Operation Research (Optimization) Linear Programming Problem A company wants to
ID: 354116 • Letter: O
Question
Operation Research (Optimization)
Linear Programming Problem
A company wants to manufacture three products over a 2-year (4 quarters) planning horizon. The table below provides the revenue (i.e. selling price) for each product. The table also presents the number of worker-hour to produce one unit of each product.
Product
Selling Price (1st year)
Selling Price (2nd year)
worker-hour to produce one unit
A
1100
1250
13
B
1100
1200
14
The table below provides the maximum demand for each period, which are expected to be similar for all the products:
Quarter
1
2
3
4
Year 1
200
200
250
300
Year 2
220
220
250
300
The company has a commitment to produce and ship 75% of the maximum demand for each period. The company has 60 workers available. Each worker can work for 160 hours per quarter. Each worker costs $30 per hour (including benefits). Overtime is allowed with the cost of 50$ per hour (including benefits). 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.
1. What are the variables?
2. What are the Objective Function and the constraints of this problem?
Product
Selling Price (1st year)
Selling Price (2nd year)
worker-hour to produce one unit
A
1100
1250
13
B
1100
1200
14
Explanation / Answer
1.
2.
if E(i+1)-E(i) <= , value = 0
if E(i)- E(i + 1) <= 0, value = 0
Constraints are
Pa1+ Pb1<= 200 >= 0.75*200
Pa2+ Pb2<= 200 >= 0.75*200
Pa3+ Pb3<= 250 >= 0.75*250
Pa4+ Pb4<= 300 >= 0.75*300
Pa5+ Pb5<= 220 >= 0.75*220
Pa6+ Pb6<= 220 >= 0.75*220
Pa7+ Pb7<= 250 >= 0.75*250
Pa8+ Pb8<= 300 >= 0.75*300
Inv (i) = Pa(i+1)+Pb(i+1) - Pa(i)+Pb(i) >= 0
Pa(i) * 13+ Pb(i) * 14 = (E(i)* 160 + O (i)
All variables >= 0
The variables are units produced of A in each quarter Pai for i=1 to 8 units produced of A in each quarter Pbi for i=1 to 8 The number of employees in each quarter Ei for i=1 to 8 Hours of OT per quarter Oi for i=1 to 8Related Questions
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