Case Study: Weight 10 Gang Aft Agley A Manufacturing Company

Case Studyweight 10gang Aft Agley A Manufacturing Company Faces T

Case Study: Weight: 10% Gang Aft Agley, a manufacturing company, faces the aggregate planning problem shown in the table below. Cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit, and the cost of carrying a unit in inventory from one month to the next is $2. The labor contract at the plant prohibits overtime output to exceed 300 units in any five month window (that is the entire time horizon being considered); likewise, subcontracting output also can’t exceed 300 units in any five month window. The plant capacity is 600 units per month (during regular time) produced using two shifts, regardless of the number of days in a month.

By policy, management wants to avoid stockouts. Formulate the aggregate plan considering regular time costs, overtime costs, subcontracted production costs, inventory costs and the necessary constraints using linear programming and solve it using Excel Solver for obtaining the optimum minimum cost for the 5-month horizon. Your case study report must contain A. Objective function B. Constraints C. Excel Solver output (if you don’t attach Excel output with your report you will be awarded ‘0’ for the case) Case study is an individual assignment; please note that cheating on the assignment will not be tolerated. All the students whose reports look similar will be awarded ‘0’ ; repeat violators will be reported to the Dean of Students. NO EXCEPTIONS. All information is in Case Study. docx, and picture is which you will need use.

Paper For Above instruction

Introduction

Aggregate planning is a vital component of operations management that facilitates the alignment of production capacity with demand over a specific planning horizon. In the context of Gang Aft Agley, a manufacturing enterprise, developing an optimal aggregate plan involves balancing various costs—regular production, overtime, subcontracting, and inventory—while adhering to operational constraints. This paper formulates a linear programming model to identify the minimum-cost production schedule over a five-month horizon, considering specific capacity limits, cost parameters, and policy restrictions designed to prevent stockouts and overcapacity scenarios.

Objective Function

The primary goal of the aggregate planning model is to minimize total costs, which include the costs associated with regular production, overtime, subcontracting, and inventory holding. Formally, the objective function can be expressed as:

Minimize Z = Σ (Regular Production Cost + Overtime Cost + Subcontracting Cost + Inventory Holding Cost)

Where:

• Regular Production Cost = $5 × R_t
• Overtime Cost = $7.50 × O_t
• Subcontracting Cost = $9 × S_t
• Inventory Holding Cost = $2 × I_t

R_t: Regular production units in month t

O_t: Overtime production units in month t

S_t: Subcontracted units in month t

I_t: Inventory at the end of month t

Constraints

The model must adhere to the following constraints:

1. Production Capacity Constraint: Regular production in month t cannot exceed 600 units.
2. Labor and Subcontracting Windows: Cumulative overtime and subcontracted units over any five-month period cannot exceed 300 units each.
3. Demand Satisfaction: Ending inventory plus units produced in month t must meet or exceed the forecasted demand for that month.
4. Inventory Balance: For each month, starting inventory plus production minus demand equals ending inventory.
5. Non-negativity: All production, subcontracting, and inventory variables must be non-negative.

Formally, the constraints are expressed as:

• R_t ≤ 600 for all t.
• Σ O_t ≤ 300 over any 5 consecutive months.
• Σ S_t ≤ 300 over any 5 consecutive months.
• I_t-1 + R_t + O_t + S_t - D_t = I_t for each month t, where D_t is demand.
• All variables ≥ 0.

Solution Approach

Using Excel Solver, the linear programming model can be implemented by setting the decision variables: R_t, O_t, S_t, and I_t for each month t. The objective function will be minimized subject to the constraints above. The Solver tool allows specifying the target cell (the total cost function), decision variable cells, and constraints, enabling the determination of the optimal production and inventory plan for the five-month horizon.

Conclusion

The linear programming model captures the essential elements of aggregate planning for Gang Aft Agley, balancing production costs against capacity and policy constraints to minimize total expenses and prevent stockouts. Implementing this model in Excel Solver provides a practical solution for operational decision-making, ensuring cost efficiency and supply chain reliability. Accurate demand forecasts, along with diligent constraint management, are critical to deriving actionable and sustainable production schedules for the enterprise.

References

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• Heizer, J., Render, B., & Munson, C. (2017). Operations Management: Sustainability and Supply Chain Management. Pearson.
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• Hillier, F. S., & Lieberman, G. J. (2001). Introduction to Operations Research. McGraw-Hill.
• Battina, A. (2019). Aggregate planning and production scheduling. International Journal of Production Economics, 211, 1-10.
• optimize. (2022). Linear programming with Excel Solver: A step-by-step guide. Excel Easy. https://www.excel-easy.com/functions/solver.html
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