A Company Must Meet On-Time Demands In Quarter 1

A Company Must Meet On Time The Following Demands Quarter 1 3000

A company must meet on time the following demands: quarter 1, 3000 units; quarter 2, 2000 units; quarter 3, 4000 units. Each quarter, up to 2700 units can be produced with regular-time labor, at a cost of $40 per unit. During each quarter, an unlimited number of units can be made with overtime labor, at a cost of $60 per unit. Of all units produced, 20% are unsuitable for sale and cannot be used for demand. Also, at the end of each quarter, 10% of all units on hand spoil and cannot be used to meet any future demands. After each quarter’s demand is satisfied and spoilage is accounted for, a cost of $15 per unit is assessed against the quarter’s ending inventory. Assume 1000 units are available initially.

Sample Paper For Above instruction

The management of a manufacturing company faces a critical challenge of fulfilling quarterly demands efficiently while minimizing costs associated with production, storage, and wastage. This paper presents a comprehensive formulation of this problem as a production planning model, utilizes optimization tools to identify optimal production strategies, and conducts sensitivity analysis to inform managerial decisions.

Introduction

Effective production planning is fundamental for manufacturing firms aiming to meet demand while controlling operational expenses. The scenario involves meeting specific demands in three sequential quarters, with constraints on regular and overtime production capacities, spoilage, and inventory costs. The core objective is to develop a model that guides optimal production quantities and inventory management to minimize total costs over the planning horizon.

Model Formulation

The model encompasses decision variables, parameters, and constraints reflective of the problem's dynamics. Let us define the necessary variables:

• Production in regular time for quarter t: R_t
• Production in overtime for quarter t: O_t
• Ending inventory after quarter t: I_t

Parameters include demand (D_t), spoilage rate, initial inventory (I_0 = 1000 units), and costs. The key assumptions are that 20% of all units produced are unsuitable for sale, thus effectively reducing the usable units, and 10% of on-hand inventory spoil at the end of each quarter.

The model's constraints are as follows:

1. Demand satisfaction: The usable units from regular and overtime production, adjusted for spoilage, must meet quarterly demand.
2. Production capacity: Regular-time production does not exceed 2,700 units per quarter.
3. Inventory balance: Inventory carried forward accounts for spoilage and demand fulfillment.

Mathematically, for each quarter t:

• Usable production: 0.8*(R_t + O_t)
• Inventory update: I_t = (I_{t-1} (1 - 0.10)) + (0.8 R_t + 0.8* O_t) - D_t

The objective function aims to minimize total costs, including regular and overtime labor costs, inventory holding costs, and spoilage expenses:

Minimize Z = ∑_{t=1}^3 [40 R_t + 60 O_t + 15* I_t]

Implementation in Spreadsheet

Using spreadsheet software, the variables are instantiated in cells, with formulas capturing the relationships described above. Solver is employed to identify optimal production quantities R_t and O_t for each quarter, respecting capacity constraints and feasible inventory levels. The initial solution involves setting variable bounds, defining the objective cell, and applying Solver’s solving method for linear programming.

Results and Analysis

The solution indicates weekly production plans balancing regular and overtime capacity, with inventory levels adjusted to minimize total expenditure. Notably, the model identifies whether the company should rely on overtime production or adjust inventory strategies, based on cost implications.

The total cost of implementing this plan is computed from the optimized production and inventory levels. Additionally, the Solver’s Sensitivity Report reveals how variations in demand affect costs and when additional overtime capacity might become economically advantageous.

Sensitivity Analysis

By increasing the demand in quarter 1 by one unit, the analysis shows an incremental increase in total costs, quantifying the sensitivity of the operation to demand fluctuations. The critical overtime cost threshold in quarter 2 is identified as the point where the cost of overtime labor equals the cost of additional regular capacity or inventory costs, guiding managerial decisions on capacity investments.

Conclusion

This modeling approach provides a strategic framework for production planning under capacity, spoilage, and cost constraints. It supports managerial decision-making by quantifying trade-offs and identifying cost-saving opportunities, especially in scenarios involving fluctuating demand and capacity constraints.

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