ISYE 3104 Summer 2003 Homework 7 Solution

ISYE 3104 Summer 2003 Homework 7 Solution

Chapter 12Inventory Management

DISCUSSION QUESTIONS:

1. With the advent of low-cost computing, do you see alternatives to the popular ABC classification?

The advent of low-cost computing should not be seen as obviating the need for the ABC inventory classification scheme. Although the cost of computing has decreased considerably, the cost of data acquisition has not decreased in a similar fashion. Business organizations still have many items for which the cost of data acquisition for a “perpetual” inventory system is still considerably higher than the cost of the item.

1. What is the different between the standard EOQ model and the production inventory model?

The standard EOQ model assumes instantaneous delivery (delivery of the entire lot is made at one instant of time), whereas the Production Inventory Model assumes that delivery takes place at a constant rate over time.

1. What are the main reasons that an organization keeps inventory?

Reasons for an organization to maintain inventory include:

• The decoupling function:
• inventory can be used to decouple stages in the production process within an organization
• inventory can be used to decouple the production process from instabilities or irregularities in supply of raw materials or labor
• inventory can be used to decouple the production process from unstable demand and thus (a) allow production scheduling to develop a “smoother” schedule, and (b) avoid shortages or stockouts
• Quantity discounts:
• inventory can be used to enable the organization to purchase goods in larger lot sizes and take advantage of quantity discounts
• A hedge against inflation:
• investing in inventory now assures one that the price will not increase

1. Does the production model or the standard EOQ model yield a higher optimal order quantity if set up costs and holding costs are the same? Why?

The production inventory model will yield a higher EOQ than the standard model, other things equal, because the maximum inventory level (and thus the effective carrying charge) is less.

1. What is meant by “service level”?

In the context of the discussion developed in class, service level refers to the fraction of operational cycles during which the system will not experience a stockout – this is known as type-1 service level.

There is another notion of service level used in inventory control theory –known as type-2 service level – that is defined as the fraction of customers to whom the product or service is delivered when and as promised.

Notice that the safety stock necessary to meet a service level requirement x will depend on the employed definition of service level. In general, type-1 requirements are more stringent – and therefore, they require more safety stock for their satisfaction – than type-2.

1. How would a firm go about determining service level?

Service level is a difficult parameter to determine. Basically, the firm uses its subjective judgment to balance the cost of additional inventory against the cost of lost goodwill due to stockouts or shortages.

1. Describe the difference between a fixed-quantity and a fixed-period inventory system.

In a fixed-quantity inventory system, when the quantity on hand reaches the reorder point, an order is placed for the specified quantity. In a fixed-period inventory system, an order is placed at the end of the period. The quantity ordered is that needed to bring on-hand inventory up to a specified level.

END-OF-CHAPTER PROBLEMS

Problem 12.2

He decides that the top 20% of the 10 items, based on a criterion of demand times cost per unit, should be A items. (In this example, the top 20% constitutes only 58% of the total inventory value, but in larger samples the value, but in larger samples the value would probably approach 70% to 80%.) He therefore rates items F3 and G2 as A items. The next 30% of the items are A2, C7, and D1; they represent 23% of the value and are categorized as B items. The remaining 50% of the items (items B8, E9, H2, I5 and J8) represent 19% of the value and become C items.

Problem 12.12

(a) Economic Order Quantity:

Q = = = 149.1 or 149 values

Where: D =annual demand, S = setup or order cost, H = holding cost

(b)Average inventory = 74.5 values

(c)Number of orders per year = = = $26.8 or 27 orders

(d)Assuming 250 business days per year, the optimal number of business days between order is given by:

Optimal number of days = days

(e)Total annual inventory cost = Order cost + holding cost

=

=671.14 + 670.50 = 1,341.64

(f)Reorder point = demand during lead time

= 16 units/day x 5 days = 80 values

Problem 12.14

(a)Total cost = order cost + holding cost =

For

For

For

For

For

As expected, small variations in order quantity will not have a significant effect on total costs.

(b)Economic Order Quantity:

where: D = annual demand, S = setup or order cost, H = holding cost

Problem 12.18

(a)Production Order Quantity, noninstantaneous delivery:

= 1217.2 or 1,217 units

where: D = annual demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily production rate

(b)

(c)

(d)

Problem 12.20

Under present price of $50.00 per unit, Economic Order Quantity:

where: D = annual demand, S = setup or order cost, H = holding cost, p = price/unit

Total cost = order cost + holding cost + purchase cost

= 500.00 + 500.00 + 50,000 = $51,000

Under the quantity discount price reduction of 3%:

Total cost = order cost + holding cost + purchase cost

= 200.00 + 1212.50 + 48,500 = $49,912.50

Therefore, the pumps should be ordered in batches of 200 units and the quantity discount taken.

Problem 12.26

Calculation for EOQ: S = $50, H = 50%, D = 9,600

(a)

(b),(c)

(d) Other considerations include the perishability of the chemical and whether or not there is adequate space in the controlled environment to handle 1,200 pounds of the chemical at one time.

Problem 12.28

(a)Z = 1.88

(b)Safety stock = = 1.88(5) = 9.4 drives

(c)ROP = 50 + 9.4 = 59.4 drives

Problem 12.30

In this case, we are not given a specific service level, but a stock-out cost. So, our objective is to select a safety stock level that minimizes the incremental annual cost of carrying the extra stock and experiencing the expected stock outs. Based on the above data regarding the demand experienced in a reorder period, the candidate safety stock levels and the corresponding induced costs are as follows:

The safety stock that minimizes total incremental cost is 50 units. The reorder point then becomes 100 units + 50 units = 150 units.

EXTRA CREDIT

1. What are the types of waste JIT is designed to remove?

JIT is designed to remove all waste—including the waste found in storing, queues, inspection, adjusting, delays, and defects – actually anything that does not add value to a product from the customer’s perspective. You can refer to the PwerPoint presentation on the relevant topic, posted in the course Web page, for more discussion on this question.

1. What is the difference between a “pull” and a “push” system?

A pull system is a JIT system that moves material only as it is needed. A push system sends material to the next workstation at the convenience of the sender, not as it is needed. Thus the inventory level can get very large.

1. What are the types of variability that JIT is expected to help remove?

Variability is removed in a JIT system by systematically identifying and attacking it wherever it may occur. Variability may be caused by both internal and external factors such as employees, machines, suppliers, engineering drawing, or customer capriciousness.

1. What is the impact on JIT of reducing setup costs?

According to the EOQ formula, and the broader inventory control theory, an effective way to reduce the economic lot sizes is by reducing setup costs. In many environments, setup cost is highly correlated with setup time; thus, reducing setup times is a major concern in JIT philosophy.

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