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# Benefits of Linear Programming Technique for Production Processes

 ✓ Paper Type: Free Assignment ✓ Study Level: University / Undergraduate ✓ Wordcount: 3047 words ✓ Published: 1st Dec 2020

Application of Resource Integration Technique

This case study represents how Linear Programming technique is beneficial for Pak n Save to improve its production process in Dough mixing (preparing Muffins) and Baking (preparing Cakes) sections. Linear Programming is the numerical technique which can be adapted to resolve the most ideal conclusion from a given set of guidelines that are expressed in linear form. (Techopedia. (n.d.). This technique will help Pak n Save staffs in placing the products in the shelves on time so that the customers can purchase as and when they need it.

Step 1: Preparing table representing data:

Pak n Save makes two products Cake and Muffin which are sold very frequently. They are made in two different machines. The Baking time for cake in Machine A (Dough mixing) is 45 mins and 18 mins in Machine B (Baking). Muffin: processing time in Machine A (Dough mixing) is 15 mins and 10 in machine B (Baking). The Muffins has to be limited to 20 units

 Machine type Muffins (M) Cakes (C) Time available (Hours per week) Dough mixing (A) 200 100 12000minutes (200 hours) Baking (B) 180 90 10800 minutes (180 hours) Profit (per product) \$4 \$7

Table 1.1 Production details of Muffins and Cake

Step 2: To generate a model from the table:

Maximise profit = \$4M* + \$7*C                 (Objective function)

The primary objective of Pak n Save is to maximize its profit by selling Cakes and Muffins. Subjective to the constraints such as Dough mixing, Baking and Non-negativity constraints.

200*M + 100*C ≤ 12000                   (Dough mixing constraint)

180*M + 90*C ≤ 10800                     (Baking constraint)

M, C ≥ 0; M, C must be integral          (Non- negativity constraint)

Step 3: Converting the constraints to equations

In this step, we need to add up all the three constraints with slack time in order to balance the extra time involved in Baking and Dough mixing. We need to add zero time for both the given constraints in the objective. In the Dough mixing constraint, we consider one-minute slack time for Muffins when the slack time for Cake is zero and vice versa. While, in the non-negativity constraint, both cakes and muffins are assumed to be greater than equal to zero.

Objective:

\$4M* + \$7*C + \$0*S1 + \$0*S2

Subject to constraints:

200*M + 100*C + 1*S1 + 0*S2 = 12000

180*M + 90*C + 0*S1 + 1*S2 = 10800

M, C, S1, S2 ≥ 0

Here S represents slack variables

Step 4: Plotting the Graph

Fig. 1.2 Graphical representation of Linear Programming model

In the above graph, the purple shaded region denotes a feasible region where the two constraints meet at the point of intersection.

(Contribution of Student S1: Name and ID, Do include it in the submitted report)

Step 5: Equation of the constraints:

Placing all the equations again for the further steps,

Maximise profit = \$4M* + \$7*C      (Objective function)

200*M + 180*C ≤ 12000           (Dough mixing constraint)

180*M + 90*C ≤ 10800            (Baking constraint)

M, C ≥ 0                                    (Non- negativity constraint)

Step 6: Validating the solutions:

In order to get an optimal solution all, the three given equations should be satisfied.

For co-ordinates (0,108)

=\$4*108 + \$7*0 = \$432

For coordinates (48, 0)

=\$4*0 + \$7*48= \$336

For coordinates (20,78)

= \$4*78 + \$7*20 = \$452                       (Optimal Solution)

AMRI700, Optimal Resource utilization technique. (n.d.).

Analysis of Results, Limitations and Recommendations

The Linear Programming Model is the most suitable technique not only in finding the optimal solutions but also helps in making a quantitative decision such as planning, organising, forecasting etc. (Britannica, T. E. (2017, July 18). It is also beneficial in business that involves supply chain, logistics and warehouse. The idea behind using the LP technique is that it provides an optimal solution to any given issues that lie on the intersection point, or an utmost point of the feasible region. Therefore, it is very crucial to determine only those values which are located at the edge point. The optimal solution will be one among them. (Heizer,J. & Render,B.,2017)

Limitations:

• The LP model is positioned on the expectation of consistent returns. But in the real world scenario, the returns are either declined or raised that an organisation can only realise during its production process. Linear Programming (LP): Meaning and Limitations. (2016, March 02).
• Regardless of whether a particular objective task is set, it may be difficult to discover different mechanical, money related and different challenges which might be functional in seeking the given target. Linear Programming (LP): Meaning and Limitations. (2016, March 02).
• The LP technique cannot be used in solving issues like uncertainty, weather forecasting etc. Wisdom Jobs India. (2018).
• The LP method only focuses on a particular objective such as to increase the profit or reduce the cost. In today’s competitive business atmosphere, any business doesn’t totally rely on one specific goal. Limitations of the LP model. (n.d.).

Recommendations:

• In the graph chart, the best way for Pak n Save to maximise its profit would be producing Cakes and Muffins per day from the accessible working hours of 200 hrs for Mixing the dough and 180 hrs for Baking.
• It is also advisable for Pak n Save being a large organisation to use MS solver in order to get an optimal solution if the constraints tend to exceed 100. This will help them achieve the solution within a short span of time.

