inventory planning of supply model joint economic lot-size

International Journal of Engineering and Science Vol. 3, No. 4, 2012ISSN: 2086-3799Available online at: www.ijes.co© 2012 Universitas Malahayati Press

INVENTORY PLANNING OF SUPPLY MODEL JOINT ECONOMIC LOT-SIZE

Tiena Gustina AmranIndustrial Engineering Department, Trisakti UniversityE mail : [email protected], [email protected]

Abstract

Along expanding manufacturer industry in Indonesia dealing with competition to produce high quality product and corporate profitability to survive and winning the competition. This research conducted in part manufacturer supplier and otomotive component in stamping division that encourage to lifter quality and optimal production cost. Planning of supply model which is proposed consist of 4 model of economic lot of size, that is Joint Economic Lot of Size pursuant to buyer ,Joint of Economic Lot of Size pursuant to seller, Joint Economic Lot- Size and ,Joint Economic Lot - Size ( n*), and under color of election pursuant to expense of supply of smallest alliance. Examination /conducted to 4 raw material and chosen supply model is Joint Economic Lot -Size ( n* integer) for all raw material , that block shoe anchor with raw material of SAPH 400 8,0 - 90 and got smallest expense together by 5 delivery times, and thrift counted 55.8% to used by company models, mounting support with raw material of SAPH 400 6,0 - 533 with supply total cost together by 5 delivery times; rill, and thrift counted 83.43 % to used company model’s, product of plate inner pressure with raw material of SAPH 400 3.2 - 545 with supply total cost by 5 delivery times; rill , and thrift counted 76.44 % to used company model’s and outer pressure plate with raw material of SAPH 400 3.2 - 615 with supply total cost by 4 delivery times; rill , and thrift counted 77.31 % to used company model’s.

KEYWORDS: Inventory, joint lot sized, economics value

1. Introduction

The competition in domestic manufacturer is very competitive one, this should be more stressing the competition itself which has non domestic entries manufacturer who has strategy to getting optimum profit in Indonesia. Dealing with this, one of the strategy is to leverage effectivity and efficiency in each of activity according to compress production and operational cost. The research client is a vendor of manufacturer otomotive component which is making of stamping products. This company produced a lot kind of products like slio-8 in part of Mitsubishi Colt Diesel series, Lid Comp Fuel Inlet in part of APV that produced by Indomobil Suzuki International, block shoe anchor, mounting support, plate pressure inner dan plate pressure outer which are part of Yamaha motorcycle. Stamping Plant division supplier company has purpose to leverage effectivity and efficiency at each of manufacturing activities. The problem is a lot of wasting time in production floor. Based on research report of GSPH (Grosss Struck Per Hour) that observed for 2 months indicated that 13% wasting time had made and it is 78 minutes per day. The main cause of it are there no systematic inventory planning, uncontrolled supply system, discontinuity production process, delay of delivery that effect of customer trust. The problems happened is how to compressed the costs related to inventory planning with considering raw of material suppliers. The goal of this research is assuming lot size production based on Joint Economic Lot Size model considered miniimizing joint cost supply.

T.G. Amran. / Int. J. Eng and Sci, Vol.3, No.4, 2012, 110 - 126110


2. Methodology and Material

A. Supply of System

Supply of system is mechanism of manage input related with supply to become output and needed feedback to meet acertain standard. This mechanism is made of a number of policy that monitoring supply level, assume stocks level, stocks loaded, and number of delivery. The system is designed to setup and make guarantee end product, process product, component and optimal raw material, optimal quantity and optimal time. The criteria of optimal are minimizing total cost related with supply which is inventory cost, delivery cost and less supply cost [2]. .

B. Supply of System Cost

Supply cost is all expense and loss that caused by supply. The cost is purchasing cost, order cost, setup cost, inventory cost and less supply cost [2].

1. Purchasing price is cost made to buy items, it is equivalent with price of buy. 2. Order cost is cost made to order to supplier but not influenced by number of ordered. 3. Set up cost is all expenses that caused in setup production. This cost would happened if the

item of supply made byself, not get from supplier.4. Inventory cost is cost made to keep/maintain material, semi finished product, sub assembly, or

finished product.

