Inventory Part 2

Copyright © 2014 - Fadi Kotob

SESSION 6


Chapter 12 !

Managing Inventories Part 2


Adapted - Collier & Evans (2013). OM4, South-Western, Cengage Learning. ISBN-13: 978-1-133-37242-4

!

Last week, I started covering chapter 12 “Managing Inventories”. !

What do you remember from what was covered?


Learning Objectives

- Explain and calculate the economic order quantity and inventory cost

- Briefly explain the importance of safety stock and service levels when managing a fixed order system when demand is uncertain

- Briefly explain the principal decisions when managing a fixed period system

- Briefly explain some of the additional types of inventory systems

- Explain the different approaches that an organisation could use to minimise the problem of inaccurate inventory



It is a classic economic model developed in the early 1900s that minimises total cost, which is the sum of the inventory holding cost and the ordering cost. !

The EOQ Model

This week I will start by explaining the Economic Order Quantity (EOQ).

What is the Economic Order Quantity (EOQ)?



• EOQ is based on the following assumptions:

- Only 2 types of costs are relevant: ordering/setup (S) and holding (H)

- Demand is constant

- Demand for items is independent (Only a single item (SKU) is considered)

- There is certainty in demand, lead time and supply

- The entire order quantity (Q) arrives in the inventory at one time.

- No stockouts are allowed.

The EOQ Model Assumptions

FROM THESE ASSUMPTIONS, LET’S MOVE TO LEARN HOW TO CALCULATE EOQ & THE ANNUAL INVENTORY COST

© 2 0 1 3 O M 4 C e n g a g e L e a r n i n g . A l l R i g h t s R e s e r v e d . M a y n o t b e s c a n n e d , c o p i e d o r d u p l i c a t e d , o r p o s t e d t o a p u b l i c l y a c c e s s i b l e w e b s i t e , i n w h o l e o r i n p a r t .

CHAPTER 12 MANAGING INVENTORIES


!

•The Economic Order Quantity (EOQ) can be calculated using the formula below:

Adapted - Boyer & Verma (2010). Operations and Supply Chain Management for the 21st Century, South-Western, Cengage Learning. ISBN-13: 978-0-618-74933-1 !Adapted - Krajewski, Malhotra & Ritzman (2013). Operations Management Processes And Supply Chains, Pearson Education Limited, ISBN: 9780273766834

EOQ = 2DCo Ch

The EOQ Calculation

Where:

D = Annual Demand

Co = Ordering Cost Per Order

Ch = Annual Holding Cost Per Unit

How to calculate annual ordering cost and annual holding cost?



�8Copyright © 2011 - Fadi Kotob

The EOQ Model Annual Inventory Cost Calculation

• Annual holding cost= (Average cycle inventory) × (Unit holding cost)

= (Number of orders/Year) × (Ordering or setup costs)

• Annual ordering cost (Co)

!!Adapted - Krajewski, Malhotra & Ritzman (2013). Operations Management Processes And Supply Chains, Pearson Education Limited, ISBN: 9780273766834

(Ch) Q

2=

(Co) D

Q=

= Annual holding cost + Annual ordering cost

• Total annual inventory cost

Where:

Q = Order Quantity

Ch= Annual Holding Cost Per Unit

Where:

D = Annual Demand

Co = Ordering Cost Per Order




• A museum of natural history opened a gift shop which operates 52 weeks per year.

• Top-selling SKU is a bird feeder. • Sales are 18 units per week, the supplier charges $60 per unit. • Ordering cost is $45. • Annual holding cost is 25 percent of a feeder’s value.

!

EOQ & Inventory Cost Exercise


Question:

• What is the EOQ?

• What is the annual inventory cost?

Operating Weeks = 52

Sales Per Week = 18 Units

Cost Per Unit = $60

Ordering Cost Per Order (Co)= $45

Annual Holding Cost Per Unit (Ch) = 0.25% Of Cost

Let’s start by understanding the data




What Is The EOQ?

Question:

•What is the economic order quantity for this item?

!!!Answer: !!EOQ=

Annual Demand (D) = 18 * 52 = 936 Units

Ordering Cost (Co) = $45

Cost Per Unit = $60

Annual Holding Cost (Ch) = 0.25% Of Cost

EOQ = 2DCo Ch

2(936)(45)

0.25 * 60

= 74.94 or 75 units


Now we can answer the second questions, “What is the annual inventory cost?”




