OPRE6302 Operations Management Assignment 3 Q1 Harold Grey

OPRE6302 OPERATIONS MANAGEMENT Assignment #3 Q1. Harold Grey owns a small farm that grows apricots in the Salinas Valley

Harold Grey owns a small farm that grows apricots in the Salinas Valley. The apricots are dried on the premises and then sold to a number of large supermarket chains. Based on past experience and committed contracts, he estimates that the sales over the next five years in thousands of packages will be as follows: Year Forecasted Demand (thousands of packages). Grey currently has three workers on the payroll. Assume that each worker stays on the job for at least one year. He estimates that he will have 10,000 packages on hand at the end of current year. Assume that, on average, each worker is paid $25,000 per year and is responsible for producing 30,000 packages. Inventory costs have been estimated to be 4 cents per package per year, and shortages are not allowed. Based on the effort of interviewing and training new workers, Grey estimates that it costs $500 for each worker hired. Severance pay amounts to $1,000 per worker. (a) Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next five years. (b) Evaluate the cost of the plan found in (a). (c) Develop a linear-programming model for the least-cost production plan.

Paper For Above instruction

Harold Grey’s apricot farm faces a classic operations management challenge: determining the most cost-effective workforce plan to meet forecasted demand over a five-year period without incurring shortages. This problem involves analyzing staffing requirements, costs, and inventory considerations to develop a sustainable, efficient production strategy that minimizes total costs, including labor, inventory, and hiring or severance expenses. The primary goal is to establish a constant workforce size to satisfy demand while adhering to constraints related to inventory and costs, and to formulate a linear programming model to optimize this plan.

Introduction and Context

Efficient workforce planning is fundamental in agricultural operations where perishability, demand variability, and costs are critical factors. The case of Harold Grey’s apricot farm exemplifies this, requiring careful balancing of labor, inventory levels, and costs. The key challenge is to determine the minimal workforce that can produce the projected demand without shortages and with minimal total costs. Given that each worker produces 30,000 packages annually and that inventory costs are relatively low at 4 cents per package, the plan must also consider hiring, severance costs, and inventory holding costs.

Workforce Requirements Calculation

To determine the minimum constant workforce, we first analyze the demand forecast with respect to production capacity and inventory. The demand in thousands of packages for five years, along with the initial inventory of 10,000 packages, sets the starting point. Since shortages are not allowed, each year’s demand must be met by a combination of current workforce output and inventory adjustments. The production capability per worker (30,000 packages/year) guides the staffing plan.

Annual Workforce Estimation

Considering the forecasted demands, the minimum workforce requirement per year can be calculated by dividing the annual demand by each worker’s annual output (30,000 packages). For example, if the demand in year 1 is D1 in thousands, the required workforce (W1) must satisfy W1 ≥ D1 × 1,000 /30,000. This calculation must be adjusted for inventory carried over from previous years to avoid shortages. Since the inventory at year-end is part of the system, the inventory balance equations are critical in formulating the problem.

Cost Evaluation and Total Cost Analysis

Once the minimum workforce plan is determined, the total cost includes labor costs, hiring/training costs, severance payments, and inventory holding costs. Labor costs are straightforward: workforce size × $25,000. Hiring costs at $500 per worker apply when increasing workforce to meet demand, while severance costs are relevant if reducing or adjusting staffing levels. Inventory costs accrue at 4 cents per package per year for excess stock. The analysis involves summing these costs over the five years, considering the workforce stability assumption in part (a) of the question.

Linear Programming Model Development

The problem lends itself to a linear programming formulation where decision variables include annual workforce sizes, hiring and firing amounts, and inventory levels. The objective is to minimize the total cost over five years, subject to constraints such as demand satisfaction, workforce continuity, and inventory balance. The model components include:

• Variables for workforce each year (W1, W2, W3, W4, W5)
• Variables for hiring and severance (if adjusting workforce)
• Inventory variables each year (starting and ending)

Constraints ensure that each year’s production (workforce times 30,000) plus beginning inventory equals demand plus ending inventory, with non-negativity and logical bounds on hiring and firing. The LP formulation enables optimizing the workforce plan to minimize total costs efficiently.

Conclusion

Through analyzing the demand forecast, production capacity, and associated costs, a comprehensive workforce and inventory plan can be formulated for Harold Grey’s apricot farm. The linear programming model helps identify the least-cost strategy, ensuring demand fulfillment without shortages and maintaining cost-effectiveness over the five-year horizon. Proper implementation of this plan would optimize farm operations, reduce unnecessary expenditures, and sustain the business’s profitability.

References

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