A company needs an appropriate production plan for two products over the period
ID: 354622 • Letter: A
Question
A company needs an appropriate production plan for two products over the period of two years. Table below provides the selling price for each product in each year and the demand for each month. The table also provides the worker-hour to produce one unit for products A and B.
Product
Selling Price (1st year)
Selling Price (2nd year)
worker-hour to produce one unit
Demand (1st year)
Demand
(2nd year)
A
1100
1250
13
200
200
B
1100
1200
14
200
200
The company has 60 workers available. Each worker can work for 500 hours per year. Each worker costs $30 per hour. Overtime is allowed with the cost of 50$ per hour. The manager is also allowed to hire and lay off workers if necessary. The costs of hiring a new worker in the first year and the second year are estimated to be $2600 and $2800, respectively. The costs to lay-off a worker in the first year and the second year are estimated to be $1400 and $1600, respectively. Moreover, the manager is allowed to keep and use inventory. The company expects the holding costs to be $5 for one period (per item) and remains constant over the planning horizon for all the products.
Q: Develop the mathematical formulation to maximize the profit (clearly define all the variables and list all your assumptions).
Product
Selling Price (1st year)
Selling Price (2nd year)
worker-hour to produce one unit
Demand (1st year)
Demand
(2nd year)
A
1100
1250
13
200
200
B
1100
1200
14
200
200
Explanation / Answer
Net approx profit before taxes for Product A in the first year
Using this logic, the costs for year 2 for product A, year 1 and 2 costs for Product B can be calculated to derive profit.
Reason to consider 8 staff ( emergency leave, loss of work hours, unforeseen events, weekly offs )
Product Selling Price (1st year) Selling Price (2nd year) worker-hour to produce one unit Demand (1st year) Demand (2nd year) A 1100 1250 13 200 200 B 1100 1200 14 200 200 No of workers 60 Hours per worker per year 500 Cost per hour 30 New hire cost 1st year 2600 New hire cost 2nd year 2800 Layoff costs 1st year 1400 layoff costs 2nd year 1600 Fix cost per product 5 Product A 1st Year Selling price per product 1100 Number of products needed ( Demand ) 200 N.o of hours taken by a worker to product 1 product 13 N.o of products a worker can produce in 500 hours ( 1 Year ) 38.46154 N.o of workers 60 N.o of products a worker can produce in 1 hour 0.077 Total products 60 workers can produce in an year 2307.692 *Assuming demand for product A is only 200, the 60 workers have a capability to produce 2307.692 products Therefore, over supplied products 2108 Therefore, n.o of workers over staffed (approx) 54.75325 Adding buffer workers, in case of any unforeseen event, weekend offs and emergency leaves, I would consider 50% of actually required staff for product A. Even if there is an unexpected increase in demand for product A, the buffer workers can meet the demand. Therefore, actual required workers 8 So total man hours taken to produce the 200 products ( 200 * 500 / 38.5 ) 2597.403 Cost per hour 13 Therefore, cost per 200 products over 2598 hours 33774 Now cost of product A Selling price per product 1100 Demand 200 Total revenue for Product A in 1st year 220000 Less Fixed cost for product A (200*5) 1000 Layoff costs of Labour (52*1400) 72800 Labor cost for 200 products over 2598 man hours 33774Net approx profit before taxes for Product A in the first year
Using this logic, the costs for year 2 for product A, year 1 and 2 costs for Product B can be calculated to derive profit.
Reason to consider 8 staff ( emergency leave, loss of work hours, unforeseen events, weekly offs )
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