Annual Cycle Inventory Exercise

Question:


= (Average cycle inventory) × (Unit holding cost)

= (75/2) × ($0.25 * $60) = 37.5 * $15

C = (Ch) + (Co)Q

2D Q

= 562.50


1. Calculate annual holding cost

Annual Demand (D) = 18 * 52 = 936 Units

Cost Per Unit = $60

Ordering Cost (Co)= $45

Annual Holding Cost (Ch) = 0.25% Of Cost

Ordering Quanitity (Q) = EOQ = 75 Units

Answer:

= (Number of orders/Year) × (Ordering or setup costs)

= ((936 units/year) / (75 order size)) × $45

= 12.48 orders per year * $45 setup cost = $561.6

2. Calculate annual ordering cost

Annual Holding Cost = $562.50

Annual Ordering Cost = $561.6




Annual Cycle Inventory Exercise

Annual cycle inventory cost

= Annual holding cost + Annual ordering cost

= $562.50 + $561.60 = $1124.10


Answer:

C = (Ch) + (Co)Q

2D Q

Question:


Annual Holding Cost = $562.50

Annual Ordering Cost = $561.6

!THE ANNUAL CYCLE INVENTORY COST IS $1124.10



• When demand is uncertain, using EOQ based on the average demand will result in a high probability of a stockout.

• This is why safety stock is often kept to deliver the required service level. – Safety stock is additional planned on-hand inventory that

acts as a buffer to reduce the risk of a stockout. – A service level is the desired probability of not having a

stockout during a lead-time period.

Ordering In A Fixed Order System When Demand Is Uncertain

Calculations relating to 12-4b on page 264 are not examinable

Other calculations covered in the lecture are examinable



The Periodic Review Or Fixed Period System!

An alternative to a fixed order quantity system is a fixed period system (FPS)—sometimes called a periodic review system—in which the inventory position is checked only at fixed intervals of time, T, rather than on a continuous basis.

Two principal decisions in a FPS:

1. The time interval between reviews (T), and

2. The replenishment level (M)



The Periodic Review Or Fixed Period System Graph

Calculations relating to 12-5b on page 267 are not examinable

Other calculations covered in the lecture are examinable




Other Types of Inventory System

Adapted - Boyer & Verma (2010). Operations and Supply Chain Management for the 21st Century, South-Western, Cengage Learning. ISBN-13: 978-0-618-74933-1

• Other Inventory Systems: – ABC Systems – Bin Systems – Can Order Systems – Base Stock Systems – The Newsvendor Problem




ABC Systems


• ABC Systems:

• Classifies inventory in categories based on importance

• Allocate control efforts accordingly to importance

• Uses the 80/20 rule (20% of items usually account for 80% of the value)

!– Category A contains the most important items

• “A” items account for a large dollar value but relatively small percentage of total items (e.g., 10% to 30 % of items, yet 60% to 80% of total dollar value)

– Category B contains moderately important items

– Category C contains the least important items

– “C” items account for a small dollar value but a large percentage of total items (e.g., 50% to 60% of items, yet about 5% to 15% of total dollar value)

– Preferred to order C items in large quantities and carry excess safety stock especially if the setup cost is high




Bin, Can Order and Base Stock Systems


• Bin System: • An inventory system that uses one or two bins to hold a

quantity of the item being inventoried • New order placed when one bin is empty or reaches an order

point !

• Can Order System: • An inventory system that reviews the inventory position at fixed

time intervals • New order placed to bring the inventory up to an expected

target level, but only if the inventory position is below a minimum quantity

• Method that mixes both the continuous and periodic systems !

• Base Stock System: • An inventory system that issues an order whenever a

withdrawal is made from inventory




Newsvendor Problem


• Newsvendor Problem: a technique that determines how much inventory to order when handling perishable products or items that have a limited life span

• Shortage Cost: the lost profit from not being able to make a sale, plus any loss of customer goodwill

• Excess Cost: the different between the purchase cost of an item and its salvage or discounted value




Achieving Inventory Accuracy


• The inventory count on the system is often different that the physical inventory on hand !!

• Resolving this issue: - Dedicate employees to issue and receive orders - Place inventory in a locked and secured location - Cycle Counting


Thank You For Your Time


Chapter 14 !

Operations Scheduling


Learning Objectives


- Explain the concepts of scheduling and sequencing.

- Describe staff scheduling and appointment system decisions.

- Explain sequencing performance criterias and rules.

- Describe how to solve single and two resource sequencing

problems.

- Explain the need for monitoring schedules.



Scheduling and sequencing are some of the more common activities that operations managers perform everyday in every business.

