An Application of SLA in Small Business Sectors with Multi Item Inventory Management.

Lateral transshipment plays an important role in inventory management. As the extension the service level adjustment (SLA) which combines preventive lateral transshipment with emergency lateral transshipment, increase the system performance level and decrease the total cost of the system in small business sector. At finally we give a numerical study of multi item small business sector, we examine SLA will be more effective in multi item small business sectors.

: Lateral transshipment in supply chain lateral transshipment replenishment Symbols and Notations:  AP(t)-Adjustment period  i,j,k is an indices indicates retailer i,j, and k  I,J,K is a set of retailers with J is a set of retailer with more stock than desired ,J ∁ ,K is a set of retailer with less stock than desired ,K ∁ ,J∩ =∅  NRnumber of retailers  RPreview period  Llead time for lateral transshipment from a supplier to the retailer

Retailer-3
Retailer-n  DE i (t)demand of the retailer i at time t  DE i,AP(t) (t)demand of the retailer during the adjustment period AP(t)  m(DE i,AP(t) (t))mean of the retailer during the adjustment period AP(t)  (DE i,AP(t) (t))standard deviation of the retailer during the adjustment period AP(t)  i (t)order quantity of the retailer i at the end of the period  i (t)inventory of the retailer i at time t  i (t)on hand inventory of retailer i at time t  i (t) -Stock out of retailer i at time t  i (t) -quantity back order of retailer i at time t  i,AP(t)service level adjustment period of retailer i at time t  holding cost of any retailer per unit stock  PCpenalty cost of any retailer per unit stock  TPC-transportation cost of any retailer per unit  ORC-ordering cost of any retailer per unit stock  LTRS i (t)-quantity for lateral transshipment that retailer i can take from other retailer at the end of period t  LTERS i (t)-required quantity for lateral transshipment except ONH i (t) from transshipment target stock level for retailer i at the end of period t  AQS i (t)available quantity to supply at period t  Int(.)function that return integer values  αservice level of SLAP in upperorder fulfilled from stock  βservice level of SLAP in targetorder fulfilled from on hand inventory  γ -service level of SLAP in lowerorder fulfilled from lateral transshipment  φ(.)denotes probability density function of normal distribution with mean 0 and S.D 1  QX jkquantity of lateral transshipment from retailer j to k at the end of period t  Te jktdecision variable takes the value 1 if lateral transshipment is performed between j and k at period t.

Research Method:
The study is related to the retailer who having better understanding and is ready to increase their service level. The retailer will vary with their demand and independent to the other retailer. Normally retailers are located much closer to each other than their supplier. The retailer follows ordered up to policy (R, S) at the end of each period the retailers must place an order to increase their inventory. Table 1 gives the values to find order up to level. The lead time is too short for the lateral transshipment while compare with the original lead time with the supplier. Each retailer is focus on multi item. In this study we propose service level adjustment for small business sector that uses the SLAP based on the concept of safety stock. As we consider in our study with multi item inventory in a small business environment. We use a periodic review policy on each item. Since in a multi item inventory model each item carries random demand and hence all items are kept under identical conditions and use periodic review policy. Spare parts inventories supply chain consist of multiple local ware houses and one are few central warehouses. Since the technology is improved today even the small business environment also keeps their inventory in systems. If they doing by periodic review policy they can easily cocoordinating by SLA.

]
Where AP(t)= A -t The study will relax the implementation of inventory control method in previous. Assume that there are 3 types of retailer in an echelon at the end of period t. Let J is a set of retailer having high stock level to meet customer's demand. Similarly K be a set of retailer having low stock level at a given time t. In calculation find the on hand inventory and backordering by the following equalities ONHi(t)= ONHi(t-1) -DE i (t)

→ A Int (A) < ONHi(t)-BAO i (t)
Find the Set of retailer K that satisfies m i (AP(t))+ z σ i (AP(t))+0.5 → B Int(B) ≥ ONH i (t)-BAO i (t) If set J and K exist then find the quantity for lateral transshipment in the given period t by LTERS j (t) = max{int{m j (RP(t) + z σ j (RP(t)) + 0.5} , 0}-(ONH j (t) -BAO j (t) ) , j∈ J If AP(t)=0 then LTERS j (t)=0 LTRS k (t) = ONH k (t) -max{int{m k (AP(t) + z α σ k (AP(t)) + 0.5} , 0}, k∈ K If AP(t)=0 then LTRS k (t)=0 To adjust the required quantity between retailer j to k use the following expression AQS j (t) = int (BAO j (t).∑ LTRS k (t))/ Σ BAO j (t) Now the transshipment process is completed calculate the no of quantity transshipped and update the current stock of retailer j and k as follows QX k,j (t) = min[max(AQS j (t)) , max(LTRS k (t)))] Now LTERS j (t) -QX k,j (t)→LTERS j (t), for jϵJ LTRS k (t) + QX k,j (t)→LTRS k (t), for kϵK The service level adjustment analysis in the current period is completed. The total cost of the system is given by C total = Σ t { Σ i (h.ONH i (t) +v.BAO i (t)) + Σ k Σ j (a.QX k,j (t)+c.Te k,j (t))}

Numerical Study:
The demand is normally distributed and we assume the SLAP is divided into 3 levels α, β, γ. When α denotes upper level of Adjustment period and β denotes the target level of Adjustment period finally γ denotes the lower level of Adjustment period. All must satisfies the condition that γ<β ≤ α, 0<γ, α<1. Let us fix the upper level between 0.6 to 0.8, target level as 0.4 to 0.6 and for the lower level 0.1 to 0.3. Table 2 gives the average and standard deviation of the 5 retailers.  Table: 2 mean and standard deviation of retailers By applying the calculation the quantity shipped from retailer 2 to retailer 3 is 4. And the total cost is ensured by the system is $1, 20,000. If SLA is not used among the Echelon the system is ensured with the total cost of $1, 34,000. This is depicted by figure 2. In this study we derive the Service level adjustment analysis in inventory systems. This was evaluated in small business sector with multi item. In numerical study , this is clear that the total cost of the system if it follows SLA is $1, 20,000, and the total cost of the system if it does not follows SLA is $1, 34,000. Hence the system saves by $14, 000 per period. This study finally shows that even in a small business sector SLA can be