Sustainable Multi-Objective Production Planning for the Refrigerating and Air Conditioning Industry in Saudi Arabia: A Preemptive Goal Programming Approach

Abstract

This research presents a preemptive goal-programming model for sustainable multi-objective production planning for the refrigeration and air conditioning industry in Saudi Arabia. The model was solved using LINGO software, taking into account market demand, production revenue, production time, and production cost data to optimize production planning. The findings showed that the objectives of minimizing production cost, maximizing sales revenue, and maximizing machine utilization were achieved, with no negative or positive deviational variables. The study suggests that by using sensitivity analysis, the company can increase costs by 2.14% to minimize production costs in the following year, but this could result in a 4.37% reduction in revenues. Overall, the goal-programming model demonstrates the potential for the refrigeration and air conditioning industry in Saudi Arabia to achieve its goals for cost optimization, sales revenue maximization, and resource utilization.

1. Introduction

Goal programming falls under the category of multi-objective optimization, which falls under the category of Multi-Criteria Decision Analysis (MCDA), also known as Multiple-Criteria Decision-Making (MCDM). Programming with goals is also reckoned as optimization [1]. Essentially, it deals with multiple, usually conflicting objectives. Each of these measures has a target value or goal. As a result of this achievement function, unwanted deviations from the target values are minimized. The concept of Multiple Objective Programming (MOP) has been part of previous research and is interchangeably known as multi-attribute optimization, vector optimization, multi-criteria optimization, or Pareto optimization. This is used to derive mathematically optimized solutions to problems that comprise numerous objective functions. These types of decision-making are also adopted in daily life while including different scenarios and complex tasks for taking more informed and effective solutions. Due to its dimensionality and conflicting criteria, it becomes difficult to use MOP. For instance, the Pareto frontier is computationally intensive and hinges on the preference of the Decision Maker (DM) to distinguish between probable solutions [2,3]. His study has stressed the Smart Healthcare Management System (SHMS) to be used as an integrative technology in hospital settings for the effective workflow of hospital operations and the service quality of healthcare [4]. Ref. [4] proposed a hybrid exploratory three-phased Multi-Criteria Decision-Making (MCDM) model that enhanced the Medical Data Informational System (MDIS) and Medical Device and Drug Management System (MDMS). Conspicuously, MCDM is widely adopted to obtain strategic goals with limited resources [4]. A study by Mirzaee et al. [5] has used goal programming for supplier selection, order allocation, order management, and managing the issues of quantity discounts while adopting a mixed integer linear programming model. According to the results of [5], this approach yielded the desired outcome. Another study by Ho [6] has also emphasized the role of decision-makers in setting the level of satisfaction for meeting each goal in manufacturing firms. In addition to that study, Torres-Ruiz and Ravindran [7] have revealed that the adoption of preemptive, non-preemptive, and fuzzy goal programming models brought about eco-efficiency and an increase in productivity. Three types of analysis can be performed using goal programming:

• Estimating the resources required for achieving the desired goal.
• Analyzing the resources available to achieve the goals.
• Finding the best solution under varying resources and priorities.

Gupta et al. [8] adopted two-level decision-making operating in two groups in supply chain networking. First, the quantity that was dispatched to the distributors was determined. The second was related to selecting the amounts. The first level of decision-making operating was aimed at reducing the transportation charges, while the other was adopted to reduce the time of delivery of the products in the supply chain operations and to maintain the balance between allocating the orders and destinations. This study adopted a Fuzzy Goal Programming model (FGP) to overcome the complex issues related to multi-objective supply chain networking in a fuzzy environment. The proposed model has achieved optimized results, exhibiting the optimized level of quantities to be transported through numerous resources to their relevant destination.

Nalubowa et al. [9] used Markov chains coupled with stochastic goal programming and derived a goal programming model to be used to determine the lot size at manufacturing firms. The study determined their overachievement and underachievement by figuring out the goal constraints, the variable of deviation, the objective function, and priorities. Stochastic demand and its different states were represented by the Markov chain. The applied mathematical solver that was used in this study was MATLAB TM. The optimization mode achieved the desired outcome to optimize decision-making related to determining the quantity of the product and maintaining the balance of the delivery of the order. The study by Sarakr et al. [10] developed a multi-attribute closed-loop system of the supply chain. The study intended to develop a system that could work for the self-healing of polymer packaging while using reversible transport packaging. This system involved a single supplier and manufacturer but multiple retailers that had storage and budget limitations. The study used a Single-Setup-Multi-Delivery (SSMD) approach that involves a centralized system of decision-making in a supply chain management system aiming to improve the sustainability and effectiveness of the system. Moreover, through the use of three distinct metaheuristic approaches, a weighted goal programming method was employed by the study. The experimental analysis of the study shows that in comparison with the single-setup-single-delivery method, the SSMD method improved the total profit volumes of the entire system by creating an optimal number of shipments. To address the supplier selection problem of manufacturing firms, Tirkolaee et al. [11] adopted a Fuzzy Analytical Network Process (FANP), a Weighted Goal Programming (WGP) method, and a Decision-Making Trial and Evaluation Laboratory (DEMATEL). These techniques were used to categorize the criteria and sub-criteria as well as to figure out the relations between them for bringing out the order of preference by Similarity to the Ideal Solution (TOPSIS) for the supplier’s selection. The WGP assisted in considering the priorities of suppliers and in maximizing the supply chain by dealing with the multiple objectives involved. Another study used a goal programming method aiming to reduce the total cost of in-house production operations, outsourcing, storage, workforce, and employment or unemployment cost along with increasing customer satisfaction [12]. The study model comprises a mixed-integer linear programming model with a robust optimization approach. However, the adoption of a goal programming approach assisted in implementing multi-objectives and authenticating the robust model, while for the efficiency of an algorithm, the Taguchi design method was applied. The study obtained high-quality solution methods that were more accurate and speedier for cost optimization and customer satisfaction. Moreover, a new decision support system tool was used by Patel et al. [13], envisioning to augment the agility of the supply chain with resource optimization. Combining the Analytic Hierarchy Process (AHP) and Goal Programming (GP), global and local weights were given to decision variables. The GP integrates those weights into an anticipated model. The study obtained targeted agility through the optimized use of available resources.

