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

K-talkie $ 20 pesumt (excluding labog čoSt foo one dalk coos kets in Decembe 10 Total wosktna horsspe labo mon -> Cost fo

うもa5PswM petMonth Back ơsdesing charts tatk'es manuaess s month → Number 4 hours peteu lky -talk'e 210 → "Total number 4 coos khors pedaboos No. 8 côoskes in Deternber x Total coot hourr spes labo46 numbes → Numbes to at enisHn abou = 1600110

3 >COS Cost *b nan ufacbacin wa talkfe Cost labos fixed cost , x1 x 20 tost manu fabrin COSt 320o manufattust $5600

demand in etanbesSo -demanin defembe 160-5o Gemand in manth 8 sana 66 ustna extstng labo Tota cost manufa huesk

→ Let us compre costs fes 1ㆁunits fosad 3 opHons ploe an manufa ttuxe 6 units in a Mon-Hh cost emplot ee 400 t-240 $ 64 0 $6o pet 6units Fos o units

7 othes Costs - fixed cost % 20 pesunt 1oX 20 → Toba, manu $boo other opHon makina employees oJeiH me → Total latos cost fos okTHme", $100x25 250 → Rxed cost, $20x10 ー3200

Thesefose the cheapeopHon aol Li → total Cost manufaaingandaxtm →Total Cost d manufathat ng 'n Februa's labos ovesHme - FIXed Cost + Labo*s Cast 2.5 1oY5

-Tobo Cost 8 manufa thh $ u300 2400 13.5 $5o |ュ$ 683.75 $3200 + $2406,t $2756十$$0 Thesefase At d poemlsespof table → Cost 3 manufacturing in norsch $3600 $2400 +45o -$ 6oSo