Understanding Scheduling & Sequencing

Good schedules and sequences lead to efficient execution of manufacturing and service plans and better customer service.

WHAT IS SCHEDULING AND SEQUENCING?



• Scheduling refers to the assignment of start and completion times to particular jobs, people, or equipment. ➢ Examples: scheduling restaurant employees, airline

crews and planes, sports teams, factory jobs

Understanding Scheduling & Sequencing

• Sequencing which is a concept related to scheduling refers to determining the order in which jobs or tasks are processed. ➢ Examples: emergency room patients, automobile

models on an assembly line, outgoing flights on runways



!

Scheduling applies to all aspects of the value chain, from planning and releasing orders in a factory, determining work shifts for employees, and making deliveries to customers.

Scheduling Applications & Approaches

Scheduling tools include: • Spreadsheets • Software packages • Web-based tools

We will cover 2 common applications of scheduling that are prevalent in operations management. These are:

• Staff scheduling • Appointment systems



!

Staff scheduling attempts to match available personnel with the needs of the organisation by:

Staff Scheduling

1. Accurately forecasting demand and translating it into the quantity and timing of work to be done.

2. Determining the staffing required to perform the work by time period.

3. Determining the personnel available and the full- and part-time mix.

4. Matching capacity to demand requirements and developing a work schedule that maximises service and minimises costs.



!

The Problem: Consider the minimum number of workers required for each day of the week and schedule employees so that each has two consecutive days off and all demand requirements are met.

The Staff Scheduling Problem & Solution Procedure

Solution Procedure: 1. Locate the set of at least two consecutive days with the

smallest requirements, circle the requirements for these days, and assign a worker to all days not circled.

2. Subtract 1 from the requirement of each day not circled, removing existing circles, and repeat this process until all requirements are satisfied.



Example: T. R. Accounting Service is developing a workforce schedule for three weeks from now, and has forecast demand and translated it into the following minimum personnel requirements for the week. ! Day Mon Tue Wed Thur Fri Sat Sun Min Personnel 8 6 6 6 9 5 3

Employee 1:

New requirements:

Employee 2:

New requirements:

The Staff Scheduling Example



Remaining assignments:

The Staff Scheduling Example Continued

Employee 3:

New requirements:



Exhibit 14.2 Final Accountant Schedule

The Staff Scheduling Example Continued



!

Appointment Systems Appointments systems on the other hand can be viewed as a reservation for service time and capacity.

Appointment Systems

Four decisions:

1. Determine the appointment time interval.

2. Determine the length of each workday and time off-duty.

3. Decide how to handle overbooking.

4. Develop customer appointment rules that maximise customer satisfaction.



After covering the scheduling applications and approaches, let’s start by explaining sequencing which is required when several activities must be processed using a common resource.

Sequencing

First, it is important to understand the sequencing performance criteria and the sequencing rules.



!

The criteria is often classified into 3 categories:

1. Process-focused performance criteria

2. Customer-focused due date criteria

3. Cost-based criteria

Sequencing Performance Criteria



Process-focused performance criteria looks at information about

the start and end times of jobs and focus on shop performance

such as equipment utilisation and work in process inventory.

Two common measures which are:

• Flow time • Makespan

Sequencing - The Process Focused Performance Criteria



Flow time is the amount of time a job spent in the shop or

factory.

Fi = ∑pij + ∑wij = Ci - Ri

where Fi = flow time of job i ∑pij = sum of all processing times of job i at workstation or area j (run + setup times) ∑wij = sum of all waiting times of job i at workstation or area j Ci = completion time of job i Ri = ready time for job i where all materials, specifications, and so on are available




!

Makespan is the time needed to process a given set of jobs.

M = C - S


where M = makespan of a group of jobs

C = completion time of last job in the group

S = start time of first job in the group



Customer focused due dates considers the due dates promised

to customers or the internally pre-determined shipping dates.

Two common measures which are:

• Lateness

• Tardiness

Sequencing - The Customer Focused Due Date Criteria



!

• Lateness is the difference between the completion time and the due date (either positive or negative).

• Tardiness is the amount of time by which the completion time exceeds the due date.

(Tardiness is defined as zero if job is completed before due date.)

Li = Ci - Di [14.3]

Ti = Max (0, Li) [14.4]

Sequencing - The Customer Focused Due Date Criteria

where

Li = lateness of job i

Ti = tardiness of job i

Ci = completion time of job i

Di = due date of job i



Cost based criteria focuses on costs which typically include:

• Inventory

• Changeover or setup

• Processing

• Materials handling

Sequencing - The Cost Based Criteria



!