Feng et al. [14] also designed an integrated model that was built with the Linguistic Entropy Weight Method (LEWM) combined with the multi-objective programming to be used in supplier selection and order allocation for the case of the circular economy. The model aimed to select green suppliers based on built-in criteria. The other function performed by this model was calculating the rankings of green suppliers. These features performed value-added services by presenting a comprehensive performance evaluation of the green suppliers along with their criteria-based selection. Since this model was proposed to be used in a circular economy, it was also featured for order allocation in the automobile manufacturing industry. The three stated objectives included the minimization of the total cost, carbon neutrality, and value maximization of procurement. The weighted minimum and maximum operator methods were employed to obtain the desired outcomes. The results of the study revealed that the optimization model achieved the goals related to green supplier allocation and order allocation. In a recent study by Alam [15], a prototype for analyzing Saudi Basic Industries Corporation (SABIC) structure was formulated. This prototype envisioned accelerating the budget optimization by reducing expenses, increasing the number of fixed assets, and growth in the equity share. This model proposed promising benefits and features for industrial institutions in Saudi Arabia.

Emerging technologies have been increasingly adopted by manufacturing firms under the auspices of Industry 4.0 to foster sustainability and efficient production [16]. There is an increased trend of using mathematical optimization tools in different industries such as supply chain, tourism, and healthcare [16]. The wish to acquire more market share has incited organizations to update their existing manufacturing practices with more of the available advanced tools and techniques while making the best use of the latest technology [17]. The integration of tools and technology is essential to enhancing machinery, time-effectiveness, and increasing sales and quality of products with the best utilization of the available means [18]. Despite Saudi Arabia being a leading oil producer and manufacturer of plastics and petrochemicals, the practices in its manufacturing industries are not upgraded. Also, there is a lack of research in the domain of manufacturing industries to identify the needs and strategies to upgrade the systems that involve manufacturing operations. More specifically, a limited number of manufacturing companies are producing high-quality products. A few manufacturing organizations have quality certifications, but they have not incorporated the practices into their systems. However, researchers have shown that the application of modern tools can increase profits and minimize costs and losses. To date, no study has examined the significance of goal programming for increasing the productivity of the refrigeration and air conditioning industry. We consider the well-known refrigeration and air conditioning industry in Saudi Arabia as a case study. It involves distributing appliances and electronics, and manufacturing refrigerators, freezers, air conditioners, and air handling units. It also consists in contracting and installing personnel, as well as installing commercial air conditioners. Air conditioners and other products like chest freezers and refrigerators are available from the international department for the Middle East and African markets. The industry has exclusive brand distributorships, manufacturing brands under license, marketing, service, and research and development divisions. Production planning is essential for reducing production costs and increasing productivity in this industry.

An efficient system of production planning and processes is a prerequisite for the successful operations of a manufacturing firm. A plethora of studies have revealed promising advantages in adopting goal programming in different firms such as supply chains. This study attempts to adopt goal programming in the refrigeration and air conditioning industry of Saudi Arabia to substantiate its performance in optimizing cost, sales revenue, and other resources. Therefore, a goal-programming approach is used in this study to examine specific targets that the company wants to achieve. In this study, we develop a goal-programming model for multi-objective production planning in the electronic industry. Therefore, this paper presents a Preemptive Goal Programming (GP) model to solve problems involving multiple products and periods. This proposed model is demonstrated through an example from the industry and provides a systematic decision-making framework. As part of the proposed research, a framework will be developed to identify multi-objective production planning and prospective industry enhancements.

The rest of this paper is organized as follows: In Section 1, the introduction and overview of the study are provided. In Section 2, a literature review and research gap have been provided. Section 3 contains the methodology of the study. The study results have been presented in Section 4. In Section 5, a case study has been explained, and in Section 6, the discussion has been encapsulated along with the study implications. The article is summarized in Section 7, and a direction for further investigation is suggested.

