Production planning and scheduling HW/Homework 1:

Production planning and scheduling HW/Homework 1:

A product is produced in batches of 100 units. The machine requires one hour for setup. The processing time is one minute per unit, but the machine can process

5 units simultaneously. What is the rate of production? What takt time can the supply chain manager assume for this batch?
Why is it useful to study competitiveness measures of a firm? Where can they be used?
A popular buzz word for the last few years has been zero inventory. What does it require you to do?
A production plant is not operating at 100% (utilization) of its equipment capacity. The marketing manager may find this unacceptable. As a supply chain

manager, who do you explain that it may not always be advisable to push more material to increase utilization?
In a stable system, it has been found that average inventory is approx. worth $10K. The total annual sales are $35K. Calculate the number of inventory turns.

Calculate the average amount of time the product spends in the system (lead time).
A production manager has found that machines are breaking down more frequently than in the past, and hence the overall lead time in the factory has risen by

20%. The rate of production and demand has not changed. What will be impacted and by how much in the system?
Supply chain managers like to see stable amounts of inventory because stable inventory is easier to manage. Due to regular machine failures and other sources

of variability, the manager is forced to use variable daily production in the system. The current scenario is shown in the Table below. A change recommended to the

manager is to force a production of approx. 100 units per week. Show that this leads to a more stable inventory situation. (Compute sample variance in starting

inventory before and after the change is made).

Week Starting Inventory Production Demand
1 200 100 93.61
2 206.39 74.45 87.5
3 193.34 69.17 88.04
4 174.47 89.64 102.24
5 161.87 144.86 110.35
6 196.37 134.68 86.9
7 244.15 16.56 118.61
8 142.11 213.71 102.33
9 253.49 53.5 82.24
10 224.74 21.99 115.33
Note that the above runs according to the following rule:
SI(t+1) = SI(t) +P(t)-D(t)
Where SI(t) denotes the starting inventory at time t, P(t) denotes the production during time t, and D(t) denotes the demand during time t.
Batch of material visits 5 workstations in sequence to be converted to finished product. Each batch has 100 units. The setup time at each workstation is 1

hour. The processing time is 1.2 minutes per unit. The material-handling time from one machine to the next via a fork-lift truck is 1 hour. Find the lead time of the

batch.
Assume that in the previous problem, the lot is split into 10 transfer batches where each transfer batch is 10 units. As a result, it is possible to install a

conveyor, which implies that material-handling time between machine is negligible. Compute the new lead time. Compute the reduction in lead time and reduction in WIP

achieved.
The following data (in the table below) is available for the sales in the last 10 years. A forecasting model (M) based on exponential smoothing and time

series analysis predicts the sales to be S(t)= 55000+ 1400t. Use linear regression (time-series) to develop your own model (R). Compute the forecast according to your

model (R) and the given model (M) for the next time period. Combine the two forecasts to develop the best combined forecast.

t Sales(t)
1 60,108
2 64,302
3 59,935
4 62,795
5 62,673
6 66,675
7 67,973
8 71,967
9 74,683
10 73,346
A simple exponential smoothing forecasting model is to be used with
α = 0.1. The current smoothing parameter is of the model (S_t) is given as 156.8. The demand for the next time period is 170. Update the S-value.
An experienced marketing specialist has an error variance of 4.5 while a computer model has an error variance of 5.6. The expert predicts 210 as the sales

volume for the next time period, while the computer algorithm predicts 214. Compute the best combined forecast.
A company buys a component for 35 cents. It has extra capacity and can invest an additional $5000 to make the component in-house, which will cost 23 cents per

unit. Find the breakeven point at which it will be worthwhile producing the component in-house.
A firm needs to decide between MTS and MTO. The setup cost is $125, which is approximately the same under both scenarios. In the case of MTO, an additional

average cost of $85 is incurred per order, due to some inevitable backordering. In case of MTS, the manager expects about $500 annual expenses for tracking inventory,

in addition to regular inventory holding costs which are estimated at an annual rate of 40% of the value of the item. The total demand for this item, which is worth

$8, is 2300 annually according to a forecast. Under MTO, about 20 orders are expected per year for the same annual demand. Please perform calculations to determine

whether this item should be MTS or MTO.