The are many sequencing rules that can be used. These rules

are divided into 2 categories:

1. Rules for fixed set of jobs

2. Rules for intermittent set of jobs

Sequencing Rules



!

Sequencing rules for a fixed set of jobs are:

!

• Shortest Processing Time (SPT) ➢ SPT sequencing maximises resource utilisation and

minimises average flow time and work-in-process inventory.

!

• Earliest Due Date (EDD) ➢ EDD minimises the maximum job tardiness and

lateness.

The Sequencing Rules For Fixed Set Of Jobs



!

Priority rules when new jobs arrive intermittently:

• First come-first served (FCFS) used in many service delivery systems and does not consider any job or customer criterion.

• Fewest number of operations remaining (FNO) but does not consider the length of time for each operation.

• Least work remaining (LWR) – the sum of all processing times for operations not yet performed.

• Least amount of work at the next process queue (LWNQ) – amount of work awaiting the next process in a job’s sequence. Rule tries to keep downstream work stations and associated resources busy.

The Sequencing Rules For Intermittent Set Of Jobs



!

We will illustrate scheduling on a single resource scheduling

problem and on the two resourcing sequencing problem.

Application Of Sequencing Rules



!

• Process a set of jobs on a single processor.

➢ FCFS (First come-first served) rule works well when

processing times are relatively equal.

➢ SPT (Shortest processing time) sequencing finds a

minimal average flow time sequence.

➢ EDD (Earliest due date) rule minimises the maximum

job tardiness and lateness.

Application Of Sequencing Rules Single-Resource Sequencing Problem



Job Processing Time (days) Due Date 1 4 15 2 7 16 3 2 8 4 6 21 5 3 9

FCFS Sequencing Rule Example



SPT Sequencing Rule Example




EDD Sequencing Rule Example




Exhibit 14.3 Comparison of Three Ways (By-the Numbers, SPT, and EDD) to Sequence the Five Jobs

Comparing The Three Sequencing Rules



For a two-resource sequencing problem, S. M. Johnson developed a sequencing rule to minimise the time needed to process a given set of jobs (Makespan). The steps to achieve this are:

1. List the jobs and their processing times on Resources #1 and #2.

2. Find the job with the shortest processing time (on either resource).

3. If this time corresponds to Resource #1, sequence the job first; if it corresponds to Resource #2, sequence the job last.

4. Repeat steps 2 and 3, using the next-shortest processing time and working inward from both ends of the sequence until all jobs have been scheduled.

Application Of Sequencing Rules Two-Resource Sequencing Problem



There are 5 jobs to be completed with each job requiring first a shearing operation (Resource #1) and then a punch-press operation (Resource #2).

STEP 1 1. List the jobs and their processing times on Resources #1

and #2.

Two-Resource Sequencing Example



STEPS 2 & 3 2. Find the job with the shortest processing time (on either resource).

3. If this time corresponds to Resource #1, sequence the job first; if it corresponds to Resource #2, sequence the job last.

Two-Resource Sequencing Example Continued

Job 2 has the shortest processing time; since it is on Resource 2, schedule it last. Job 5 has the next shortest processing time; since it is on Resource 1, schedule it first:



STEPS 4 4. Repeat steps 2 and 3, using the next-shortest processing time and working inward from both ends of the sequence until all jobs have been scheduled.

Continuing, choose job 3 and finally job 4:

Next, both job 1 on the shear have the next shortest time. Choose job 1:




If jobs are completed by order number, the punch press often experiences idle time awaiting the next job. The makespan is 37 days.

Exhibit 14.5 Gantt Job Sequence Chart for Hirsch Product Sequence 1-2-3-4-5




Johnson’s Rule results in a reduction in makespan from 37 days to 27 days, as shown in the Gantt chart.

Exhibit 14.6 Gantt Job Sequence Chart for Hirsch Product Sequence 5-1-4-3-2 Using Johnson’s Rule




!

• Finally, it is important to bear in mind that even with a great schedule, things could go wrong. This is why it is important to monitor how schedules are progressing on a continuing basis. Reschedules are a normal part of scheduling. !

• Gantt chart is a useful tool for monitoring schedules. This helps to track jobs that are behind, on, or ahead of schedule.

Schedule Monitoring & Control

Final Notes - Your Tasks For This Week

!– Review the lecture slides and the notes you have taken

!– Read chapters 13 and 17

!– Read the materials covered in the tutorial

!– Continue working on assignment 2, part 2



Thank You For Your Time

Documents

Inventory Part 2