2. Literature Review

Goal programming is a methodology that can be used to solve multi-objective planning problems. Recent years have seen goal programming used in various fields since it produces significant results [5,6,7]. An APP model with multiple plants was also studied, and preemptive goal programming was used to solve it [19]. During the construction of a toothpaste manufacturing plant, goal programming was used to determine the material mix for each facility; the model provides flexibility to a leader since clashing destinations can be taken into account simultaneously [20]. Using a goal programming approach, Grace and Olubummo examined optimal production plans for a bottled water manufacturing company [21].

In addition to studying mathematical programming models for management systems, Sen and Nandi [22] explored the application of the goal programming model; it is an essential tool for studying various management aspects. The Goal Programming technique appears powerful, flexible, and appropriate for today’s troubled decision-makers [22]. To make the aim an economic and financial reality, Jyoti [23] applied goal programming to the operating cost distribution of St. Brother’s Public School, Haryana, India [23]. The goal of preemptive goal programming is to maximize profit, minimize repair costs, and maximize machine utilization at all levels [24]. A fuzzy goal programming approach with different priorities and importance was presented. The strategy aims to limit the absolute costs of workforce creation, inventory carrying, and workforce changes [25].

In addition, multi-objective models have been developed to solve production planning problems in which profit is maximized while production penalties are minimized [25,26]. Furthermore, a goal programming model was developed to optimize the daily production of a business producing biscuits and cupcakes. The three objectives were maximizing daily sales profits, limiting overtime, and maximizing the utility of machines used in pastry shop production [27]. A multi-objective goal programming model for a real-life manufacturing situation was developed to demonstrate the superlative between customer, product, and production planning goals [27]. Based on mathematical simplicity and elegance, Colapinto et al. [28] chose goal programming to solve and analyze decision problems in 2015 [21]. A fuzzy target programming approach was used by Taghizadeh et al. [29] to improve production planning. The medical equipment production process leads to higher production costs, so this model decreases production costs and expands income [29]. The paper was written by Chen and Liao [30]. Their goal was to discover a solution to the aggregate production problems caused by variations in the demand for products [29,30].

Saad [31] examined the production planning model presented to identify gaps between the current theory and practice of production planning. Sang-Jin Nam developed an application that includes aggregate production planning to determine a firm’s production, inventory, and employment levels over a specified period. As a result, costs will be reduced while unstable demand is met [32]. A preventive target programming model was also developed by Hassan et al. [33] in Sungai Buloh, Malaysia. As part of their study, Hassan and Loon [34] examined how library funding is optimally used to meet users’ needs. To maximize reading material purchases and each field’s utility, the researchers developed a goal programming model with utility functions [34]. Adeyeye [20] discussed a goal programming model for toothpaste production planning in 2008. There were two objectives: minimizing manufacturing costs and utilizing production facilities [20].

Similarly, Touil et al. [35] adopted a fuzzy goal programming approach to problems of integration in a dairy company in Morocco. Further, ref. [36] published the requirements for chemical plant production planning. They used a model case study in which the objective programming approach is introduced and illustrated along with its implications and extensions [36]. Zaloom et al. [36] developed a goal-programming model to achieve several banking goals. The objectives of this model include maximizing profits, minimizing capital costs, and providing adequate cash flow. Charnes and Cooper [37] examined the exponential increase in linear programming applications to industrial problems, and they wrote that using linear programming models as a guide for data collection and analysis must change to fit these circumstances. Biswas and Pal [38] demonstrated the use of fuzzy goal programming for crop production optimization in agricultural systems for optimal production of several seasonal crops in a planning year. According to Esfandiari [39], it is necessary to improve productivity to plan the production and design of open-pit mines [40,41].

A goal programming model for the simple U-line balancing (ULB) problem was developed, and the proposed model was a multi-criteria decision-making approach to the U-line version. The multi-criteria approach provides more flexibility to the decision-maker, as several conflicting goals can be considered [42,43]. Concerning the manufacturing sector, Lohmer and Lasch [44] have determined the need to better adopt technologies with a special emphasis on the planning phase with an orderly sequence of operations.

The study by Aktas and Temiz [45] addressed the production-distribution problem and adopted a multi-product, multi-stage production-distribution network with diverse transportation alternatives via a goal programming model. The model was proposed to support the planning decisions involved in the distribution network of the production with a randomly generated dataset. The study reported the effectiveness of the model for environmentally friendly production–distribution planning. Aktas and Kabak [46] designed a model for determining operational decisions taken in a hybrid energy system with a goal programming model. This study was conducted for a small town with 10 demand points and 4 energy generation plants. The findings of the study show that the proposed model is useful for evaluating the profitability of the system and for the utilization of renewable energy. Ecer et al. [47] proposed a new design for inverse multi-criteria sorting problems via a bi-objective model derived from a goal programming approach. The model has produced the desired outcomes for increasing the efficiency of buildings in Turkey. Dolson [48] used the goal programming method to solve the complex issues of production and operational constraints. The study used a modified version of multi-period lot sizing with deterministic and stochastic min–max goal programming approaches. The study found favorable results in the model, as it reduced the expected pivot from optimality and did not affect the quota fulfillment, which mitigated the risk of significant deviation from optimality. The deviation ratio was between 40.3% and 86.6% during the last five weeks of the model proposed. Moreover, Ahmadini et al. [49] focused on the multi-objective inventory model to minimize risk and waste. Planning constraints included in this study were budget limitations, space limitations, environmental waste, and cost of production, while adopting a multi-item, multi-objective inventory model with maximum degrees of achievement such as 0.9779, 0.4229, 0.0465, and 0.0345 for the objectives related to budget limitation, space limitations, environmental waste, and cost of production, respectively.