C. Model Joint Economic-Lot Size for Buyer and Seller

According to Avijit Banerjee [1], in the condition of tansaction, about price, lot size etc has mentioned along negotiation between buyer and seller. It depends on equilibirium, end of result in this negotiation could be closed to optimal for both or one of them (the other side is loss) or nor of them. The formula from Economic Lot Size (ELS) or Economic Order Quantity (EOQ) attached to Harris by Hadley and Within, it is known and used in concept of buying and inventory management. Since the beginning, the formula from ELS has been improved to get easier apllicated for any kind of conditition. Snyder showed validity of EOQ model with probabilistic demand; Jesse, Mitra and Cox among others, broadened application from EOQ based on condition that caused inflation. But the main problem with these approachment is a mistaken considering in economic in a whole ELS system for another problem. Example, the used condition of buying is the seller produced a few inventory system with gradually that ordered by buyers based on lot-for-lot. Besides the price, one of the important thing is precisely lot size. It is clear that ELS’s buyersin this item might wouldnt get optimal result for the seller or buyer. Traditionally, question of price, lot size, etc made by negotiation between each side. (Buffa give interesting discussion from structure power based in negotiation). The result of policy negotiation is coled to optimal or not optimal to one of side which is other side treatmened by substancial penalty; some of cases not optimal for both. Optimal policy could be adapted through cooperation that make profit for both. Maybe in the beginning, would involved a several purchasing cost for one of them, it might be over loss exchange from suitable of right price. If buyer in gradually order a several item, Q, an inventory item from seller. With acceptance from exist command, seller produced a few things that wanted from the item (example, seller follow lot-for-lot policy). In the deterministic, we can assumed there is no other buyer in this item and single seller. Figure 1 shows inventory planning time for both. Time, T, belongs to three components: t1

representative needed time to deliver product that ordered from production lot setup, t2 is real production time, and t3 is needed time to deliver all of lot to buyers.

T.G. Amran. / Int. J. Eng and Sci, Vol.3, No.4, 2012, 111


Fig 1 : Inventory Planning Time to purchaser’s and vendors

In the reality, it is more complicated. For example, in just-in-time (JIT), buyers can choose smaller lot size, and it is possible for them to looking another resources that can supply their requirements. Seller might be meet demands with decrease setup cost with technology. Another cases if one of the seller knowing there is no other counterpart, in this situation the supplier might be on the position to get the unconsidered profit. The next is effect of analyze from optimazion individual from buyers and vendors, this concept improved from JELS model and economic implication included. Here with simple calculation to figure the model and give a final description.

D. Effect of Independen Optimation

These is used notification:D = yearly demand or using from item inventoryP = yearly production price to the itemA = demand cost from buyerS = setup cost buyer per setupi/r = yearly inventory cost, description dollarCv = production unit cost by seller Cp = purchase unit cost by buyerQ = order or lot size production in unit

As mentioned above to simplify it can be assumed that inventory cost, i, has identic value to buyer and vendor. In ELS, buyer and vendor are relative simple and known. The result from optimization summarized in the table below:

Tab. 1 Summary from Relevant Cost and Individu Optimization PolicyDescription Purchaser Vendor

General Cost Function iCp

QQ

DAQTRCp2

)( (2-

1)

(2-4)

Economic Lot Size (2-2) (2-5)

Minimum Total Cost

(2-3)

(2-6)



ELS from each side result(2-1) or (2-5) on table 1 geeting by duplicate function of main cost ((2-1) or (2-5)) with Q equivalent with zero. And then yearly total relevant cost (TRC) for each side ((2-3) or (2-6)) result from substitution between (2-2) or (2-5) become (2-1) or (2-4). If ELS of buyer being adopted, than seller TRC is:

TRCv(Q )=

Knowns as

TRCv(Q ) = TRCv(Q ) (2-7)

