Posted: June 18th, 2021

Inventory management

I’m stuck with proposing an LP model for this problem can u please walk me through developing the model “formulas for this”
A Retailer is facing the following yearly deterministic (demand are known in advance) demand for a given product sold a price of p=30 $/unit. 

Month       1     2   3      4     5   6     7   8      9  10      11 12   
Demand   120 65  220 10   0  150  60 100  0   200   50   20 

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The retailer is making the replenishment from a local supplier who sells the items at a per-unit cost of c=20$. Moreover, whenever the retailer makes an order from the supplier, he should pay a fixed transportation cost of 100 $ ( regardless of the quantity carried). 
❑In addition to the purchasing cost and transportation cost, the store is also carrying a holding cost of h=0.20$/ unit/ month. 
Assume the following 
❑The amount of items held for one month is simplified as to leftover at the end of the month Max (Available Quantity at the beginning of the month -Demand), 0) 
❑Assume that there is no Lead Time, if you order at any day you get your items same day
❑Retailer cannot make more than one order per month
❑Retailer must satisfy all the demand 
the retailer wants to find the best replenishment strategy (When and How Much To order) to meet all demands at the minimum cost /highest profit. 
To understand the cost dynamics consider the following example: 

If the retailer orders 200 units at month 1. The associated costs are as follows: Transportation Cost (100)+ Purchasing Cost (200*20=4000) +
Holding Cost ( Leftover=(200-120)*0.2=80*0.2=16)=4016$
If the retailer orders 100 units at month 1. The associated costs are as follows: Transportation Cost (100)+ Purchasing Cost (100*20=2000) + Holding Cost ( Leftover=(0)*0.2=0)=2100$ 

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