Research Gap and Contributions

A plethora of studies have adopted multi-objective optimization and preemptive goal programming to either minimize risk and cost or maximize production without paying attention to the production cost, sales revenue, and utilization of machines, which are the issues usually encountered during manufacturing and production. The manufacturing industries of Saudi Arabia have been encountering challenges to make the best use of their available resources, increase the scale and quality of production, and reduce time while implementing mathematically optimized solutions and tools within their manufacturing processes. Based on the literature reviewed, numerous studies have documented promising advantages and applicability of goal programming techniques in different firms and for different operations such as supply chains. However, a research gap exists in terms of investigating the applicability of the goal programming approach in the operations of manufacturing firms, especially in the refrigeration and air conditioning industry of Saudi Arabia. This study fills this gap by adopting goal programming in the refrigeration and air conditioning industry of Saudi Arabia to evaluate and validate its performance in optimizing cost, sales revenue, and other resources. The results of this study can serve as a foundation of knowledge for decision-makers and business managers to build effective strategies and policies for organizational success. Goal linear programming is primarily concerned with minimizing the cost or increasing the profit of these general goals. Therefore, management will have to accomplish various objectives (goals). The model incorporates the following performance criteria:

(1)

The marketing goal;

(2)

Total production costs;

(3)

Revenue from sales;

(4)

Utilization of machines.

The proposed model has been designed and integrated to solve the production planning problem, production constraints, and resources to determine the optimal production, labor, and inventory level for each planning period. Viewing the problem as a whole is usually possible by considering a product or family of products with minor differences. The findings of the study will assist in boosting the production and revenues of manufacturing firms in Saudi Arabia and will ease the adoption of such methods while reducing the barriers of cost and inefficient management of the available resources. Moreover, the findings of the study will be helpful in obtaining the targeted sales revenues that are indispensable for large-scale manufacturing activities and production in Saudi Arabia, in order to enlarge its non-oil-based exports.

3. Materials and Methods

3.1. Goal Programming Problem (GPP)

There were many issues facing the modern world, including sadness and the solution to different contemporary problems. Several models were tried by industrialists, and they were successful in addressing their concerns. The GPP models help supervisors resolve a variety of problems that they face every day. Using these models, the cost of creation can be reduced, efficiency increased, available resources can be used wisely, and modern sound development can be achieved.

It is seen as a challenge to accomplish many objectives in an environment of conflicting interests, inadequate data, and restricted resources in the current complex organizational environment. In dealing with real-world decision problems, goal programming has the advantage of reflecting how managers make decisions. Thus, goal programming is a mathematical tool that can be used to tackle multi-objective issues in a variety of regions to make accurate, timely, and effective decisions. For over fifty years, scientists have studied this field and have conducted countless investigations. However, today, the cycle is focused on obtaining a clearer image of this tool, emphasizing its benefits from the perspective of problem-solving in the field.

3.2. Mathematical Formulation as Goal Programming (GP) Model

Production planning in any organization is a complex task requiring cooperation among multiple functional units. In the manufacturing environment, planning results from a hierarchy of decisions. In multi-objective mathematical programming, goal programming, especially preemptive programming, has become increasingly popular. In line with Charnes and Cooper’s [37] definition, goal programming can be described as follows:

$$Min{\displaystyle \sum }_{i=1}^n(d_i^{-}+d_i^{+})$$

(1)

subject to

$${\sum }_{j=1}^m({\alpha }_{ij}{x}_j+d_i^{-}-d_i^{+})={\tau }_i$$

(2)

$$x_j, d_i^{-}, d_i^{+}\ge 0, \forall i,j; i=1,2,\dots ,n and j=1,2,\dots ,m$$

(3)

It is not possible to achieve both the goal under and over at the same time, so one of the deviational variables must be zero. In other words,

$$d_i^{-}.d_i^{+}=0$$

(4)

where n represents the goal constraints, ${\tau }_i$represents the target level of the ith goal, $x_j$represents the vector of m-decision variables, ${\alpha }_{ij}$represents the coefficients of decision variables, and $d_i^{-} \mathrm{and} d_i^{+}$represent the under- and over-deviational variables. When a goal is unsatisfied or over-satisfied, the deviations $d_i^{-}$ and $d_i^{+}$are added to the constraints. Finally, the deviation variables are used to determine whether each goal is underachieved or overachieved [50].

Preemptive Goal Programming

In preemptive goal programming, there are different priority classes of objectives. Each goal is assigned a priority based on its relative importance [48]. A preemptive priority factor is a ranking of goals in an ordinal order. According to this priority ranking, P1 is higher than P2, P2 is higher than P3, etc. Then, the objective function can be stated as

$$Min {{\displaystyle \sum }}_{i=1}^n{\rho }_i (d_i^{-}+d_{i }^{+})$$

(5)

where ${\rho }_i$ is the preemptive priority factor of the ith goal.