Chapter 1
Notes prepared by Abhijit Gosavi Missouri S & T Rolla, MO 65409
Abhijit Gosavi, January 9, 2012 1
Missouri University of Science and Technology Department of Industrial Engineering
Study Plan:
• We will focus on Chapter 1 of our textbook (Askin and Goldberg). • All sections except 1.5 will be covered. • The main ideas that we will cover: 1. The Industrial

Enterprise (The Firm) 2. Measuring the competitiveness of a firm 3. The Product 4. Fabrication, Assembly, and Delivery of a Product
Abhijit Gosavi, January 9, 2012 2
Missouri University of Science and Technology Department of Industrial Engineering
What is an industrial enterprise:
• An industrial enterprise is also called a firm. • Any industrial enterprise produces some product(s) that meets needs of customers. • Its very existence depends on

doing this job right! • Examples: Automobile producers, textile industries, and computer manufacturers, toy makers, and furniture factories.
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Missouri University of Science and Technology Department of Industrial Engineering
Production Systems
• The Production System (PS) is a really critical component of any industrial enterprise. • Production systems design and produce products. • All the processes

involved in the design and production of products fall under the broad umbrella of production-systems engineering.
Abhijit Gosavi, January 9, 2012 4
Missouri University of Science and Technology Department of Industrial Engineering
Production Systems: What do they do?
• At a lower level of detail, essentially, PSs convert raw material to the finished product that can be sold to a customer. • Steps required for this process of

conversion can be classified into four classes: 1. Class I: Fabrication of the components that make up the product. 2. Class II: Assembly. 3. Class III: Delivery to the

customer. 4. Class IV: Disposal of unwanted by-products and re-manufacturing of used material.
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Missouri University of Science and Technology Department of Industrial Engineering
Examples of raw materials and finished products:
• See Figure 1.1 on page 2. • Typical raw materials are natural resources: 1. trees 2. oil 3. metals 4. livestock • Typical finished products that use one or more of

these raw materials are: 1. Automobiles 2. Clothes 3. Computers
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Missouri University of Science and Technology Department of Industrial Engineering
4. Furniture 5. Toys 6. Electrical Appliances 7. Food products • In between the stage from raw material to finished product, one has intermediate products, such as: 1.

Integrated circuits 2. Paper 3. Composites 4. Metallic parts such as gears, shafts, bearings, wires, and ropes.
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Missouri University of Science and Technology Department of Industrial Engineering
Class I: Fabrication
• Operations that transform raw material. • For metallic parts, examples of fabrication operations are: 1. Turning: generating cylinders 2. Milling: removing material

to obtain a flat surface 3. Drilling: making holes 4. Grinding: removing a small amount of material to improve surface finish • For integrated circuits (computer chips):

some typical operations are: 1. Polishing wafer 2. Etching
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Missouri University of Science and Technology Department of Industrial Engineering
3. Photo-lithography 4. Stripping chip section 5. Doping 6. Sorting
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Missouri University of Science and Technology Department of Industrial Engineering
Class II: Assembly
• Putting parts together so that the “assembled” product performs the desired functions. • Assembly is often done on “lines.” • Assembling the components of a car is a

critical activity in an automobile company. • Assembly is done with the help of humans and robots.
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Missouri University of Science and Technology Department of Industrial Engineering
Class III: Delivery
• Packing the product and shipping it to customer. • May require intermediate storage in warehouses before transporting product to the retailer. • The cost of delivery

may be a significant part of the total cost of manufacturing the product.
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Missouri University of Science and Technology Department of Industrial Engineering
Class IV: Disposal
• Product recycling and disposal has been to a great extent mandated by government policies. • Re-use of material reduces production costs and costs to environment

