Baird Inc. Company produces two different components (A and B) for a major manufacturer. The manufacturer notifies the Baird sales office each quarter of its monthly requirements for components for each of the next three months. The monthly requirements for the components may vary considerably. The order shown in Table below has just been received for the next three-month period.
Component April May June
A 1000 1000 3000
B 500 5000 3000
After the order is processed, a demand statement is sent to the production control department. The production control department must then develop three-month production plan for the components. In arriving at the desired schedule, the production manager will want to identify the following:
1. Total production cost
2. Inventory holding cost
3. Change-in-production-level costs
Component A costs $20 per unit produced and component B costs $10 per unit produced. Baird determined that on a monthly basis inventory holding costs are 1.5% of the cost of the product. For modeling purposes, it is assumed that monthly ending inventories are an acceptable approximation to the average inventory levels throughout the month. After estimating the effects of employee layoffs, turnovers, reassignment training costs, and other costs associated with fluctuating production levels, Baird estimates that the cost associated with increasing the production level for any month is $0.50 per unit increase. A similar cost associated with decreasing the production level for any month is $0.20 per unit. Current inventories at the beginning of the three-month scheduling period are 500 units for component A and 200 units for component B. Baird would like to have at least 400 units of component A and at least 200 units of component B in inventory at the end of the three months.
Machine, labor, and storage space requirements for each component are given below.
Component Machine (hours/unit) Labor (hours/unit) Storage (square feet/unit)
A 0.10 0.05 2
B 0.08 0.07 3
Capacities to produce and store the components for the next three months are as follows:
Component Machine Capacity (hours) Labor Capacity (hours) Storage Capacity (square feet)
April 400 300 10000
May 500 300 10000
June 600 300 10000
Further, assume the production levels for March (the month before the start of the current production scheduling period) had been 1500 units of component A and 1000 units of component B.
Determine the number of units of each component to be produced in April, May and June that will minimize the total cost of the monthly production increases and decreases.