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A local firm manufactures cellphones. The proiected demand over the next six months is: The forecasted demand in aggregate units for April is given as 4XXX. You need to replace XXX with the last 3 digits of the average of the Students' group ID numbers, rounded up. For example, if your ID numbers are 105987, 110556 and 112337, you will use a forecasted value of 4627 cellphones for April. A normal work-day is eight hours. Hiring costs are OMR 650 per worker and firing costs are OMR 1950 per worker. Holding costs are OMR 5 per aggregate unit held per month, and backorder cost is OMR 45 per aggregate unit per month. It requires an average of 50 minutes for one worker to assemble one cellphone. The ending inventory in December of the previous year was 225 units, and the manager wants to have at least 120 units on hand in inventory at the end of June. The workforce at the end of December in the previous year was 20 workers. Workers are paid OMR 6 per hour for regular time labor. Overtime labor costs OMR 9 per worker per hour, and the maximum overtime that is allowed is 3 hours per worker each day.

(a) Find the minimum constant workforce plan for the six months and the total cost of the plan. The firm does not want any stockouts. The plan should show the production levels, workforce levels, number hired, number fired, ending inventory and shortages for each month. You may hire or fire workers only at the beginning of January. What is the cost of this plan?
(b) Determine the zero inventory (chase) plan that hires and fires workers each month to match demand as closely as possible, and the cost of that plan. No stockouts are allowed.
(c) Use the Excel sheet of the aggregate production plan developed in part (b) to find the total cost if the forecast demand for February is changed to 3500 cellphones.
(d) Formulate the problem as a linear programming model to find the best aggregate production plan.
(e) Use Excel Solver to find a feasible aggregate production plan through the conservative approach. Explain.

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Final answer:

To find the minimum constant workforce plan and its cost, we use the level production plan approach, optimizing costs to meet demand. The zero inventory (chase) plan hires and fires workers monthly to match demand, delivering cost-optimized production levels. By updating the forecast demand in an Excel sheet, the total cost is recalculated. The problem can be formulated as a linear programming model, enabling us to find the best aggregate production plan. Excel Solver can be used to find a feasible plan through the conservative approach.

Step-by-step explanation:

In order to find the minimum constant workforce plan for the six months and the total cost of the plan, we need to consider the forecasted demand and the costs associated with workforce. From the information provided, we know that the forecasted demand for April is 4XXX, where XXX needs to be replaced with the last 3 digits of the average of the Students' group ID numbers, rounded up. The average labor time required to assemble one cellphone is 50 minutes. Hiring costs are OMR 650 per worker and firing costs are OMR 1950 per worker. Holding costs are OMR 5 per aggregate unit held per month, and backorder cost is OMR 45 per aggregate unit per month. The ending inventory in December of the previous year was 225 units, and the manager wants to have at least 120 units on hand in inventory at the end of June. The workforce at the end of December in the previous year was 20 workers. Workers are paid OMR 6 per hour for regular time labor. Overtime labor costs OMR 9 per worker per hour, and the maximum overtime that is allowed is 3 hours per worker each day.

(a) To find the minimum constant workforce plan, we can use the level production plan approach. This means maintaining a constant workforce throughout the six months and adjusting production levels to meet demand. The calculations for each month involve determining the number of workers needed, production levels, hiring and firing, ending inventory, and shortages. The plan should be optimized to minimize costs while meeting demand requirements.

(b) The zero inventory (chase) plan requires hiring and firing workers each month to match the forecasted demand as closely as possible. Again, the calculations for each month involve determining the number of workers needed, production levels, hiring and firing, ending inventory, and shortages. The plan should be optimized to minimize costs while meeting demand requirements.

(c) Using the Excel sheet from the aggregate production plan developed in part (b), we can update the forecast demand for February to 3500 cellphones. By adjusting the production levels, workforce levels, and other variables, we can calculate the total cost of the plan based on the updated forecast.

(d) Formulating the problem as a linear programming model involves defining the objective function and the constraints. The objective is to minimize costs, while the constraints include labor availability, production capacity, demand requirements, and inventory targets. By solving the linear programming model, we can find the best aggregate production plan.

(e) Using Excel Solver, a feasible aggregate production plan can be found through the conservative approach. This involves setting conservative targets for labor and production levels, and then adjusting them as necessary to meet demand while minimizing costs.

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