Reflection on other techniques

Reflection on not used resource integration technique 1: Engineering Economics

Engineering economy is determining the relative economic value of the alternative initial investment and set off several feasible alternatives. In initial investment includes the money, machinery, tools and materials are required to produce goods. The all investment cost is measured by the interest rate (Amekudzi, Mohammadi, & Khistry, n.d). This technique can use for cash flow and decision making is essential to perform technique such as the price of all technical details. As a result, this method is not related to our research question.

Goal programming can be used as multiple goals to assist in making the decision. Goal programming can be minimised deviations between set goals instead of attempting to maximise or minimise the objective function directly (Cristobal, 2012). All goal programming techniques are minimisation cost, profit and time. There is not any problem related to goal programming in Pak n Save.

Sequencing can be described as an implementation section for a set of works on a variety of utility equipment. A systemic succession method is used to prioritise scheduled employment and thus determine the series of the work being performed. In the sequencing method, one machine can work only one employee. Finish first machine work then start second machine jobs. It can be used in sequencing the workforce in each machine to maximise the profit.

Ergonomic Considerations

Ergonomics is the way in which work environments, products and systems are scheduled or arranged with the aim of fitting the populace using them. Ergonomics is a subset of science that manages to find out about human ability and boundaries, and then apply this estimate on how to improve the interaction of people with tasks, frameworks and circumstances. It deals with everything related to human workplaces, health and safety, leisure and sports etcetera (Dohrmann Consulting, 2018). Pak n save is supermarket where thousands of customers visits on a daily basis and thousands of employees works there. So it is very important of it to take care of comfort, wellness and health and safety of all these peoples. So, Pak n save follows these ten principles of ergonomics to provide a better place for customers and workers:

• Work in neutral postures: Pak n save provides comfortable tables and chairs to workers so that they can work in their neutral positions instead of awkward positions which are harmful to the body. Neutral positions reduce stress on muscles and bones and allow them to work more efficiently.
•   Keep everything in reach: In Pak n save everything is arranged and put in this way that peoples either they are customers or employees they do not struggle to find it or move too much for it. For example, on the checkout counter, computer operator keeps each and everything within its range like packaging envelop, MRP scanner and so on which he needs for check out.
• Reduce excessive force: There are three types of trolleys available for a buyer which they can take according to their grocery quantity and these trollies have better grip handles due to which holder will not struggle to hold it. There is a better quality of floor in Pak n save due to which customer can easily excess with trollies and not need waste energy to move it which reduces excessive force.
• Work at proper Heights: Everything in Pak n save on selves is arranged on proper heights from where customers can easily take out their items without any problem. Also, in Pak n save they always put heavy items on a lower shelf and heavier items on upper shelves which reduces chances of any mishappening. Apart from this, the forklift is provided to workers, so that they can put excessive inventory on high heights.
• Reduce Excessive Motions: Pak n save always tries to reduce excess motion for customers. They make different sections of the same types of products like dairy products are in a different section, wines and beer have a separate section. So that customers do not need to roam all around the store to find product, they can read section hoarding and can easily find products.
• Minimise Fatigue: When anyone works at the same position for long hours then he definitely gets tired because of static load. In Pak n save there are different types of works which allows them to move and get change from the same work. Like employee who works on the computer can change with those who work on standing checkout by which they do not get tired.
• Minimize Contact Stress: Contact stress occurs when you are leaning your arm on a sharp edge or your grip hard on something. To overcome thing Pak n save provides soft edged furniture and cushions on chairs to reduce contact stress.
• Provide Adequate Lighting: There is a proper arrangement of lighting in Pak n save for worker and customers as you can do shopping at night time also without any obstacle. Improper lighting cause headache, fatigue and injuries as well.
• Move, Exercise, and Stretch: Pak n save is an open space supermarket, so employees can easily move around, stretch their body and do exercise. This will improve their productivity.

Provide Clearance: In Pak n save working counters are shaped in this way that employees can easily move their body parts and enough space behind the counter for leg and knees. Similarly, equipment in the store is designed in such a way that worker can use without difficulty like pallet Jack of the proper height, so they can see in front of them (Macleod, D., 2008).

Conclusion

According to this report, there are many types of the problem faced by Pak n save including inventory management, sales, less profit and job assignment etcetera. Based on findings, different techniques can be implemented according to their relevant problems to improve customer satisfaction and brand image of Pak n save.

For inventory and sales related issues EOQ techniques are helpful which provides different discount options to attract customers. In this report, Pak n save offers three discount option varying from 0-15% according to the quantity of buying. The report shows that the fourth option is the best discount option for Pak n save as \$42572.5 is the minimum total cost. So, it reduces holding cost and in this way, excess inventory problem is also sorted.

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In this study, it can be presented the Hungarian method algorithm for the assignment problem with the changing time. The primary goal of this technique is to efficiently process an optimal assignment when changes in different job time with workers. As the results, of the optimal solution, is a total of 29 hours in 5 jobs with respect to 5 workers. It can assign operations such as bakery to employee B, dairy product to worker A, liquor section to worker E, customers to employee C and produce section to employee D.

The Linear programming method has helped Pak n Save to not only prepare the Muffins and Cakes on time but also generating a good amount of profits. After implementing this technique, the Muffins and Cakes will be placed continuously on the shelves as it gets vacant. So, the gap between the production process and inventory storage is reduced. Now, the customers don't have to wait or go empty hand. Although Muffins and Cakes are the two most selling product of Pak n Save, Linear programming method has proven beneficial to maintain that factor in a consistent manner.

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