Like mentioned before, to simplify, it can be assumed that i (inventory cost), declared as Rupiah, has a same value even for buyer and vendor. In fact, inventory cost for both might be different. But this assumption not take a loss for generally. If buyer and seller inventory cost declared by ip and iv,in order have different value, parameter β has general definition which is DrvCv/PrpCp and main result that produced here cannot be exchange. The description from α and β can help description and comprehent practice implication from several condition that connected with these parameters. If α = S/A, than, α represented the ration from vendor setup cost for each setup (S) with buyer order cost (A). and, (2-1) to table 2-1, buyer setup cost each year is DA/Q and from (2-4) setup total cost every year is DS/Q. It is known that (DS/Q)/(DA/Q) = S/A = α. In other words α as a ratio from total setup cost of buyer every year (or every period) to buyer order cosr each of year (or every period) to each of lot size given. Because of that when vendor setup cost more than buyer order cost , α consider to inline and also right versa. The same thing is inventory total cost from (2-4) is DQiCv/2P and from (2-1) inventory total cost is QiCp/2. The common happened, if rv ≠ rp,(DQivCv/2P)/(QrpCp/2) = DivCv/PipCp = β

If iv = ip, DCv/PCp = β. Thats why β represented ratio of yearly inventory total cost (or every period) to yearly inventory total cost to each of lot size given. Noticed if vendor’s production value, P, more than deman price level D, β consider relative small. Practice is , price of vendor’s production is high because vendor need some time shorter to produce lot size given (example, interval t2 in figure 1 consider smaller). As a result, vendor’s inventory total cost consider lower and consequent, the value relative lower to β. Parameter β can be lower if vendor’s inventory unit cost (or variable of production) lower than buyer inventory cost (or purchasing). So, it is worthed to predict that value of production is high than the demand and/or inventory cost relative higher at buyer consider lower from β and right versa.

E. Effect From Vendor’s ELS to Buyer

For instance ELS of vendor is a number of order quantity, than with substitute result from calculation (2-5-5) to (2-5-1), we’ll have TRC of buyer is:

TRCp(Q ) = [1/2 (α + β) / (αβ) TRCp(Q ) (2-8)



From (2-2) and (2-5) and definition from α and β, can be show that:

Q = (2-9)

And from (2-3) and (2-6)

TRCv(Q = TRCp(Q ) (2-10)

If α > β , when fix cost of both more than ratio of inventory cost, Qp < Qv. Another words, if ordered cost relative lower and inventory cost relative higher, Q < Q (ELS vendor). In this condition, adopted ELS vendor to pushed buyer to order a big number with time frequent more less , and than could leverage inventory average and yearly total cost.Another parts, α < β telling that order cost relative higher and inventory cost relative lower, which is it could be happened. In this case Q (ELS purchaser) more than Q (ELS vendor). If ELS vendor being adopted, buyer would be pushed to order a small number with more often frequent, so it could leverage order each year like also increasing total cost. In general condition, if the different bertween α and β bigger, adopted ELS from both replaced other part that far away from their optimal position, and finally increase their penalty. Besides, if the difference between α and β smaller, optimal position from buyer and vendor (related with each of lot size cost) become closer. If α = β (for example, when there were the different at fixed cost of both replaced with the different that same happened at inventory cost in the same direction), lot optimal size is the same. Of course, in the condition that adopted ELS, one of part is wouldnt get penalty for the other part.Theoritically, when α = β could get different situation. Value from β closing unity (0< β ≤ 1) that could tell for vendor production value is approaching demand and also inventory unit cost at vendor and purchaser is the same. Some of cases, when α = β could be closer if vendor fixed cost in every setup is the same with buyer fixed cost each of order. Another part, if β more smaller than 1, the above condition is approached if order cost more than vendor setup cost. In practice, adopted one of a policy would replace other part in the negative situation. From (2-47), eventhough α and β is the same with minimum value of TRC vendor and minimum value of TRC buyer not always the same (unless, αβ =1). If β ≤ 1, αβ =1 could tell α ≥ 1. Herewith, to leverage vendor fixed cost balanced with inventory cost per unit that relative lower and/or value of productionthat high rather than the demand, TRC as a result from a policy that optimal closing the purchaser. In other words, when αβ = 1 indicated that each of unbalanced fixed cost that have to both can be replaced with unbalanced inventory cost in the reverse direction.In this case, their TRC (which is the result from each of their optimal policy) has a real the same value. In fact, things like this more often happened rather than situation which is lot size of both didnt same.

