**Why not use exponential advances in Technology and Computing power**

Traditional Inventory Optimization (IO) and Multi Echeleon Inventory Optimization (MEIO) algorithms identify cost savings opportunity based entirely on Inventory stored at specific locations. Essentially, the algorithm aggregates inventory of SKU/Product group for that location.

While it still generates value, a big gap remains. Such decisions may impact the optimality of warehouse operations. Reduction in storage inventory of a product group may mean frequent replenishments from stoage to picking area, thereby increasing operating cost or increasing probability of late or missed deliveries to the customers, as shown in the illustration below.

One of the handicaps of not making IO or MEIO more granular was the solver run time that these models usually take to run. I believe we are well positioned now to start experimenting adding more granularity to the concept.

While developing a Deep Learning based Warehouse planning algorithm at my current employer, we developed an underlying foundation optimization model that takes the concept of Inventory optimization all the way to the shop floor.

This model, takes Inventory Optimization to a whole another level of granularity. It essentially manages the Inventory in the picking area and picking process optimally, thereby minimizing total picking area warehouse optimization cost.

**The Picking Process**

Before we jump into the model structure, we will walk through the generic picking process at a high level so as to better understand the nuances of the model.

**Storage to picking**

The process of supplying is carried out in a frequent way but not for the same reference, the moment a product is about to go out of stock or has been completely out of stock, it proceeds to request the transport of the storage using a forklift from the corresponding rack to be supplied with the shelves of picking.

**Fulfillment request**

Once any of the points of a sale send the record of the sales made of any product, a request of supply of that specific SKU (Stock Keeping Unit) arrives, as well as the quantity.

### Pickup Request

This data is registered in the technology platform of the pickers indicating this information to supply this product at the specific point of sale; by using a container which will have the products requested by a store, the operator proceeds to collect these items.

### Pickupt to loading

When the container is ready, the process of labeling is carried out with the supplied information about the products, as well as the destination, they are then taken to the loading area, where they will be waiting to be transported to the different points distributed in different cities of the country.

## Model Structure

**Decision Variables**

**Ii**On hand inventory for SKU i.**Qi**Optimal order quantity for SKU i.

**Parameters**

**Ci**Maximum warehouse capacity for SKU i**Csi**Cost of maintaining a unit in stock of SKU i**Cpi**Cost of ordering a storage unit of SKU i**Li**Inbound Transportation lead time of the SKU i**Iii**The begining inventory of SKU i in the picking area**Di**Daily demand for SKU i**SSi**Safety stock of SKU i

### Objective function:

Minimize the total cost of the organization during planning horizon, in this case, it is one day.

### Constraints:

* The productivity of the workforce:* The productivity of the workforce is defined as the relationship between time, work time, delivery time, and the number of units ordered. The working day is 8 hours daily.

* Inventory:* The inventory of the reference I must be equal to the inventory in the immediately previous period, plus the order size made in that period, minus the required amount, and minus the inventory that must remain in stock, in order to guarantee the production flow.

* Picking capacity:* The number of daily units in inventory cannot exceed the capacity of the picking area.

* Security stock:* The daily units in the inventory of reference, cannot be less than the security stock.

* Constrain positive:* Ensure that the variables take positive values.

**Scope of experiment**

We tried this algorithm in collaboration with one of the largest manufacturer of herbal products in India. The manufacturer manufactures 8000+ unique SKUs and has 25+ owned DCs across India. The products chosen for this research are primarily herbal products that do not require a medical prescription, personal care products, beauty, and baby care products. The data obtained was the result of the collection of information during fieldwork in January 2020.

**Stages of Model formulation**

The construction of the model went through several stages; these are described in detail below:

**Stage 1:** Gathering the necessary information for the implementation of the model correctly as historical demand, in-place inventory for each reference, storage capacity in picking and distance from the stock storage area to the corresponding picking storage area.

