Optimisation and Simulation
The Scenario Description ABC Manufacturer located in West Midlands seeks to maximise its production profits. This manufacturer produces two types of goods, X and Y. Goods X and Y are manufactured by a 2- stages process. All initial operations are performed by machine centre I. All final operations may be performed by either machine centre A or machine centre B. Machine centres A and B are different from each other because, in general, they yield different unit rates and different unit profits for any given good. Assume that a certain amount of overtime has been made available in machine centre A for the manufacture of goods X and Y. Since tsdfsdfhe use of overtime results in changes (decreases) in unit profits denote separately, by machine centre AA, any overtime use of machine centre A. The unit times required to manufacturing goods X and Y are given in Table 1
Table 1: information of producing goods X and Y
Operation Machine Centre Good X Good Y
X1 X2 X3 Y1 Y2 Y3
1 I 0.01 0.01 0.01 0.03 0.03 0.03
2 A 0.02 0.01 0.05 0.08
AA 0.02 0.05
B 0.03 0.64 0.08
In this table, X1, X2, and X3 are introduced to denote the three possible combinations for producing goods X, and similarly, Y1, Y2 and Y3 are defined for good Y. The available hours in each machine centre are given in Table 2.
Table 2: Hours availability at each machine centre for each operation
Operation Machine Centre Hours Available
1 I 850
2 A 700
AA 100
B 900
Table 2 defines the maximum number of hours spent by each operation at each machine centre. Such definition introduces the hours' availability constraint. The unit profit achieved per X1, X2, and X3 as referred to the three possible combinations for producing X and Y1, Y2 and Y3 as similarly defined for good Y. See Table 3 for the profit profile
Table 3: Profit per part (in pounds)
Good X Good Y
X1 X2 X3 Y1 Y2 Y3
0.40 0.28 0.32 0.72 0.64 0.60
The problem is to determine how much of each good should be made through the use of possible combinations of machine centres to maximise the total profits, considering the prescribed limitations on the capacities of the machine centres.
The Coursework Tasks For this piece of individual coursework, you are required to apply optimisation modelling to deliver the tasks below:
Task 1- Analyse the problem stating its elements, including decision variables, constraint types and definitions, objective function and how it has been formulated, and other related coefficients. Do not include any numerical values in your analysis.
Task 2- Develop a linear programming model (after combining elements defined in Task 1). This encapsulates all related variables, constraints, coefficients and objective functions. Do include here numerical values.
Task 3- Develop a spreadsheet model to solve the developed linear programming model in Task 2 using Solver.
Task 4- Analyse and discuss the results/ outputs by making relevant comparisons via Excel diagrams. A sensitivity analysis should be conducted to show how available resources could be exhausted.
Report Structure (including learning outcomes, marking scheme and criteria):
The report must cover the learning outcomes (LO1-LO4):
▪ LO1: Appraise the principles and techniques associated with operations management and other related production engineering modelling techniques. [SM1], [E3LS2], [EP2]
▪ LO2: Understand and analyse logic/ flow of production operations and be able to identify deficiencies/ bottlenecks in any engineering production facility. [SM1], [SM2]
▪ LO3: Utilise both mathematical and simulation problem-solving techniques and methodologies to understand, solve then optimise problems in the area of production engineering and operations management. [SM2], [EA1], [EA3], [E3LS3]
▪ LO4: Predict and proactively resolve any operational engineering disruptions using mathematical and simulation tools to support the decision-making process for a future state design. [EA3], [SM3], [E3LS3], [E3LS4], [EP3], [AGS1]
Assessment Criteria
The following criteria will be interpreted appropriately according to the nature of the assessment and the general framework set by the module aim and learning outcomes.
For a Bare Pass Mark (40%)
• Work lacks any academic merit as adjudged by the foregoing. For an Excellent Mark (>69%)
• Show a thorough understanding of the purpose of the activity.
• Display knowledge of all the relevant principles, theories, and practices and an ability to apply them effectively.
• Provide evidence of extensive reading beyond that listed, including academic journals.
• Demonstrate an ability to select critical points, evaluate them and communicate the conclusions effectively.
• Develop and run models that reflect as realistically and sensibly as possible given situations.
• Develop and run LP models that are based on sensible and useful options that go beyond given situations.
• Provide analysis, discussion, and comment critically on the results produced by models.
• Provide solutions to business problems that are creative and practicable.
• Provide sound, supported, discussions of further research that may be needed.
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