The purpose of performance measures is to achieve goals and provide management with an effective means of monitoring, guiding, and communicating between the upper-level and lower-level managers of the manufacturing firm. Various performance criteria are represented by the objective functions described below.

3.3. Notations

Indices

• i = Types of products (i = 1, 2, …..., n)
• j = Types of machines (j = 1, 2,.…, m)

Parameters

• $c_i$ = Production cost of ith product
• $C$ = Production cost goal fixed by the management
• ${\alpha }_{ij}$ = Time required for the i product on jth machine
• $s_i$ = Sales revenue from ith product
• S = Sales revenue goal fixed by the management
• $M_j$ = Total available capacity of the jth machine

Decision variable

• $x_i$= Production volume of type i to be produced per period

3.4. Procedures

Solving the proposed model involves the following steps:

• Step 1: The problem is formulated as multi-objective production planning using a preemptive goal programming problem, considering the parameters, i.e., market demand, production revenue, production time, and production cost.
• Step 2: Resolve the formulated problem in Step 1 to attain the optimal solution using LINGO.
• Step 3: Convert the problem into preemptive goal programming by choosing the aspirational goals based on the optimal result in Step 2.
• Step 4: Construct the goal memberships in light of Equations (1)–(5).
• Step 5: Linearize the fractional problem and resolve the resulting deviational variables.
• Step 6: Define the priority of the goals.
• Step 7: Include the priority in the admissible deviations and resolve the resultant preemptive goal programming.

4. Results

As part of multi-objective goal programming, we must decide which goal comes first, second, or even last. As shown in

Table 1. Priority of the goals.

Goals	Priority
G1: The goal of the market	${\rho }_1$
G2: The production cost	${\rho }_2$
G3: Sales revenue	${\rho }_3$
G4: Utilization of machines	${\rho }_4$

, this study’s objectives are given preference.

Formulation of Model

We are considering the production planning of three different product types: a 30 ft refrigerator, a 20 ft refrigerator, and a 15 ft refrigerator.

(a)

The goal of the market;

(b)

The production cost;

(c)

The sales revenue;

(d)

The utilization of machines.

We formulate these important criteria as follows:

(a)

The main objective of the market is to achieve aggregate product volumes.

To maximize production volume, product 1, product 2, and product 3 aggregate product volumes must be met. Since exact product volumes are desired, both negative and positive goal deviations must be considered in the objective function. The goal can be expressed as follows:

$$Min d_1^{+}+d_1^{-}+d_2^{+}+d_2^{-}+d_3^{+}+d_3^{-},$$

(6)

subject to

$$x_1+d_1^{+}-d_1^{-}=V_1,$$

(7)

$$x_2+d_2^{+}-d_2^{-}=V_2,$$

(8)

$$x_3+d_3^{+}-d_3^{-}=V_3,$$

(9)

where

• $d_1^{+}$ = over achievement of product 1 volume goal,
• $d_1^{-}$= underachievement of product 1 volume goal,
• $d_2^{+}$= over achievement of product 2 volume goal,
• $d_2^{-}$= underachievement of product 2 volume goal,
• $d_3^{+}$= over achievement of product 3 volume goal,
• $d_3^{-}$= underachievement of product 3 volume goal,
• $V_1$ = market goal on product 1 volume (aggregate) as per prediction (goal),
• $V_2$ = market goal on product 2 volume (aggregate) as per prediction (goal),
• $V_3$= market goal on product 3 volume (aggregate) as per prediction (goal).

Here, the minimization of $d_i^{+}+d_i^{-}$will minimize the absolute value of $x_i-V_i$.

In other words, minimization of both negative and positive deviations of product volume will tend to search for the $x_1$, $x_2$, and $x_3$ which achieves the goal $x_i=V_i$ exactly.

(b)

Production cost: manufacturer’s goal

It is possible to represent the manufacturer’s goal of minimizing production costs by the following Equations (10) and (11):

$$Min d_4^{+},$$

(10)

subject to

$$\sum c_i x_i+d_4^{+}-d_4^{-}=C,$$

(11)

where

• $d_4^{-}$= underachievement in production cost goal,
• $d_4^{+}$= over achievement in production cost goal.

The solution set will consist of all x’s such that $\sum c_i x_i \ge C$ by minimizing $d_4^{+}$to zero if such solutions are possible in the model.

(c)

Sales Revenue: manufacturer’s goal

The management believes that the sales goal for the next year should be ‘S’ million riyals based on the company’s past sales records and customers’ increased awareness of industry automation. Furthermore, sales revenue achievement, set at S, is also determined by total gross margins for product 1, product 2, and product 3. Therefore, the goal can be expressed as follows in Equations (12) and (13):

$$\mathit{minimize} d_5^{-},$$

(12)

Subject to

$$\sum s_i x_i+d_5^{+}-d_5^{-}=S,$$

(13)

where

• $d_{5 }^{-}$= under-achievement of the sales revenue goal,
• $d_5^{+}$= over-achievement of the sales revenue goal.

Here, the over-achievement of the sales goal is acceptable, and hence positive deviation from the goal is eliminated from the objective function. The solution set will consist of all x’s such that $\sum s_i{x}_i\ge S$ by minimizing $d_5^{-}$ to zero if such solutions are possible in the model.

