Lecture –10

 

 

 

 

 

Lecture –10

Inventory Management

 

 

 

 

 

 

 

 

    Topics Covered:

 

n Economic Order Quantity (EOQ) model

n Problem on EOQ

n The Single Period Model

n Problem on Single Period Model

 n Model Questions

 

 

 

 

ECONOMIC ORDER QUANTITY(EOQ) MODEL

          Managers face conflicting pressures to keep inventories low enough to avoid excess inventory holding cost but high enough to reduce the frequency of orders & setups. A good starting point for balancing these conflicting pressures and determining the best inventory level for an item is finding the economic order quantity, which is the lot size that minimizes total annual inventory holding & ordering costs. The approach to determining the EOQ is based on the following assumptions:

1.               Only one product is involved,

2.               Annual demand requirements are known,

3.                 Demand is spread evenly throughout the year so that the demand rate is constant,

4.               Lead time doesn’t vary,

5.               Each order is received in a signal delivery,

6.               There are no quantity discount,

 

When the EOQ assumptions are satisfied, cycle inventory behaves as shown in figure below:

		Time

 

 

 

 

 

 

 

 

 

A cycle begins with Q units held in inventory, which happens when a new order is received. During the cycle, on-hand inventory is used at a constant rate and because demand is known with certainty and the lead-time is constant, a new lot can be ordered so that inventory falls to zero precisely when the new lot is received. Because inventory varies uniformly between Q and zero, the average cycle equals half the lot size Q .

The ideal solution in an order size that causes neither a few very large orders nor many small orders, but one that lies somewhere between. The exact amount to order will depend on the relative magnitudes holding and ordering cost:

 

Ø    Annual holding cost = (average inventory x unit holding cost)

                                         =(Q/2 x H)    [Q = order quantity]

                                                            [H = holding or carrying cost]  

 

Ø    Annual ordering cost = (no of order/year x ordering cost)

                                            = (D/Q x S)         [D = demand/year]

                                                                         [S = ordering cost]

 

Ø    So, Total Cost = [{(Q/2) x H} + {(D/Q) x S}]

 

 

 

 

Thus, with the given annual demand, the ordering cost per order and the annual holding cost per unit, one can compute the optimal or Economic Order Quantity by the following formula:

 

                                      EOQ = √ (2DS/H)

 

 

 

 

 

 

         

	Annual Cost

 

 

 

             

 

 

 

 

 

 

 

 

 

 

Quantity       

 

 

PROBLEM ON EOQ 

 

A museum of natural history opened a gift shop two years ago. One of the top selling items at the museum’s gift shop is a bird feeder. Sales are 18 units per week and supplier charges $60 per unit. The cost of placing an order  with the supplier is $45. Annual holding cost is 25% of a feeder’s value and the museum operates 52 weeks per year. Management choose a 390 –unit lot size so that new orders could be placed less frequently.

 

# What is the annual cost of the current policy of using a 390 unit lot size?

#Would a lot size of 468 be better?

#What is the EOQ?

THE SINGLE PERIOD MODEL

          The single period model is used to handle ordering of perishables (fresh fruits, vegetables, seafood etc) and items that have a limited useful life (news papers, magazines, spear parts for specialized equipments). Analysis of single period situations generally focuses on two costs.

01.       Shortage cost and

02.       Excess cost

 

Shortage cost may include a charge for loss of customer goodwill as well as the opportunity cost of lost sales;

                   Shortage cost (C_s) = Revenue per unit – cost per unit

 

Excess cost pertains to items left over at the end of the period. In effect, excess cost is the difference between purchase cost and salvage value. that is,

Excess cost (C_e) = Original cost per unit – Salvage value    per unit

 

The goal of the single period model is to identify the order quantity or stocking level that will minimize the long run excess & shortage cost.

 

The concepts of identifying an optimal stocking level is perhaps easiest to visualize when demand is uniform.

 

The service level is the probability that demand will not exceed the stocking level and computation of service level in the key to determining the optimal stocking level (S_o).

 

                   Service level = {Cs/(Cs ₊ C_e)} [75% Ideal]

 

 

PROBLEM ON SINGLE PERIOD MODEL 

 

Sweet cider is delivered quickly to Cindy’s cider bar. Demand varies uniformly between 300 liters to 500 liters per week. Cindy pays 20 cents per liter for the cider and charges 80 cents per liter for it. Unsold cider has no salvage value and can’t be carried over into the next week due to spoilage. Find the optimal stocking level for that quantity.    

 

 

 

 

 

Model Questions:

 

1.    Describe, with illustration, the model of Economic Order Quantity (EOQ).

2.    Describe the Single Period Model.

 

 

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