Inventory presentation for operations management

for students

1. Probabilistic models of inventory management for instantaneous demand Submitted by : Mohit Kumar Mishra (20MTS5718) Rishikesh Barela (20MTS5725) Submitted to: Kiran Garg College: Deen Dayal Upadhaya College Course: BSc Mathematical Science

2. There are two types of models for instantaneous demands :- With Discrete Stock levels With Continuous Stock levels

3. MODEL A( With Discrete Stock levels ) In this model, we have  instantaneous demand  setup cost zero discrete stock levels lead time zero This model deals with inventory situation that require one time purchase only. E.g. flowers, cosmetics or seasonal items or spare parts. Item is ordered at the beginning of the period to meet demand during that period. Demand is instantaneous as well as discrete in nature. At the end, there are two types of costs involved:- over-stocking costs Under-stocking costs

4. Let, R = discrete demand rate with probability , = discrete stock level for time interval t, t = constant interval between orders, = over-stocking cost = c + - v = under-stocking cost = S – c – /2 + Where C is the unit cost, is the unit carrying cost, the shortage cost, S the unit selling price and V is the salvage value.  

5. Then the optimal order quantity is determined when value of cumulative probability distribution exceeds the ratio / ( + by computing. < / ( + <  

6. Question: A trader stocks a particular seasonal product at the beginning of the season and cannot reorder. The item costs him ₹25 and he sells it at ₹50 each. For any item that cannot be met on demand, the trader has estimated a goodwill cost of ₹ 15 . Any item unsold will have a salvage value of ₹ 10 . Holding cost during the period is estimated to be 10% of the price. The probability of demand is as follows: units stocked : 2 3 4 5 6 probability of demand : 0.35 0.25 0.20 0.15 0.05 Determine the optimal number of items to be stocked.

7. Hence, =4 units .  

8. MODEL B( With Continuous Stock levels )  In this model, all conditions are same as in model A except that the stock levels are continuous(rather than discrete).  Therefore, probability f (R) dR will be used instead of , where f (R) is the probability density function of the demand rate R. Then the optimal order quantity is determined when the value of cumulative probability distribution is equal to / ( + by computing.  

9. THANK YOU