Shelby Shelving Case Study: Production Optimization And Fina

Shelby Shelving Case Study: Production Optimization and Financial Analysis

Shelby Shelving is a small manufacturing company producing two models of shelves: the standard Model S and the heavy-duty Model LX. The company’s production process involves three main steps: stamping, forming, and assembly. Stamping and forming are performed on shared machines for both models, while assembly is done in separate departments for each model. Currently, Shelby produces 400 units of Model S and 1400 units of Model LX per month, with Model S selling at $1800 and Model LX at $2100.

Management faces a dilemma regarding the profitability of Model S shelves. Although the shelves are selling well, the contribution margin per unit for Model S is negative because the production costs exceed the selling price. The plant engineer, Doug Jameson, suggests reducing Model S production due to its unprofitability, asserting that the shelf’s costs ($1839) are higher than its selling price ($1800). Conversely, the controller, Sarah Cranston, argues that even unprofitable units contribute to overhead absorption—particularly fixed costs—so lowering production might worsen overall profitability.

The case requires developing a Linear Programming (LP) model to analyze Shelby’s operational decisions, running Solver to optimize production, and providing a strategic recommendation based on quantitative analysis. The LP model must incorporate constraints related to machine hours, assembly capacities, costs (both fixed and variable), and labor requirements. Fixed overhead allocations are activity-based, distributed among products according to machine usage, with detailed calculations of overhead per unit for each model.

The analysis should include sensitivity assessments, such as exploring the impact of changing production levels, costs, and sales prices. Additionally, a professional presentation of findings, including the case background, assumptions, constraints, results, and managerial implications, is required. The goal is to determine whether Shelby should continue current production or reduce Model S output to improve financial health.

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Shelby Shelving’s case presents a classic scenario of production decision-making within the constraints of capacity, costs, and profitability. Developing an LP model allows precise analysis of whether adjusting Model S production enhances overall profitability or if the contribution margin, even at a loss per unit, supports maintaining current output levels for overhead absorption. This comprehensive approach integrates capacity constraints, cost allocations, and potential strategic impacts.

The key decision variables in the LP model are the quantities of Model S and Model LX shelves to produce monthly. The objective function is to maximize net profit, which is calculated by subtracting total costs—including variable and fixed overhead—from revenues generated by the units sold. Given that prices are fixed by market competition, the model aims to allocate production efficiently within existing capacity constraints.

Constraints include machine hours for stamping and forming, which are shared between models, with maximum monthly hours of 800 on each machine. Assembly capacities are limited to 1900 units for Model S and 1400 units for Model LX. These constraints can be expressed mathematically as inequalities in the LP model:

1. Forming machine hours: 0.25 × units of S + 0.17 × units of LX ≤ 800

2. Stamping machine hours: 0.3 × units of S + 0.3 × units of LX ≤ 800

3. Assembly capacity: units of S ≤ 1900 and units of LX ≤ 1400.

The costs, including specific overhead allocations, are crucial to the analysis. The overhead per unit for each model combines variable costs (from direct costs like labor and materials) and fixed overhead allocated through activity-based costing. The overhead for Model S is approximately $150 per unit, while Model LX has about $229 per unit, considering their respective machine usage and fixed overhead allocations.

Solving the LP model using Solver provides an optimal production plan that indicates whether Shelby should reduce Model S production. The analysis explores the contribution margins and whether continuing production at current levels is sustainable or if reducing Model S units would improve overall profit. In this context, despite the current loss per unit, maintaining Model S production may still be justified if the units contribute to covering fixed overhead, as Sarah Cranston argues, rather than being purely unprofitable.

The sensitivity analysis assesses the robustness of the decision, examining the impact of variations in costs, machine hours, and sales prices. If the model shows that reducing Model S shelves increases overall profitability or mitigates losses by freeing capacity for more profitable products, management might opt for reduction. Conversely, if the contribution margin is insufficient to cover fixed overhead, or if reducing production leads to underutilized capacity and higher fixed costs per unit, maintaining current production levels might be justified.

Based on the LP analysis, the recommendation should consider both quantitative results and managerial judgment. If the detailed analysis indicates that continuing Model S production adds value by contributing to fixed costs and enabling full utilization of capacity, even at a loss per unit, then the current strategy should remain. Alternatively, if the marginal analysis shows that cutting Model S shelves improves profit margins and overall financial health, then production should be scaled back.

In summary, the optimal strategy balances capacity constraints, contribution margins, overhead absorption, and strategic goals. The LP model provides a structured method to evaluate these factors quantitatively, aiding Shelby management in making data-driven decisions aligned with their competitive market environment.

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