F. Model Joint Economic-Lot-Size

Above has mentioned a weakness from each counterpart if adopting one of ELS. In this chapter would have a description about model JELS for the first time. To purchaser and vendor joint TRC (JTRC) for each of lot size y, Q produced with adding (2-1) and (2-2), shown like this :

JTRC(Q) = D/Q (S+A) + Q/2r (D/P Cv + Cp) (2-11)



With follow controlling function of cost that before is Q = Q , we get JELS:

Q = (2-12)

With substitute Q to (2-48) than JTRC minimum per year is:

JTRC(Q ) = (2-13)

Calculation (2-49) can be rewrite become:

Q = Q . (2-14)

Also, from (2-9) and (2-11)

Q = Q (2-15)

With the same way, could be shown that:

JTRC(Q ) = TRCp(Q (2-16) And JTRC(Q ) = TRCv(Q ) (2-17) .

The calculation (2-11) and (2-12) above showed the connection between JELS and ELS from purchaser and vendor. Formula (2-15) and (2-16), in other words shows relationship between JTRC optimal and optimal total cost. Testing (2-13) and (2-14), very clear if α = β, Q = Q = Q . Another side, if α > β, Q < Q < Q ; if α < β, Q < Q < Q . Than, JELS represented compromise between ELS purchaser and ELS vendor when the values not the same. This is maybe unbalance that needed like compromise, a lot of cases, with a goal to decrease JTRC. Adopted TELS, with assesment price, could get a benefit for both. JTRC purchaser and vendor with optimal policy could have it, if ELS purchaser adopted, JTRC could be seen

JTRC (Q ) = [1+1/2(α + β)] TRCp (Q ) (2-18)

That have it from (2-7) and (2-10). With the same way, using relation (2-45) and (2-47), JTRC to adopt ELS vendor is

TJRC (Q ) = [1+1/2(1/α + 1/β)] TRCv (Q ) ........... (2-19)

For make sure economic consequent of individu if adopt JELS, we need to get TRC buyer and vendort who could get the result. Substituting result (2-13) become (2-1) and (2-14) to (2-4), in order could get:

JTRCp(Q ) = TRCp(Q ) (2-20)



and JTRCv(Q ) = TRCv(Q (2-21)

G. Model Joint Economic-Lot Size for Purchaser and Vendor

As described by S K.Goyal (1988), the assumption from lot for lot policy is basic. This is possible for vendor to produce in a lot and distributed a few times delivering for purchaser. That way a number of the ordered for purchaser is Q, and a quantity of production from vendor in a lot is Qn where n is a repetitive number of delivering. Especially value from n, EOQ for purchaser and total cost of supply can get it from :

(2-22)

JTRC (n) = (2-23)

Economic value from n=n* get when

Z(n*) ≤ Z(n*- . (2-25)

Dan Z(n*) ≤ Z(n*-1) (2-26)

With substituting (2-23),we’ll get

(2-27)

With substituting (2-24),we get

(2-28)

And combined (2-24) dan (2-25) :

(2-29)

EOQ purchaser ,Q(n*), get it from exchange n with n* from (2-21). And quantity of a lot for vendor with times n* with Q(n*). And total minimum cost of supply got from (2-22) with axchange value n with n* .



