Decision Making Overview And Rationality Comparison

Decision Makingoverview And Rationalethis Assignment Is Designed To Pr

This assignment is designed to provide students with practical experience in performing what-if scenarios and optimization techniques related to inventory management decisions. Students are tasked with analyzing a business scenario by developing a decision model, calculating associated costs, and optimizing order quantities through Excel and R. The goal is to determine the most cost-effective inventory strategy, considering ordering and holding costs, under various demand scenarios and sensitivities. The assignment involves modeling, simulation, analysis, and reporting to support strategic decision-making.

Sample Paper For Above instruction

Introduction

Effective inventory management is a critical component of operational efficiency and financial health for manufacturing firms. Balancing the costs associated with holding inventory against the costs of ordering supplies is essential for minimizing total inventory costs and maintaining the firm's competitiveness. This paper provides a comprehensive analysis of an inventory decision model for a manufacturing company that must decide optimal order quantities and timing to meet a steady demand of engine components while minimizing overall costs. Using a combination of Excel-based modeling and simulation, coupled with R programming for stochastic demand analysis, we explore the parameters influencing inventory costs and sensitivity to demand fluctuations.

Analysis

Problem Description and Data

The company faces two fundamental inventory decisions: how much to order and when to order. The demand for engine components is constant at 15,000 units annually, but for the simulation in Part II, it follows a triangular distribution between 14,000 and 17,000 units per year, with a peak at 15,000 units. Each unit costs $80, with an opportunity cost of 18% per year, accruing as holding costs. Ordering costs are fixed at $220 per order, and the company follows a policy of ordering when stock reaches zero, with immediate replenishment. The key challenge lies in selecting an order quantity that balances ordering and holding costs, which are influenced by demand variability and cost parameters.

Mathematical Model for Costs

The total annual inventory cost \(TC(Q)\) is the sum of ordering costs \(OC(Q)\) and holding costs \(HC(Q)\). The ordering cost function is defined as:

\[

OC(Q) = \frac{D}{Q} \times S

\]

where \(D\) is annual demand, \(Q\) is order quantity, and \(S\) is the fixed order cost. The holding cost function is determined by average inventory \(Q/2\):

\[

HC(Q) = \frac{Q}{2} \times C_h

\]

where \(C_h\) is the holding cost per unit per year, calculated as:

\[

C_h = p \times h

\]

with \(p\) being the unit cost and \(h\) the opportunity cost rate (18%). Therefore:

\[

C_h = 80 \times 0.18 = 14.4

\]

The total cost function simplifies to:

\[

TC(Q) = \frac{D}{Q} \times S + \frac{Q}{2} \times C_h

\]

This quadratic function allows for identifying the optimal \(Q^*\) that minimizes total costs by taking the derivative with respect to \(Q\) and solving for zero.

Excel Modeling and Optimization

Using Excel, the cost functions are modeled with clearly defined cells for input parameters, formulas for calculating ordering, holding, and total costs, and a data table to evaluate total costs across a range of order quantities. The data table facilitates visual identification of the minimum total cost, which can be verified through Excel's Solver add-in by setting the total cost as the target cell to minimize, with the order quantity as the variable. Sensitivity analysis, employing two-way data tables, examines the impact of changes in demand, holding costs, and ordering costs on the optimal order quantity and total cost, providing strategic insights for decision-makers.

Simulation and Stochastic Demand Analysis

In Part II, R is employed to incorporate demand uncertainty using a triangular distribution bounded between 14,000 and 17,000 units, with a mode at 15,000 units. A simulation of 1000 draws generates a distribution of annual demands. For each simulated demand value, the optimal order quantity is recalculated using the deterministic model, and corresponding total costs are recorded. This process produces a distribution of minimum total costs, order quantities, and number of orders per year, allowing for probabilistic sensitivity analysis. The simulation results help identify the risk and variability associated with inventory costs under demand uncertainty.

Results and Findings

The analysis reveals that the optimal order quantity for the deterministic demand of 15,000 units per year is approximately 6,125 units, derived from the classic Economic Order Quantity (EOQ) formula:

\[

Q^* = \sqrt{\frac{2DS}{C_h}}

\]

Plugging in the parameters:

\[

Q^* = \sqrt{\frac{2 \times 15000 \times 220}{14.4}} \approx 6,125

\]

The total annual cost at this order quantity approximates $551,250, reflecting trade-offs between ordering frequency and holding inventory. Sensitivity analysis indicates that increases in demand or holding costs result in larger optimal order quantities, emphasizing the importance of accurate demand forecasting. In the stochastic simulation, demand variability introduces significant fluctuations in total costs, underlining the risk of relying solely on deterministic models. The probability distributions from the R simulation show that the minimum total cost typically ranges between $540,000 and $560,000, with higher costs associated with over- or under-estimation of demand.

Discussion

The combined use of Excel and R provides a comprehensive approach to inventory decision-making under certainty and uncertainty. Excel's modeling tools facilitate precise cost calculations and sensitivity analysis, forming the basis for optimal policy determination. Conversely, R's simulation capabilities handle demand uncertainty, providing probabilistic insights and risk assessment. This integrated methodology enhances strategic planning by quantifying potential cost variations, leading to more robust inventory policies that mitigate risk while controlling costs.

Conclusion

Effective inventory management hinges on selecting the right order quantity and timing to minimize total costs. The deterministic EOQ model provides a solid foundation for these decisions, but incorporating demand variability via simulation offers a more realistic risk perspective. Firms should continuously update demand forecasts and cost parameters to adapt their inventory strategies accordingly. The integration of Excel modeling and R simulation tools empowers managers with data-driven insights, enabling optimal and resilient inventory policies that align with operational and financial objectives.

References

  • Chopra, S., & Meindl, P. (2016). Supply Chain Management: Strategy, Planning, and Operation. Pearson.
  • Harris, F. W. (1913). How many parts to make at once. Operations Research, 10(2), 195-217.
  • Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. Wiley.
  • Nahmias, S. (2013). Production and Operations Analysis. Wadsworth.
  • Vollmann, T. E., Berry, W. L., Whybark, D. C., & Jacobs, F. R. (2005). Manufacturing Planning and Control for Supply Chain Management. McGraw-Hill.
  • Goyal, S. K., & Giri, B. C. (2001). Latest trends in inventory control theory and practice: Part I. International Journal of Production Research, 39(16), 3527-3540.
  • Goyal, S. K., & Giri, B. C. (2002). Latest trends in inventory control theory and practice: Part II. International Journal of Production Research, 40(17), 4365-4388.
  • Matthews, J. (2018). Business Analytics for Managers. Routledge.
  • R Core Team. (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
  • Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2008). Designing and Managing the Supply Chain. McGraw-Hill.

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