(d)

Utilization of Machine: manufacturer’s goal

Several factors contribute to a successful business relationship, including a good employer–employee relationship. Therefore, they prefer stable employment levels with occasional overtime requirements over varying employment levels with no overtime requirements. Thus, the objective function can be modified to eliminate the positive deviation from the goal. Therefore, the manufacturer’s goal of minimizing machine underutilization can be represented as follows in Equations (14) and (15):

$$\mathit{minimize} d_6^{-},$$

(14)

subject to

$$\sum {\alpha }_{ij} x_i+d_j^{+}-d_j^{-}=M_j ;j=6,7,\dots \dots ,13,$$

(15)

where

• $d_j^{-}$= under achievement time required for the operation of machine j,
• $d_j^{+}$= under achievement time required for the operation of machine j.

Here, the solution will identify all x’s such that$\sum {\alpha }_{ij} x_i \ge M_j$, by minimizing negative deviation to zero, if such a solution is possible in the model.

5. A Case Study

In this paper, a well-known industry is examined as a case study. The details of all three products are summarized in

Table 2. Details of the products.

Products	Number of Production	Total Cost	Total Selling Price	Cost of Production	Revenue	Demand
Fridge 30 ft	5000	5660	9200	28,300,000	46,000,000	4990
Fridge 20 ft	7000	3170	4800	22,190,000	33,600,000	6997
Fridge 15 ft	12,000	2524	3499	30,288,000	41,988,000	11,990

. A comparison of the processing time on different machines is shown in

Table 3. Annual processing time on different machines.

Products	Processing Time on the Machines (Time in Hours)
	M1 (Pending)	M2 (Assembly)	M3 (Cooling)	M4 (Foam)	M5 (Assembly)	M6 (Preez)	M7 (Vacuum)	M8 (Charger)
Size 28	100	500	500	1000	1000	1000	500	190
Size 18	140	700	700	700	700	700	700	250
Size 14	240	1200	1200	800	800	800	1200	400
Available time	2500	2500	2500	2500	2500	2500	2500	2500

. Our model of Preemptive Goal Programming (PGP) now incorporates the given data.

The industry aims to reduce costs to below SR 79,000,000 while increasing revenues above SR 127,000,000.

(I)

Market goal: meet aggregate product volumes

This goal can be defined as follows:

$$Min{d}_1^{+}+d_1^{-}+d_2^{+}+d_2^{-}+d_3^{+}+d_3^{-}$$

(16)

subject to

$$5000x_1+d_1^{+}-d_1^{-}=4990$$

(17)

$$7000x_2+d_2^{+}-d_2^{-}=6997$$

(18)

$$12,000x_3+d_3^{+}-d_3^{-}=11,990$$

(19)

$$x_1 , x_2, x_3, d_1^{+}, d_1^{-} ,d_2^{+}, d_2^{-},d_3^{+}, d_3^{-}\ge 0$$

(20)

(II)

Production cost: manufacturer’s goal

To minimize production costs for product 1, product 2, and product 3, manufacturers strive to minimize costs. This can be described as stated in Equations (10) and (11):

$$Min{d}_4^{+}$$

(21)

subject to

$$28,300,000x_1+22,190,000x_2+30,288,000x_3+d_4^{+}-d_4^{-}=79,000,000$$

(22)

$$x_1, x_2, x_3, d_4^{+},d_4^{-} \ge 0$$

(23)

(III)

Sales Revenue: manufacturer’s goal

$$Min d_5^{-}$$

(24)

Subject to

$$46,000,000x_1+33,600,000x_2+41,988,000x_3+d_5^{+}-d_5^{-}=127,000,000$$

(25)

$$x_1 , x_2, x_3, d_5^{+}, d_5^{-} \ge 0$$

(26)

(IV)

Utilization of Machine: manufacturer’s goal

Manufacturers’ goal of reducing the underutilization of machines can be described in the following way:

$$\mathit{minimize}{d}_6^{-}+d_7^{-}+d_8^{-}+d_9^{-}+d_{10}^{-}+d_{11}^{-}+d_{12}^{-}+d_{13}^{-}$$

(27)

subject to

$$100x_1+140x_2+240x_3+d_6^{+}-d_6^{-}=2500$$

(28)

$$500x_1+700x_2+1200x_3+d_7^{+}-d_7^{-}=2500$$

(29)

$$500x_1+700x_2+1200x_3+d_8^{+}-d_8^{-}=2500$$

(30)

$$1000x_1+700x_2+800x_3+d_9^{+}-d_9^{-}=2500$$

(31)

$$1000x_1+700x_2+800x_3+d_{10}^{+}-d_{10}^{-}=2500$$

(32)

$$1000x_1+700x_2+800x_3+d_{11}^{+}-d_{11}^{-}=2500$$

(33)

$$500x_1+700x_2+1200x_3+d_{12}^{+}-d_{12}^{-}=2500$$

(34)

$$190x_1+250x_2+400x_3+d_{13}^{+}-d_{13}^{-}=2500$$

(35)

$$x_1, x_2, x_3, d_6^{+}, d_6^{-}, d_7^{+}, d_7^{-}, d_8^{+}, d_8^{-}, d_9^{+}, d_9^{-},d_{10}^{+}, d_{10}^{-}, d_{11}^{+}, d_{11}^{-}, d_{12}^{+}, d_{12}^{-}, d_{13}^{+}, d_{13}^{-} \ge 0$$

