to samosa</p>
<p>Quantities of oil to cucur badak</p>
<p>Quantities of salt to murtabak</p>
<p>Quantities of salt to samosa</p>
<p>Quantities of salt to cucur badak</p></td>
<td><p>4.7</p>
<p>1.5</p>
<p>0.6</p>
<p>4.4</p>
<p>0.37</p>
<p>6.25</p>
<p>5.9</p>
<p>1.8</p>
<p>4.2</p>
<p>2.2</p>
<p>1.25</p>
<p>1.25</p>
<p>1.25</p></td>
</tr>
</tbody>
</table>

**Table 3**: Profit of Each Product

| **Symbol** | **Total profit** | **Profit (RM)** |
| ---------- | ---------------- | --------------- |
|            | Murtabak         | 0.20            |
|            | Samosa           | 0.10            |
|            | Cucur badak      | 0.10            |

**Table 4:** Raw Materials Per Day

| **Symbol** | **Data**           | **Total available per day (gram)** |
| ---------- | ------------------ | ---------------------------------- |
|            | Flour              | 45000                              |
|            | Onion              | 60000                              |
|            | Eggs               | 2500                               |
|            | Meat               | 6400                               |
|            | Potatoes           | 31500                              |
|            | Carrot             | 1000                               |
|            | Sugar              | 16000                              |
|            | Coconut            | 12000                              |
|            | Prawn              | 1000                               |
|            | Spice              | 25000                              |
|            | Spring roll pastry | 3500                               |
|            | Oil                | 6000                               |
|            | Salt               | 4000                               |

**Table 5**: Time Taken to Produce for Each Product

| **Symbol** | **Data**                                      | **Minutes** |
| ---------- | --------------------------------------------- | ----------- |
|            | Time taken for labour to produce murtabak     | 0.125       |
|            | Time taken for labour to produce samosa       | 0.5         |
|            | Time taken for labour to produce cucur badak  | 0.13        |
|            | Time taken for machine to produce murtabak    | 0.175       |
|            | Time taken for machine to produce samosa      | 0.006       |
|            | Time taken for machine to produce cucur badak | 0.044       |

**Hard Constraints**

1\) Total quantities of flour to murtabak and flour to cucur badak are not less than 45000g.

(1)

2\) Total quantities of onion to murtabak and onion to samosa are not less than 60000g.

(2)

3\) Total quantities of eggs to murtabak are not less than 2500g

(3)

4\) Total quantities of chicken to murtabak are not less than 6400g.

(4)

5\) Total quantities of meat to murtabak are not less than 6400g.

(5)

6\) Total quantities of potatoes to murtabak, potatoes to samosa and potatoes to cucur badak are not less than 31500g.

(6)

7\) Total quantities of carrot to samosa are not less than 1000g.

(7)

8\) Total quantities of sugar to murtabak, sugar to samosa and sugar to cucur badak are not less than 16000g.

(8)

9\) Total quantities of coconut to cucur badak are not less than 12000g.

(9)

10\) Total quantities of prawn to cucur badak are not less than 1000g.

(10)

11\) Total quantities of spice to murtabak, spice to samosa and spice to cucur badak are not less than 25000g.

(11)

12\) Total quantities of spring roll pastry to samosa are not less than 3500g.

(12)

13\) Total quantity of oil to cucur badak are not less than 6000g.

(13)

14\) Total quantity of salt to murtabak, salt to samosa and salt to cucur badak are not less than 4000g.

(14)

15\) The amount of murtabak required must be at least 74 pieces.

(15)

16\) The amount of samosa required must be at least 500 pieces.

(16)

17\) The amount of cucur badak required must be at least 2600 pieces.

(17)

**The Goals**

There are three goals in this problem. The purpose of these goals are to present the decision maker’s requirement.

1)  Total profit desired in this company are RM330 per day.

The total profits are taken from profit of murtabak, samosa and cucur badak gained per day is RM330.

(18)

2)  Minimize the overtime per staff per day is 601 minutes. There are eight staff who work in this company.

(19)

3)  Maximize the usage of machine per day is 134 minutes. This is the time taken of the usage of machine for murtabak, samosa and cucur badak.

