Question

Medisan Inc. has just signed a contract to supply walky-talkiesto the Turkish Armed Forces. During the next four months, the firm must deliver 150 in December, 160 in January, 225 in February and 180 in March.

Medisan’s factory in Temelli can produce walky-talkies at a cost of $20 per unit (labor cost is not included). To produce a walky-talky 10 hours of labor are required and there are 10 workers available at the plant at the beginning of December. Each worker can work 160 hours per month in regular hours with a rate of $1.5 per hour, and 80 hours in overtime per month with a rate of $2.5. It is possible to hire new workers or to layoff some of the existing workers at the beginning of a month. A one-time additional cost for hiring and layoff of a worker is $400 and $1000, respectively. Assume that it is possible to have non-integer number of workers. It is also possible to subcontract some of the walky-talkies to another factory at a cost of $50 each, but the subcontractor has a production capacity of 10 units. Walky-talkies can be carried in inventory to meet the demand of a future month, but this costs $5 per unit per month, but the storage has a capacity of 20 units. Backordering is also allowed with a cost of $7.5 per unit per month.

Formulate Medisan’s problem as a linear programming model.

Answer 1

Solution:

Given that

Demand for walky-talkies are

  December 150

January 160

February 225

March 180