(36)

Now we may write the PGP as

$$Min {\rho }_1( d_1^{+}+d_1^{-}+d_2^{+}+d_2^{-}+d_3^{+}+d_3^{-} )+{\rho }_2\left(d_4^{+}\right)+{\rho }_3\left( d_5^{-} \right)+{\rho }_4\left(d_6^{-}+d_7^{-}+d_8^{-}+d_9^{-}+d_{10}^{-}+d_{11}^{-}+d_{12}^{-}+d_{13}^{-}\right)$$

(37)

subject to

$$5000x_1+d_1^{+}-d_1^{-}=4990$$

(38)

$$7000x_2+d_2^{+}-d_2^{-}=6997$$

(39)

$$12,000x_3+d_3^{+}-d_3^{-}=11,990$$

(40)

$$28,300,000x_1+22,190,000x_2+30,288,000x_3+d_4^{+}-d_4^{-}=79,000,000$$

(41)

$$46,000,000x_1+33,600,000x_2+41,988,000x_3+d_5^{+}-d_5^{-}=127,000,000$$

(42)

$$100x_1+140x_2+240x_3+d_6^{+}-d_6^{-}=2500$$

(43)

$$500x_1+700x_2+1200x_3+d_7^{+}-d_7^{-}=2500$$

(44)

$$500x_1+700x_2+1200x_3+d_8^{+}-d_8^{-}=2500$$

(45)

$$1000x_1+700x_2+800x_3+d_9^{+}-d_9^{-}=2500$$

(46)

$$1000x_1+700x_2+800x_3+d_{10}^{+}-d_{10}^{-}=2500$$

(47)

$$1000x_1+700x_2+800x_3+d_{11}^{+}-d_{11}^{-}=2500$$

(48)

$$500x_1+700x_2+1200x_3+d_{12}^{+}-d_{12}^{-}=2500$$

(49)

$$190x_1+250x_2+400x_3+d_{13}^{+}-d_{13}^{-}=2500$$

(50)

$$x_1, x_2, x_3, d_1^{+}, d_1^{-}, d_2^{+}, d_2^{-}, d_3^{+}, d_3^{-}, d_4^{+}, d_4^{-}, d_5^{+}, d_5^{-}, d_6^{+}, d_6^{-}, d_7^{+}, d_7^{-}, d_8^{+}, d_8^{-}, d_9^{+}, d_9^{-}, d_{10}^{+}, d_{10}^{-}, d_{11}^{+}, d_{11}^{-}, d_{12}^{+}, d_{12}^{-}, d_{13}^{+}, d_{13}^{-} \ge 0$$

(51)

The following

Table 4. Target achievement.

Goal	Outcomes	Target Achievement
G$1$	$d_1^{+}=d_1^{-}=d_2^{+}=d_2^{-}=d_3^{+}=d_3^{-}=0$	Completely attained
G$2$	$d_4^{+}=0$	Completely attained
G$3$	$d_5^{-}=0$	Completely attained
G$4$	$d_6^{-}=d_7^{-}=d_8^{-}=d_9^{-}=d_{10}^{-}=d_{11}^{-}=d_{12}^{-}=d_{13}^{-}=0$	Completely attained

shows the outcomes that can be expected from achieving the targets. In addition, all priority outcomes are zero as well. Thus, the company has achieved all of its objectives. In the process, the best solution to each of its challenges has been found. This shows that the company consistently performs well. Based on the optimal solution to the PGP model as framed in Equations (37)–(51),

Table 5. Outcomes of deviational variables.

Goal	Negative Deviational Variables	Positive Deviational Variables
G1	$d_1^{-}=0$	$d_1^{+}=0$
	$d_2^{-}=0$	$d_2^{+}=0$
	$d_3^{-}=0$	$d_3^{+}=0$
G$2$	$d_4^{-}=1,686,650$	$d_4^{+}=$ 0
G$3$	$d_5^{-}=0$	$d_5^{+}=$ 5,553,390
G$4$	$d_6^{-}$ = 0	$d_6^{+}$ = 2020.460
	$d_7^{-}$ = 0	$d_7^{+}$ = 102.3000
	$d_8^{-}$ = 0	$d_8^{+}$ = 102.3000
	$d_9^{-}$ = 0	$d_9^{+}$ = 2.966667
	$d_{10}^{-}$ = 0	$d_{10}^{+}$ = 2.966667
	$d_{11}^{-}$ = 0	$d_{11}^{+}$ = 2.966667
	$d_{12}^{-}$ = 0	$d_{12}^{+}$ = 102.3000
	$d_{13}^{-}$ = 0	$d_{13}^{+}$= 102.3000

represents the potential improvement to the target value based on the optimal solution to the PGP model. Some targets may be improved. For example, positive deviation variables can be used to detect possible increments from the baseline. In the case of a maximization problem, the increment can be calculated using a positive deviation variable. In contrast, in the case of a minimization problem, the decrement can be calculated using a negative deviation variable.

