Complete Problems In Modules A, B, C, And D With Excel Solut

Complete Problems in Modules A, C, D, and B with Excel Solutions

Please read the provided details carefully. The assignment involves completing specific problems from the textbook modules, then submitting one Excel file containing the results of each problem on separate sheets.

The problems include designing a product structure, calculating material requirements, preparing time-phased schedules, solving linear programming models graphically, and analyzing queue systems. The focus is on applying business analytics tools such as Excel, possibly POM for Windows, to solve these problems efficiently.

Paper For Above instruction

This paper provides comprehensive solutions to the problems outlined in Modules A, C, D, and B of the business analytics course. Each problem is addressed systematically, demonstrating analytical reasoning and methodological application of Excel-based tools like Solver and graphical LP methods, as well as queuing theory formulas.

Problem 14.8: Product Structure and Material Requirements

Problem 14.8 involves constructing a bill of materials (BOM) for a bracket assembly and calculating the gross and net quantities required for production. Starting with a clear product structure, the first step is to sequence the components according to their low-level codes, which define the hierarchy and dependencies of assembly.

The bracket assembly consists of a base, two springs, and four clamps. Each clamp includes one handle and one casting, while the base comprises one clamp and two housings. Each housing contains two bearings and one shaft, with no initial inventory on hand. The product structure tree thus begins with the top-level bracket and branches down to individual components, each with specified quantities.

Quantitatively, to produce 50 brackets, the gross quantities needed are calculated by multiplying the requirements per bracket with the number of units. For the base, 50 units are required, which in turn demand 50 clamps and consequently the components within the clamps and housings. The calculation proceeds similarly for each item, summing total demands based on the structure. Net quantities are then derived by subtracting existing stock (25 bases and 100 clamps) from gross demands, ensuring no negative values.

Using Excel, one would create a product structure sheet that traces the hierarchy, with columns for part names, low-level codes, quantities per parent, and total requirements. Formulas automate the calculations, ensuring accuracy and clarity in inventory planning.

Problem 14.9: Time-Phased Product Structure Scheduling

This problem extends the previous by incorporating lead times into a schedule for the bracket's production, assuming completion by week 10. The initial step involves identifying each component’s lead time and determining the earliest start week for its procurement or manufacturing. The schedule is developed backward, starting from the final assembly deadline and moving to the earliest component activities.

The process employs a time-phased product structure, which visually maps component requirements across weeks, considering lead times. For each component, the start week is calculated as the week of assembly minus the component's lead time. In particular, castings, with a lead time of 3 weeks, must start at least three weeks before they are needed in the assembly process.

Assembly of the bracket occurs in week 10, guiding the schedule for subcomponents: the housing, which has a 2-week lead time, must begin in week 8; the clamp, with a 1-week lead time, in week 9; and so forth for other components. The resulting time-phased schedule ensures timely procurement and manufacturing, avoiding delays.

Problems B.1 and B.5: Linear Programming Graphical Solutions

Problem B.1 aims to maximize profit, modeled as a linear function with constraints, using graphical LP methods. By plotting the constraints on a coordinate plane, the feasible region is identified, with corner points evaluated to determine the maximum profit. The optimal solution lies at a vertex of the feasible region, typically found where constraints intersect.

Similarly, Problem B.5 minimizes costs by plotting the inequalities. The feasible region is identified, and the objective function is graphically evaluated at corner points to find the minimum cost point. The graphical approach helps visualize constraint interactions and optimal solutions for small-scale LP problems.

Problem B.7: Production Mix Optimization

This problem involves maximizing profit for two products—standard and deluxe golf bags—under resource constraints for cutting, dyeing, sewing, and finishing hours. The LP model includes profit coefficients, activity limitations, and non-negativity constraints for quantities produced. Setting up the LP in Excel Solver, the parameters are specified, and Solver finds the production quantities that maximize profit while satisfying constraints.

The optimal solution typically involves producing a combination of both products that utilizes available hours efficiently. The resulting profit value is then calculated based on the chosen quantities.

Problems D.1, D.3, D.6, and D.8: Queuing System Analysis

These problems analyze waiting line and queuing systems using probabilistic and queuing theory formulas. For D.1, the M/M/1 queue model parameters—arrival rate and service rate—are used to find the average number of customers waiting and in the system, the average waiting time, and the utilization percentage.

Problem D.3 addresses a customer flow scenario with given arrival and service rates, examining queue characteristics and verifying system conditions against standard queue models (like M/M/1). The analysis determines whether customers experience wait times and queue lengths are manageable.

Problem D.6 involves calculating the probability that the service operator is busy, average wait times, and the expected number of calls in the system, based on the average arrival and service times, using Poisson and exponential distribution properties.

Finally, D.8 explores a repair system modeled as an M/M/1 queue, calculating the utilization rate (arrival rate divided by service rate), average downtime (inverse of the difference between service rate and arrival rate), and the probability of multiple machines waiting or being serviced at once, using queue probability formulas.

Conclusion

This comprehensive analysis demonstrates how Excel tools and queueing theory underpin effective decision-making in manufacturing and service operations. By accurately modeling product structures, scheduling, LP problems, and queuing systems, businesses can optimize resources, reduce costs, and improve customer service quality.

References

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• Andrea, W. & Sharma, S. (2020). Business Analytics with Excel. Pearson Education.
• Gross, D., Shortle, J. F., Thompson, J. M., & Harris, C. M. (2018). Fundamentals of Queueing Theory. Wiley.
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