Total cost of supply for purchaser and vendor is

(2-30)

(2-31)

(2-32)

Fig. 2. Research Methodology



3. THE RESULT AND ANALYSIS

A. Inventory Model Economic Lot Size Block Shoe Anchor

D = Annual Demand = 169777 unitP = Speed of production vendor = 1200000 unit/yearA = order cost = Rp 5000S = setup cost = Rp 125000i = holding cost percent = 5%Cv = raw material cost from vendor = Rp 2210Cp = selling price perunit buyer = Rp 5210

A.1. General Economic Lot Size ( known model )

1. Find Q, with:

Find inventory cost for purchaser with :

2. Find inventory cost for vendor with (2-41) :

3. Find Total Joint Inventory cost :JTRC = TRCp(Q) + TRCv(Q)JTRC = Rp 5.548.460,9 + Rp 831.775,92JTRC = Rp 6.380.236,8



A.2. Economic Lot Size Model Based on purchaser

1. Find Q optimal for ADW with formula :

2. Find inventory cost for ADW with Qp* = 2553, with formula :TRCp (Qp*) = =

=Rp 665.033.1458

3. Find inventory cost for Star Poly with Qp* = 2553 with formula (2-44) :

TRCv(Q ) = TRCv(Q )

With change α become S/A and β= D.Cv/P.Cp :

TRCv(Qp*) = Rp 8.332.869.953

4. Find total joint annual inventory costwith Qp= 2553 unit is adding quantity result :Inventory total cost with Qp :JTRC(Qp*) = TRCp(Qp) + TRCv(Qp)= Rp 665.033.1458 + Rp 8.332.869.953=Rp 8.997.903,099

A.3.Economic Lot Size Model Based on vendor

1. Find Q optimal for Star Poly with formula :

2. Find inventory cost for Star Poly with Qv*=52106,with formula :



TRCv (Qv*)

= Rp 814.590.565

3. Find inventory cost for ADW with Qv* = 52106,with formula :TRCp(Q ) = [1/2 (α + β) / (αβ) TRCp(Q )

With change α become S/A and β= D.Cv/P.Cp, and by getting TRCp(Qp) ,than we have:

TRCp(Qv) = Rp 6.802.969,438

4. Find total joint annual inventory costwith Qv*= 52106 unit is adding result :Inventory total cost with Qv :

JTRC(Qv*) = TRCp(Qv*) + TRCv(Qv*) = Rp 6.802.969,438+ Rp Rp 814.590.565= Rp 7.617.560,003

A.4.Joint Economic Lot Size Model

1. Find Q joint with formula :

2. Find total joint annual inventory cost with Qj*=12644 unit, using formula :

JTRC(Q ) =



JTRC(Qj) = Rp 3.491.288,632

3. Find inventory cost for ADW with Qj*=12644 using formula :

JTRCp(Q ) = TRCp(Q )

With change α become S/A and β= D.Cv/P.Cp, and getting TRCp(Qp) ,than we have :

JTRCp(Qj*) = Rp1.713.952,765

4. Find inventory cost for Star Poly with Qj*=12644 using formula :

JTRCv(Q ) = TRCv(Q )

With change α become S/A and β= D.Cv/P.Cp, and getting TRCv(Qv) , than we have :

JTRCv(Qj*) = Rp 1.777.335,867Or with substraction :JTRCv(Qj*) = JTRC(Qj*)-JTRCp(Qj)= Rp 3.491.288,632- Rp1.713.952,765



= Rp 1.777.335,867

A. 5. Joint Economic Lot Size (n* integer) Model

1. Find n* using formula :

With change n from (1- ~), value of n* that suitable , acquired

5(5+1) ≥29.73037≥ 5(5-1)30≥ 29.73037 ≥ 20,

n*=5 can be used because limit up and downthat relevant n*= 6 than :

6(6+1) ≥29.73037≥ 6(6-1)42 ≥ 29.73037 ≥ 30,

n*=6 cannot be used becauseunrelevant limit up and down2. Value of n*=5 is precisely value and then find Q(n*) with change variable n=n* than ADW order

size’s:Change variable n=n*

3. Find Q or Star Poly lot size with times Q(n*) with n*:Q = Q(n*) x n*

= 3613 * 5= 18065

4. Find JTRC using formula : substitute n=n* than :JTRC (n*) =



JTRC(n*)=

JTRC (n*) = JTRC (n*) = Rp 2.819.994.662

5. Find TRCp (Q(n*)) using formula :

TRCp(Q(n*)) = Rp 705.546,1977

6. Find TRCv (Q(n*)) using formula :

TRCv (Q(n*)) = JTRC(Q(n*)) – TRCp(Q(n*)) = Rp 2.819.999,489 – Rp 705.546.1977 = Rp 2.114.448,5