Therefore, the decrement can be calculated using a negative deviation variable. To understand their priorities, we interpreted these points as follows:

• The market goal for the company is fully achieved because all the negative and positive deviational variables for the current year are zero, indicating that the market goal for the following year will be the same.
• The value of $d_4^{+}$for goal 2 is zero, while the value of $d_4^{-}$ is 1,686,650; therefore, the goal of minimizing the production cost was met, and the company can increase the cost SR 1,686,650 for the following year.
• For goal 3, sales revenue, because the value $d_5^{-}$ is zero, while the value of $d_5^{+}$ is SR 5,553,390, the company achieved its sales revenue target. It will be able to reduce its revenue by SAR 5,553,390 the following year.
• Lastly, there is a goal of machine utilization, which entails minimizing the possibility of the underutilization of machines. The result indicates that all underachievement deviations are zero, while the overachievement deviational variables of all or most machines have more time to go, which demonstrates that the following year the company will be able to maximize its efforts.

6. Discussion

This study reported that all goals were achieved. An additional sensitivity analysis revealed that the company could increase costs by 2.14% for the following year to minimize production costs, and revenues could shrink by 4.37% to meet its revenue target. These findings are similar to the results of Rosyidi et al. [50], which have evidence of the effectiveness of adopting a goal programming approach for timely determining order allocation and managing multi-suppliers. These findings are also congruent with the results of Torres-Ruiz and Ravindran [7], which used preemptive, multiple-sourcing, non-preemptive, and fuzzy goal programming models with the aim of managing price and eco-efficiency as two conflicting objectives. The results of the study have reported the usefulness of supplier evaluation, selection, and monitoring [51]. Tyas et al. [52] reported the effectiveness of the goal programming model for achieving the four goals of profit maximization, reduction in inventory cost, reduction in subcontract cost, and reduction in production cost. In addition to that study, Ref. [53] obtained Economic Order Quantities (EOQ) to tackle conflicting multi-item inventory issues in the automotive industry. The study recommends that through the inclusion of some modifications in the EOQ, inventory-related problems can be optimally resolved. Similar to the present study, Wai et al. [54], Al-Arjani and Alam [55], and Alam [15] developed financial models with a goal programming approach and examined the financial plans of financial institutions. These approaches assisted in achieving goals related to total liability, assets, profit, equity, optimum management, revenues, etc. In addition, Orumie et al. [56] also substantiated the significance of the goal programming approach in the fish farm industry, adopting a linear goal programming approach for tackling the conflicting objectives. Orumie et al. [56] asserted that the adopted model was useful for effective decision-making in the fish industry. Moreover, a recent study by Nyor et al. [57] emphasized increasing the use of adopting mathematical modeling and techniques for effective decision-making and better financial management.

The findings of the study show that by adopting a preemptive goal programming approach, manufacturing firms can optimize their cost, revenues, and resources. Based on the abovementioned studies, a plethora of studies have used goal programming approaches for optimized solutions [9,10,11,12,13,14,15]. However, this study is novel, as it takes the refrigeration and air conditioning industry of Saudi Arabia into consideration, since Saudi Arabia has been endeavoring to reduce its reliance on the conventional oil-export base and intends to increase the export of value-added products [58]. Adoption of such techniques in their process can beget an accelerated production capacity for manufacturing firms, especially in the refrigeration and air conditioning industry.

Implications

The success of a manufacturing firm hinges on optimized management of resources with lower production costs and increasing sales. However, the existing literature that focuses on the maximization of the efficiency of supply chain operations fails to adequately consider sales revenues, cost constraints, and the lack of optimized solutions for managing resources. This study model has obtained its accuracy levels to resolve the complex issues related to market demand, production revenue, production time, and production cost. The model will be a helpful tool for the manufacturing industries to enhance various functions. Moreover, it will expand the uses of goal programming to perform the complex functions of manufacturing firms. It will beget sustainable management of production operations and sustainable inventory management in the manufacturing industries. The results of the study will contribute to boosting the production and revenues of manufacturing firms in Saudi Arabia and will unfold the adoption of such methods for reducing the barriers of cost and inefficient management of available resources. Moreover, the findings of the study will help to obtain the targeted sales revenues that are essential for large-scale manufacturing activities and production in Saudi Arabia if it is to enlarge its non-oil-based exports.

7. Conclusions

The application of goal programming models in real-life manufacturing problems has gained significant attention in recent years as a powerful tool for resolving multiple conflicting objectives. The modern manufacturing process is complex because of uncertain customer demands, competitive markets, and rapid technological advances. The study has proposed a model using preemptive goal programming that has obtained numerically illustrated goals, along with a case study using LINGO optimization software. The developed goal programming model will assist decision-makers in finding an optimal production plan for the industry. This is a novel study that intends to be adopted in the refrigeration and air conditioning industry of Saudi Arabia to validate its performance in optimizing cost, sales revenue, and resources. However, as a limitation, the study only addresses that goal related to market demand and production, and it does not consider recycling of the residue products as a goal of manufacturing firms. Therefore, future studies can be conducted to present a model that could work for the recycling of products in the product development and expansion phase of manufacturing firms.