The most challenging aspect of developing the model was, as always, not model development but getting our hands on extremely granular data pertaining to warehouse operations, much of it was not available. We had to perform additional analysis and shop floor time studies to extract the data needed.

Some examples of challenging data points are in the appendix

**Stage 2:** Based on the data found, we proceed to determine:

- the costs of maintaining the units in inventory,
- of making an order and the waiting time to supply, and
- the lead time of the product, with which we proceeded to calculate the minimum security stock to have a 95% service level.

**Stage 3:** Through **linear programming**, a supply planning model was built, with the Solver tool in which the decision variables were established such as the optimal quantity of inventory, order size, restrictions of maximum inventory capacity, productivity and minimum level of inventory whose objective is to minimize the costs of the operation of supply and storage in picking.

**Ii:**in the inventory of each SKU**Optimal on hand units****Qi:**size for each SKU**Optimal order****SSi:**, the minimum level of inventory that allows meeting the customer’s demand with a service level of 95%. A value of k and d of 1.64 for a normal distribution corresponds to this percentage.**Safety Stock****Li:**is the time that elapses between the order being placed and the delivery of the order.**Lead time****Restriction on Inventory:**This restriction guarantees that the customer’s demand is 100% satisfied.**Restriction on Capacity:**This restriction ensures that the units in the inventory do not exceed the maximum capacity of the distribution center.**Restriction on productivity**: With this restriction, it is ensured that the productivity goals will be met within the available times of the working day.

## Appendix: Sample list of required data points (Challenging data points highlighted)

**ABC:** Classification of products in categories ABC according to the rotation of the said reference. Code: «Article code» or «Reference number».

**Product Location:** Coordinates of the product location in the distribution center as its respective one; sector, hall, level, rack, and position.

**Sector:** Zone of the warehouse to which it belongs.

**Hall:** Hall in which the shelf is located.

**Level:** Level of the rack in which it is found numbered from 1 which is the closest to the ground.

**Rack:** Subdivision of the shelf where it is located

**Position:** Specific position of the product inside the cubicle

**BUO:** Basic ordering unit.

**Available:** Units of the product in the storage area.

**Demand:** Units demanded by the client; information of its historical data granted by the company.

**Daily demand +desviation:** It is equivalent to the daily demand summation of said reference plus the deviation of that demand.

**Daily demand destivation:** It is the deviation of the daily demand for that product.

**Reorder:** This point indicates when the order must be placed either in hours or days of optimal inventory using the tool Solver = Ii/Di

**Order:** Q Is the optimal order size for each reference, this value is extracted from running the optimal supply model by means of the solver tool. To this item belong the following four columns: Hour, Days, Q, and shelving. Q = Qi

**Hour:** Duration of inventory in stock in hours. = Inventory on hand units/(Demand + Deviation units/8 (hr))

**Days:** Duration of the inventory in stock in days

**Q:** Corresponds to the optimal order size for each reference. This value is extracted from the execution of the optimal supply model by means of the Solver tool.

**Shelving:** Round the order size Q, according to the multiple of the BUO.

**Available/Hour inventory:** Equivalent to the product among the reference units on the shelf for the hours of inventory on shelving = Available x Hour/Shelving

**Demand/Hour inventory:** It is equivalent to the product between the daily demand and the deviation from the reference for the hours of duration of the inventory on shelving, all the above about 8 hours a day of the working day = ((Daily demand + deviation x hour)/Shelving)/8

**Horizon:** In this, the working days of the week are divided into 4-time slots of three hours each, and the units in stock are calculated with the following conditional equation.

AV/Hours <= Reorder (Hours); Order ( hours) + AV/Hours -(Demand x3)

AV/Hours >= Reorder (Hours) ; AV/Hours -(Demand x3)

**Logistic operator direct workforce cost:** It has one operator.

= 1 hour X INR 65hour

**Forklift cost:** It has one machine. = 1 hour x inr 249/hour

**Ordering cost:** It has one machine and one operator = 1 hour x inr 371/hour