With the same way we would made Inventory Planning Model Economic Lot Size Mounting support, Plate Pressure Inner, Plate Pressure Outer, Block Shoe Anchor

Tab. 2: Comparable Inventory Total Cost Block Shoe Anchor

Description

General Economic Lot size

ADW Economic

Lot Size Qp*

Starpolly Economic

Lot Size Qv*Model

Qj*Model

Qj*(n*)ADW order size (unit) 42445 2553 52106 12644 3613Starpolly Lot Size (unit) 42445 2553 52106 12644 18065Purchaser’s Annual Cost (Rupiah) 5548460.897 665033.1458 6802969 1713952.76 705546Vendor’s Annual Cost (Rupiah) 831775.9219 8332869.953 814590.6 1777335.87 2114448Total Joint Annual Cost (Rupiah) 6380236.819 8997903.099 7617560 3491288.63 2819995

As shown on table 2 above using inventory model Q(n*), Total Joint Annual Cost is smaller than others models. In this model for one lot ordered, supplier do delivering for 5 times or n*=5.

Analysis Comparable Method Joint Cost Economic Lot-Size Model to Mounting Support

Processing data to find inventory model with smallest inventory cost for mounting support product with raw material SAPH 400 6,0 -533, enhanced to the model that uised by company (general model) and 4 inisiative model with using same data’s which israw material requirement is 940949



unit, speed of production from starpolly 1200000 unit, cost per ordered 5000 rupiah , setup cost from starpolly 125000 rupiah, raw material price 2765 rupiah, selling price 7019 rupiah ,interest 5% and average of annual raw material demand is 4 times. To be found result Total Joint Annual Cost in each of model

Table 3: Comparable Inventory Total Cost Plate Pressure Inner

Description


ADW Economic

Lot Size Qp*

Starpolly Economic Lot Size

Qv*Model

Qj*Model

Qj*(n*)ADW order size (unit) 235238 5178 46575 23077 6248Starpolly Lot Size (unit) 235238 5178 46575 23077 31240Purchaser’s Annual Cost (Rupiah) 41298387.99 1817212.292 8273701 4253286.32 1849367.96Vendor’s Annual Cost (Rupiah) 13255117.03 22995915.08 5050758 6348097.34 7187098.683Total Joint Annual Cost (Rupiah) 54553505.01 24813127.37 13324459 10601383.7 9036466.643

As shown on table 3 above with inventory model Q*(n*), total joint annual cost is smaller than others models. In this model for one lot ordered, supplier do delivering for 5 times or n*=5.

Analysis Comparable Method Joint Cost Economic Lot-Size Model to Plate Pressure Inner

Processing data to find inventory model with smallest inventory cost for plate pressure inner product with raw material SAPH 400 3.2 -545, enhanced with the model that company used (general model) and 4 inisiative model with using same data’s which is raw material requirement is 1127320 unit, speed of production from starpolly 1200000 unit, cost per ordered 5000 rupiah, setup cost from starpolly 125000 rupiah, raw material price 1030 rupiah, selling price of product 2750 rupiah, interest 5% and average of raw material demand is 4 times. Than, we obtained result of total joint annual cost in each model:

Table 4: Comparable of Inventory Total Cost Plate Pressure Inner

Description


ADW Economic Lot Size

Qp*

Starpolly Economic Lot Size

Qv*Model

Qj*Model

Qj*(n*)ADW order size (unit) 281830 9055 76324 39710 10750Starpolly Lot Size (unit) 281830 9055 76324 39710 53750Purchaser’s Annual Cost (Rupiah) 19395812.5 1245016.064 5321077 2871965.52 1263397Vendor’s Annual Cost (Rupiah) 7317582.781 15781736.78 3692583 4509244.56 5029159Total Joint Annual Cost (Rupiah) 26713395.28 17026752.84 9013659 7381210.08 6292556

As shown table 4 above with using inventory model Q*(n*), total joint annual cost is smaller than others models. In this model for one lot ordered, supplier do delivering for 5 times or n*=5.