(20)

**Aspirational Levels**

In this problem, aspirational levels are determined based on the frozen food’s company requirement. It should be combined with the objective functions to develop the goals.

There are three aspirational levels as follows:

1)  First aspirational level

The total profit desired in this company is RM330. In this research, first aspirational level is based on the first objective which is as follow:

2)  Second aspirational level

The overtime per staff per day is 601 minutes. Therefore, in this research, the second aspirational level is based on the second objective which is as follow:

3)  Third aspirational level

The usage of machine per day is 134 minutes. In this research, third aspirational level is based on third objective which is as follow:

**Priority Structures**

The priority structures:

1)  First priorities ()

In this research, the first priority is based on the first goal and this will result in the achievement function. It can be obtained as follow:

Minimum

2)  Second priorities ()

In this research, the second priorities are based on the second goals and third goals and this will result in the achievement function. It can be obtained as follow:

Minimum

**Achievement Function**

Goals are formed from combination of objective function and the aspirational level and will conclude into achievement function.

The achievement function is:

Minimization = \[\]

# RESULTS AND DISCUSSION

**Results Discussion**

Based on the result obtained using LINGO 13.0, all the objectives and goals are achieved. A goal that is met will depend on the deviational variables. If the value of deviational variable or priority level gives zero value and meet the prescribed deviational variable, thus the goal is met. To obtain the goal, all the deviational variables must be reviewed on each of the objectives. Table 6 below shows the result.

**Table 6**: Summary of the Complete Results

| **Results of deviational variables** | **Deviational variables** | **Priorities** | **Goal achievement** |
| ------------------------------------ | ------------------------- | -------------- | -------------------- |
| **=100**                             | \=0                       | \=0            | Fully achieved       |
| **=500**                             | \=0.5                     | \=0            | Fully achieved       |
| **=2600**                            | \=0                       |                |                      |
|                                      | \=0                       |                |                      |
|                                      | \=0                       |                |                      |
|                                      | \=0.9                     |                |                      |

In the first priority level, negative and positive deviational variables represented symbols and in computer programming. The goal for the first priority level is to obtain at least RM330. From the table 6, the objective function for the first priority is zero which is. Thus, the first priority, is achieved and the first objective is met. For the second priority, there are two deviational variable for negative deviation variable and two positive deviation variables which represent,, and . There are two goals for the second objective which are minimizing overtime and maximizing the utility of machines used in the frozen food production planning. Both goals are placed in the same level because it based on the decision maker and it also has the same unit measure which is in minutes. The objective functions show that the value for and are zero as shown in the table above. The negative variable, give the value 0.5 minutes. The value stated shown that it is less about 0.5 minutes in order to achieve the goal. The variable that should be minimized in this objective function is. While the positive variable for is 0.9 minutes and the result obtained is more than 0.9 minutes in achieving the desired goal. In addition, is the variable that should be minimized in order to achieve the goals. As a result, it is shown that both goals has been achieved. In overall, the results obtained are fully achieved for first and second priorities. Thus, the objectives and the goals of this research are achieved in order to get the optimum solution.

**Comparison Results**

**Table 7**: Comparison Results

| Symbol | Type of variable      | Original data | Optimum value |
| ------ | --------------------- | ------------- | ------------- |
|        | Number of murtabak    | 150           | 100           |
|        | Number of samosa      | 840           | 500           |
|        | Number of cucur badak | 2600          | 2600          |

Table 7 shows that the comparison result between the original data and the optimum value calculated from LINGO 13.0. The solution shows that the number of murtabak and the number of samosa are exceed the optimum level which are 50 pieces for the number of murtabak and 340 pieces for the number of samosa whereas the number of cucur badak is in the optimum level which is 2600 pieces. This solution can be expected to help in the planning of frozen food production in order to achieve the necessary target.

**CONCLUSION**

In conclusion, goal programming is a suitable technique used in optimizing food production planning. Sinha and Sen (2011) concluded that the goal programming model (GP) is a powerful tool that draws upon highly developed and tested approaches in linear programming, whereas Babic and Peric (2011) argued that the GP has demonstrated as an useful procedure in finding the optimal solution. Furthermore, based on available resources, this model can help increase food production for small and medium enterprise. A similar methodology could be utilized by other SMEs or industries for future planning.

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