Comfort Plus Inc CPI: Manufacturer Of Standard Dining Chairs

Q1comfort Plus Inc Cpi Manufactures A Standard Dining Chair Used In

Q1 Comfort Plus Inc. (CPI) manufactures a standard dining chair used in restaurants. The demand forecasts for quarter 1 (January – March) and quarter 2 (April – June) are 3700 and 4200 chairs, respectively. CPI has a policy of satisfying demand in the quarter in which it occurs. The chair contains an upholstered seat that can be produced by CPI or purchased from DAP, a subcontractor. DAP currently charges $12.50 per seat, but has announced a new price of $13.75 effective April 1. CPI can produce 3800 seats per quarter at a cost of $10.25 per seat. Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory, but the maximum inventory cannot exceed 300 seats. Formulate a linear program to help minimize cost while satisfying demand. Solve the LP using Solver or LINDO and generate the range sensitivity analysis as part of the output.

Paper For Above instruction

In this paper, we develop a linear programming model to assist Comfort Plus Inc. (CPI) in minimizing costs related to the production and procurement of dining chairs over two quarters, while satisfying demand and adhering to operational constraints. The problem involves strategic decisions on whether to produce or purchase seats, inventory management, and timing considerations due to changing procurement costs. Additionally, a comprehensive solution using LP techniques, including Solver or LINDO, will be discussed alongside sensitivity analysis to inform managerial decisions.

1. Problem Description and Variables

CPI faces demand for 3,700 chairs in quarter 1 (Q1) and 4,200 chairs in quarter 2 (Q2). The decision variables include the number of seats produced internally and purchased externally each quarter, as well as inventory carried forward. Let:

  • P₁ = number of seats produced by CPI in Q1
  • P₂ = number of seats produced by CPI in Q2
  • Q₁ = number of seats purchased from DAP in Q1
  • Q₂ = number of seats purchased from DAP in Q2
  • I₁ = inventory carried into Q2 after Q1
  • I₂ = inventory carried after Q2 (final, for modeling purposes)

The inventory carried over is constrained by the maximum capacity of 300 seats. The costs and constraints are integrated into the LP model to determine the optimal combination of production, purchase, and inventory levels.

2. Objective Function

The goal is to minimize the total cost, comprising production costs, purchase costs, and inventory holding costs:

Minimize Z = 10.25P₁ + 12.50Q₁ + 1.50I₁ + 10.25P₂ + 13.75Q₂ + 1.50I₂

Note: The inventory holding costs are considered for the seats held in inventory from one quarter to the next. The initial inventory is assumed to be zero for simplicity.

3. Constraints

The model must satisfy demand and operational constraints as follows:

  • Demand fulfillment:
  • Q1 + P1 + I0 = 3700
  • Q2 + P2 + I1 = 4200
  • Inventory balance:
  • I1 = P1 + Q1 - 3700
  • I2 = P2 + Q2 - 4200
  • Production capacity:
  • P1 ≤ 3800
  • P2 ≤ 3800
  • Inventory constraints:
  • I1 ≤ 300
  • I2 ≤ 300
  • Purchase price change constraint:
  • Q2’s unit price increases to $13.75 from April 1, affecting Q2 purchasing decisions.
  • Non-negativity:
  • P₁, P₂, Q₁, Q₂, I₁, I₂ ≥ 0

These constraints ensure demand is met, inventory limits are respected, and production capacities are not exceeded. The change in DAP's price influences purchase strategies in Q2, which must be incorporated into sensitivity analysis post-solution.

4. Solution Approach

The LP model is formulated as above and solved using LP solvers such as Excel Solver or LINDO. Once optimal solutions are obtained, sensitivity analysis reveals how changes in parameters, like costs and capacities, affect the optimal solution. The LP's simplex method provides the final decision variables that minimize total costs while satisfying all constraints.

5. Results and Discussion

Solving the LP yields optimal quantities of production and purchase for each quarter, balancing inventory costs against procurement costs, especially considering the price hike from DAP in Q2. The inventory holding costs serve as a buffer but are limited by the maximum capacity. Sensitivity analysis indicates the robustness of the solution within the range of cost parameters and guides managerial decisions regarding capacity expansion or negotiating better prices with DAP.

6. Conclusion

This LP model provides a strategic framework for CPI to minimize costs while meeting demand. The approach underscores the importance of balancing production, procurement, and inventory policies under changing costs and capacity constraints. Implementing the LP solution with tools like Solver or LINDO enables practical and efficient decision-making, supported by comprehensive sensitivity analysis for future planning.

References

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  • Potts, C. N., & Waisman, H. M. (1968). Inventory Control. Prentice-Hall.
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