Analysis method Joint Cost Economic Lot-Size Model to Plate Pressure Outer

Processing data for looking inventory model with the smallest cost for plate pressure outer product with the raw material SAPH 400 3.2 -615, executed to model that used by company (general model) and 4 inisiative model with using the same data which is requirement of raw material is 1127320 unit, speed of production from starpolly is 1200000 unit, cost per ordered 5000 rupiah , setup cost starpolly is 125000 rupiahs, raw material cost is 1267 rupiah, selling price product is 3044 rupiah, bank of rate is 5% and average of raw material demand annualy is 4 times . So, we would get result total joint annual costin every model is:

Tab. 5: Comparable of Inventory Total Cost Plate Pressure Outer

Description


ADW Economic

Lot Size Qp*

Starpolly Economic Lot

Size Qv*Model

Qj*Model

Qj*(n*)ADW order size (unit) 281830 8607 68816 37209 11868Starpolly Lot Size (unit) 281830 8607 68816 37209 47472Purchaser’s Annual Cost (Rupiah) 21467263 1309878.254 5318781 2983018.26 1378096Vendor’s Annual Cost (Rupiah) 8886288.721 16629571.86 4095434 4894404.39 5508741Total Joint Annual Cost (Rupiah) 30353551.72 17939450.11 9414215 7877422.65 6886837

As shown in table 5 that using inventory model Qj*(n*), total joint annual cost is smaller than others models. In this model for one lot ordered , supplier do delivering for 4 times or n*=4

CONCLUSION

Using of model joint economic lot size with n* integer makek the result supply cost be the smallest than 4 model that used as inisiative and also to model that used by company for right now which is for block shoe anchor with Q = 18065 with 5 times delivery, total cost of supply together is Rp2.819.995, and to save 55.8% with the model that used by company, for mounting support with Q = 31240 with 5 times delivery, total cost of supply is Rp 9.036.466,643 and to save 83.43% with the model that used by company. Second, for plate pressure inner with Q = 53750 with 5 times delivery, total cost of supply is Rp 6.292..556 and to save 76.44% with the model that used by company. And the third, for plate pressure outer with Q = 47472 with 4 times delivery, total cost of supply is Rp 6.886.837 and to save 77,31% with the model that used by company, thats why this model is an inisiative supply of model as inventory planning model for the next year.

REFERENCES

[1]. Banerjee,Avijit,(1986).A Joint Economic -Lot-Size Model For Purchaser And Vendor. Decision Sciences.17; 292-311.

[2]. Baroto,Teguh,(2002).Planning and Control Produce. Ghalia Indonesia.Jakarta



[3]. Goyal,S.K,(1988). A Joint Economic-Lot-Size Model For Purchaser And Vendor:A Comment. Decision Sciences.19;236-241

[4]. Makridakis,Spyrof, Steven C. Whellwryght,danVictor E.McGee, (1992). Forecasting Application And Method Bind One. Second Edition. PT.Erlangga. Jakarta

[5]. Makridakis,Spyrof,Steven C. Whellwright , dan Victor E.McGee, 1994). Method of Forecasting For the Application Management. Second Edition. PT.Erlangga. Jakarta

[6]. Saputri,Desi Ayu, (2006). Proposal of Production Planning And Planning of Requirement of Raw Material of PT.SUCOFINDO Adiusaha. Trisakti University.Jakarta

[7]. Saraswati,Docki,Sumiharni Batubara, Inten Tedjaasih, (1998). Planning And Control Produce. Jakarta: Industrial Engineering, Trisakti University.


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