Multi-item Location Inventory Models

Evren Sarınalbant

Contents

Facility location models Location-inventory models Multi-item concept Integration of multi item to L-I Conclusion

Facility Location Models

Models considering location of new facilities subject to transportation costs

Most basic form of location problems Minimize the total distance between new

facility and the existing ones

Facility Location Models

F1

F2

F6

F5

F3

F4

New Facility

Facility Location Models

Distance calculations• Rectilinear distance

• Euclidian distance

Location-allocation models determine which existing locations will be served by the new facility

Facility Location Models

Location on networks aims to locate one or more facilities on a network

Networks consist of predetermined candidate points and/or the routes between them

(Nahmias 2001)

Location Inventory Models

An extension of location allocation models

Integrate:• Fixed cost of opening a new facility

• Transportation costs

Location Inventory Models

• Cost of holding safety stock

Generally, location of distribution centers in a three-tiered supply chain

Determining optimal number,location of DCs and the allocation of retailers to these DCs for single product

Location Inventory Models

Location Inventory Models

Why Location Inventory?Importance of logistics has enhanced

Companies aim to reduce transportation and inventory costs to gain competitiveness

Centralization is proved to be cost effective (Eppen 1979)

Customer responsiveness affects the market share of the firms

Location Inventory Models

Location-allocation models come up with intuitively suboptimized solutions since inventory costs are not considered

Inventory control sytems are used after the design of supply chain. Lee and Billington (1992) underlined that a common pitfall in SCM is the seperation of supply chain design from operational decisions

Location Inventory Models

Relevant literature studies on L-I

Nozick and Turnquist (1998) considered integration of inventory impacts into a fixed-charge model for locating DCs. They calculated inventory levels and stockout rates for multiple DCs in order to catch a linear trend. Then, incorporated these impacts into the model.

Location Inventory Models

Erlebacher and Meller (1999) constructed a location inventory model. Their model is a detailed one consisting of fixed costs of opening DC, inventory cost of single item (safety stock) and transportation costs. They use squared Euclidian distance metric. They determine the optimal number and locations of DCs by using some heuristics

Location Inventory Models

Daskin et al (2002) constructed an inventory location model which determines the optimal locations of DCs from a set of candidate points and solved by using Lagrangian relaxation embedded in branch&bound

Multi Item Concept

In recent years, it is realized that road to survival passes through variability.

Therefore, inventory control in a multi-item environment became more important to achieve a good customer responsiveness and reduction in costs

Multi Item Concept

In the location-inventory models constructed upto now, single-item inventories were considered.

However, in design of supply chains, multi-item systems are frequently encountered. The issues that may affect the design of system in multi-item environments are:

Multi Item Concept

Intercorrelated product demands, meaning an increase in demand of one product can increase or decrease the demand of others (positive-negative correlation)

Ex: Demand of harddisk drives affects the demand of mainboards (positive correlation)

Ex: Demand of CD-writers affects the demand of large size harddisks (negative correlation)

Multi Item Concept

Hausman et al (1997) considered multi item inventory systems and analyzed joint-demand fulfillment probability with respect to correlated demands of items.They used a multivariate normal distribution for the demands and done a probabilistic analysis for no stockouts to determine order-up-to level for each item

Multi Item Concept

Autocorrelation, meaning demand of an item in one period can affect the other period

Ex: In durable goods sector, high demand in one period may cause it to decrease in the next period

Priority of items, some items may be more important for distributor. (more profit margin, more sensitive customers)

Multi Item Concept

The holding and shortage costs may change from item to item. The penalties which are incurred by shortage of particular items may be larger than the other. (because of supply contracts)

Some items need to be kept under special conditions, so that they can affect the location of DC.

Integration of Multi-item with L-I

By looking at the previous information, it is beneficial to design the supply chain by using location inventory models considering multiple items.

In order to accomplish this, one must integrate demands of these items into the objective function

Integration of Multi-item with L-I

The problem is constructing a model which incorporates multi-item inventory costs and the factors that may affect the optimal location of DCs in a supply chain where supplier’s and retailers’ locations are known and fixed.

Integration of Multi-item with L-I

In the study of Daskin et al,

Integration of Multi-item with L-I

Integration of Multi-item with L-I

In order to reach to multiple item case, a multivariate normal distribution can be applied for each item demand by the help of the study done by Hausman et al.

Conclusion

Location-inventory models has taken attention in OR recently.

Therefore, there are few papers in the literature which analyzed this issue.

After my literature search, there seems to be no studies on multi-item location inventory

A detailed analysis should be done on this subject

Questions&Comments