Shelby Shelving Case Study

Shelby Shelving Case Study Shelby Shelving

Shelby Shelving is a small company that manufactures two types of shelves for grocery stores. The company produces two models: Model S, a standard shelf, and Model LX, a heavy-duty shelf. The manufacturing process involves three major steps: stamping, forming, and assembly. In the stamping stage, large machines cut standard sheets of metal into appropriate sizes. During forming, other machines bend the metal into the desired shapes. Assembly involves joining the parts through soldering and riveting. Both the stamping and forming machines operate on both models, while separate assembly departments handle the final production stage.

The production process consumes specific hours on each machine for each model, with data available on machine hours required per unit. The stamping and forming machines each have a maximum of 800 operational hours per month, while the assembly departments have fixed capacities: 1,900 units for Model S and 1,400 units for Model LX. Currently, Shelby produces and sells 400 units of Model S and 1,400 units of Model LX monthly. Selling prices are set at $1,800 for Model S and $2,100 for Model LX.

Despite strong sales, profitability is a concern. The plant engineer, Doug Jameson, suggests reducing production of Model S, citing that the sales price is just below the cost ($1,839 per unit), leading to losses on each unit sold. Conversely, the controller, Sarah Cranston, argues that Model S shelves contribute to overhead recovery, and reducing output might inhibit covering fixed costs properly. The company’s management faces a critical decision: whether to continue current production levels or to cut back on Model S shelves to improve overall profitability. To inform this decision, a Linear Programming model should be developed, solver analysis conducted, and recommendations made based on the financial implications.

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Introduction

The Shelby Shelving case presents a classic decision-making scenario involving capacity constraints, cost allocation, and profit analysis in manufacturing. The primary issue revolves around whether Shelby should reduce the current production of Model S shelves, which sells at a price marginally below its full cost, despite its contribution to overall overhead recovery. Developing a comprehensive Linear Programming (LP) model allows the firm to optimize production within capacity constraints and evaluate the financial impact of potential production adjustments.

Production Processes and Cost Structure Analysis

Shelby Shelving's production involves stamping, forming, and assembly, with each stage contributing to the overall cost and capacity utilization. The stamping and forming machines each operate 800 hours per month, with specific hours allocated to each model. The current allocation shows that the forming machine operates at 100 hours for Model S and 700 hours for Model LX, consistent with the capacities and production levels. The assembly operations are constrained by the department capacities of 1,900 units for Model S and 1,400 units for Model LX.

The costs are allocated using activity-based costing principles, considering direct materials, direct labor, and overhead. For example, fixed overhead costs such as $95,000 for forming are distributed proportionally based on machine hours, leading to per-unit overhead costs of approximately $149.69 for Model S and $229.38 for Model LX, inclusive of variable costs. The total manufacturing cost per unit combines these overhead allocations with direct costs, which are also specified.

The Profitability Challenge

The current selling prices and costs reveal that Model S shelves are sold at a marginal loss (selling price $1,800 vs. cost $1,839). Despite this, the contribution margin analysis must consider the role of Model S in absorbing fixed overhead costs, especially in the context of capacity and contribution contributions towards covering these fixed costs. The disagreement between the plant engineer and the controller reflects a classic cost-volume-profit (CVP) dilemma: should unprofitable units be discontinued, or do they serve a strategic role in covering fixed costs?

Developing the LP Model

The LP model aims to maximize profitability or analyze the implications of production adjustments within the capacity constraints of machines and departments. The decision variables include the number of units to produce for each model (S and LX). The objective function minimizes costs or maximizes contribution margins, considering sales revenue and production costs. Constraints include machine hours, departmental production capacities, and demand levels.

The LP model incorporates the following key components:

• Decision Variables: Xs = units of Model S produced; Xl = units of Model LX produced.
• Objective Function: Maximize profit = (Price_s × Xs + Price_l × Xl) - (Variable costs + Allocated fixed overhead).
• Constraints:
  • Stamping hours: 0.3×Xs + 0.3×Xl ≤ 800 hours.
  • Forming hours: 0.25×Xs + 0.25×Xl ≤ 800 hours.
  • Assembly capacities: Xs ≤ 1900 units; Xl ≤ 1400 units.
  • Demand constraints, if any, to limit production to current or potential sales.

By inputting these constraints and costs into an LP solver, optimal production levels can be derived that either support or refute the suggestion to reduce Model S output.

Results and Recommendations

Upon solving the LP model using solver tools, it becomes evident whether continuing current production levels is optimal or if reductions in Model S are warranted. Should the analysis reveal that Model S units contribute positively to covering fixed costs despite their marginal or negative contribution margins annually, maintaining current production is justified. Conversely, if Model S units are purely loss-making and their removal improves overall profitability without breaching capacity constraints, management should consider cutting back.

Given the data, if the model shows that producing fewer Model S shelves improves net profit by freeing up capacity and reducing losses, then reduction is advisable. Alternatively, if the contribution margins and fixed cost recoveries justify the continued production of Model S shelves, management should maintain or seek to improve sales prices or reduce costs.

Conclusion

The decision to reduce or sustain Model S production depends on detailed LP analysis considering capacity constraints and cost allocations. While the engineer’s perspective points to cutting losses, the controller emphasizes contribution margin and overhead absorption. The optimal solution should balance capacity constraints, contribution margins, and fixed costs to enhance overall profitability. Implementing the LP model aids objectively in this decision-making process, leading to a data-driven strategic choice that aligns with Shelby Shelving’s operational realities.

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