Inventory control models

EPL Model

Learning objective

After this class the students should be able to:

• calculate the order quantity that minimize the total cost inventory, based on the EPL model and

• analyze the implication of this model using what-if through the Excel software.

Time management

The expected time to deliver this module is 50 minutes. 30 minutes are reserved for team practices and exercises and 20 minutes for lecture.

Inventory & inventory system

Inventory is the set of items that an organization holds for later use by the organization. An inventory system is a set of policies that monitors and controls inventory. It determines how much of each item should be kept, when low items should be replenished, and how many items should be ordered or made when replenishment is needed.

Basic types of inventory

independent demand,

dependent demand, and

supplies.

Independent Demand Independent demand items are those items that we

sell to customers.

Dependent demand items are those items whose demand is determined by other items. Demand for a car translates into demand for four tires, one engine, one transmission, and so on. The items used in the production of that car (the independent demand item) are the dependent demand items.

Supplies are items such as copier paper, cleaning materials, and pens that are not used directly in the production of independent demand items

Why hold Inventory

Each team is invited to discuss for 10

minutes about what they figure out to be

the reasons that the organizations

maintain inventory. At the and, they have

to present a list of their supposed

reasons.

Five reasons

1. To decouple workcenters;

2. To meet variations in demand;

3. To allow flexible production schedules;

4. As a safeguard against variations in delivery time; and

5. To get a lower price.

The cost of Inventory

Holding costs;

Setup costs;

Ordering costs; and

Shortage costs.

Notation

D = Demand rate (in units per year).

c = Unit production cost, not counting setup or

inventory costs (in dollars per unit).

A = Constant setup (ordering) cost to produce

(purchase) a lot (in dollars).

h = Holding cost

Q = Lot size (in units); this is the decision variable

Economic Lot Size Production Model

We use the same notation and assumptions of the EOQ model, but now P ( that not is instantaneous) designates the production rate, and t designates the time needed to produce the lot. Then, Q= P x t

The problem Beth Krider, Manager of Production for Zap

Electronics, is making production plans for microphones for portable recorders. The rate of production (P) is 4,000 microphones per month, and the (D) demand rate is 1,000 microphones per month. The cost of each microphone is $6.75, and the inventory holding percent is 0.2.

She is wondering whether this lot size gives the lowest cost.

Cumulative production and Demand

4,000 microphones were made in January, and in February, March, and April, no microphones were produced. 1,000 microphones were sold in January, resulting in an inventory of 3,000 microphones on February 1. The inventory is used up in February, March, and April, so that on April 30 there is no inventory. Then the whole cycle repeats.

Monthly inventory of microphones

The maximum inventory is 3,000 microphones, and the average inventory is 3,000/2 = 1,500 microphones. Note the similarity between this problem and the EOQ problem we have already shown

Now A, the ordering cost, designates the setup cost for producing a lot of the microphones.

P designates the production rate, and t designates the time needed to produce the lot.

P

QtandtPQ

Average Inventory Level The maximum inventory is

QP

DtDtP

1

The average inventory is

22

1 QFor

Q

P

D

where

P

DF

1

The Factor F Demand rate (D) must be less

than or equal to the production rate (P). If D = P, production just meets the demand. In this case, the factor is 0, and so is the inventory. If the production rate is very large compared to the demand, D/P is very small. In such cases, the factor is near 1 and the average inventory is Q/2, the same as in the EOQ problem. The straight line shows how the factor depends on the value of D/P.

The Costs Annual holding cost

22

1 iCQFiC

Q

P

D

Where C=cost of each microphone and i =interest rate

Annual setup cost = D/Q x A

AQ

D

The total cost To carry out the calculations, we need the other parameters of

the problem.

Cost of each microphone: C = 6.75 Percent of holding cost: i = 20% Setup cost: A = $28

Then,

Annual holding cost = 4,000 x 3/4 x 6.75 x 0.2/2 = $2,025 Annual setup cost = 12,000/4,000 x 28 = $84 Annual total cost = $2,109

The model

Q

ADhD

PQQY2

1

002

2

dQ

QYd

dQ

QdY

PDh

ADQ

1

2*

Appling the conditions for optimization, we find the optimal value for order quantity and Cost

PDhADQY 12*

Conclusion

We calculated the optimal production lot size

and the costs and found that Q* = 814.68,

and the total cost is $824.87.

This is $1.284.13 less than Beth's solution of

ordering 4,000 microphones three times a

year.

What-if

Each team is invited to built a model in the Excel software and develop what-if analysis (10) minutes

What-if

What-if

Open excel file

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4

5

6

7

8

9

10

11

12

13

14

15

16

17

A B C D

ModelEconomic

ProductionFormules

Demand D 12,000 12,000Cost per unit C $6.75 $6.75Percent to hold i 20% 20%Ordering cost O 28 28Production rate P 48,000 48,000Lot size Q* = (2DO/Ci/(1-D/P)^0.5 815 =(2*D5*D8/D12/(1-D5/D9))^0.5Number of orders D/Q 15 =D5/D10Unit holding cost H=C*i $1.35 $1.35Annual holding cost QH/2*(1-D/P) $412 =D10*D12/2*(1-D5/D9)Annual ordering cost NO $412 =D11*D8Combined cost QH/2*(1-D/P)+NO $825 =D13+D14Annual purchase cost DC $81,000 =D5*D6Total cost $81,825 =D15+D16

What-If Analysis for Microphones

Reference

Operations Analysis Using Excel. Weida; Richardson and Vazsony, Duxbury, 2001,Chapter 6.