Fig.1Graphical fig.1 of inventory level the purchasing cost

Fig.1Graphical fig.1 of inventory level the purchasing cost

Fig.1Graphical demonstration of inventory control diagram3.1.

Fixed ordering costThe fixed ordering cost in the length of a finite horizon 0, t_1 TC_A=A (5)3.2. Purchasing cost According to fig.1 of inventory level the purchasing cost of ?TC?_P=(CD(e^(??t?_1 )-e^((?t_1)/2)))/?-(?Q_1 t_1)/2 (6)3.3.

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

Holding cost excluding interest costWe locate the average inventory quantity to obtain holding cost?TC?_h=I_h ?_0^(t_1)??I(t)dt-I_(hQ_1 t_1 )/2=?_0^(t_1)??(D(e^(??t?_1 )-e^((?t_1)/2)))/?dt-I_(hQ_1 t_1 )/2=(I_h D)/?^2 (e^(?t_1 )-2e^((?t_1)/2)+1)-(???I?_h Q?_1 t_1)/2 ?? (7)3.4. Optimal inventory level and optimal time To obtain the EOQ by optimizing the total cost TC=?TC?_A+?TC?_h+?TC?_P (8)By subsisting Eq.

(5, 6, 7) in Eq. (8) Then TC=A +(CD(e^(??t?_1 )-e^((?t_1)/2)))/?-(??Q?_1 t_1)/2+(I_h D)/?^2 (e^(?t_1 )-2e^((?t_1)/2)+1)-(??I_h Q?_1 t_1)/2 (9) Deputy the t_1=(2Q_1)/(D-?Q_1 ) in Eq. (9) TC=A +(CDQ_1/(D-??Q?_1 ))-C(?Q_1?^2/(D-??Q?_1 ))-(?I_h ?Q_1?^2)/((D-??Q?_1)) (10) Deviating Eq. (10) with respect to Q_1(d?TC?_1)/(dQ_1 )=CD(D/(D-??Q?_1 )^2 )-C( (2DQ_1-???Q?_1?^2)/(D-?Q_1 )^2 )-?I_h ((2DQ_1-???Q?_1?^2)/(D-??Q?_1 )^2 )=0 ?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2) Or?Q_1?^*=D/? 1+(1-?C/(C+?I_h ))^(1/2) Lemma (1): a) If 0?k_1?1i) ??D?Q?_1?^* If ?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2) When k_1?? , 0?k_1?1ii) ??D>Q?_1?^* If ?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2) When k_1

x

Hi!
I'm Natalie

You need a custom essay? I have some suggestions for you...

Check it out