(because of energy savings). • About 94 % of cars and trucks in the US, according to General Motors (see pp. 11), are recycled and a staggering 75 % of the material

used in cars is from recycled sources. • Photo-copiers and computers are some of the other products made of recycled material. • Govt. has made it mandatory for many

manufacturers to process their discharge to the environment to prevent eco-damage.
Abhijit Gosavi, January 9, 2012 12
Missouri University of Science and Technology Department of Industrial Engineering
Competitiveness Measures of a firm:
• Typically, firms measure their competitiveness in the market by looking at various parameters. Some of these are 1. Prices of products. 2. Product features (cosmetic

and functional). 3. Quality of the product. • These parameters can be measured from data related to (i) products available in the market (including your own product)

and (ii) consumer-satisfaction surveys.
Abhijit Gosavi, January 9, 2012 13
Missouri University of Science and Technology Department of Industrial Engineering
Competitiveness measures … is it worth knowing what they are?
• Absolutely! Running an organization without their knowledge is like driving a car with your eyes closed! • Without a comp. measure, you can’t enter a new market. •

Comp. measures have to exploited to sustain the market share. • A low price is a good comp. measure for products that are used daily, but don’t cost a lot in the

current market. E.g., paper towels, shaving creams, and razors. • A low price is also attractive for electrical appliances like toasters, food processors, and

microwave ovens. • Special features are likely to be of greater importance for
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Missouri University of Science and Technology Department of Industrial Engineering
products that we buy infrequently but use often. E.g., cell phones, computers, cameras, and sound systems. • Quality is critical in products that cost a lot of money

or are related to our safety. E.g., cars, houses, food products, and medicines. We are concerned about the length of the life of the product, safety features etc. •

Analysis of such measures involves understanding the competition and the cost dynamics of your own firm.
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Missouri S & T Department of Engineering Management and Systems Engineering
Chapter 2
Notes prepared by Abhijit Gosavi Missouri S & T Rolla, MO 65409
Abhijit Gosavi, 2017 1
Missouri S & T Department of Engineering Management and Systems Engineering
Study Plan:
• All sections covered. • Main ideas 1. Definition of a Production System (PS), objectives, and its components 2. Classification of PSs 3. Role of inventory and types of

inventory 4. Role of information 5. Guiding principles of PSs 6. The need for scientific “modeling” 7. A systems perspective (an Industrial Engineering perspective).
Abhijit Gosavi, 2017 2
Missouri S & T Department of Engineering Management and Systems Engineering
Definition of a PS:
• Resources and procedures that convert raw material to finished products define a PS. • The PS according to modern authors (such as A & G) also includes resources for

delivery of products to customers. • Objectives of running a PS: 1. Maximizing profits 2. Providing jobs and goods to society. 3. Maintaining long-term viability. •

Components: (generally have a hierarchy; see Figure 2.1, pp. 20) 1. A Corporation — makes so-called strategic (long-term) decisions — high $ impact.
Abhijit Gosavi, 2017 3
Missouri S & T Department of Engineering Management and Systems Engineering
2. Plants — make tactical decisions, e.g., forecasting, purchasing, production, inventory strategies, and transportation strategies. 3. Departments (e.g., gear

department, heat-treatment department) — involved in operational (day-to-day) decisions, e.g., operating machines, process planning, maintenance, etc.
Abhijit Gosavi, 2017 4
Missouri S & T Department of Engineering Management and Systems Engineering
Types of Production Systems
• PSs can be classified on the basis of several factors: 1. Layout (Product or Process) 2. Key Resources (Labor-intensive or Capital intensive) 3. Product nature

(Continuous or batch production) 4. Customer orders (Make-to-order or make-to-stock) 5. Moving Material (Push or Pull) 6. Volume to Variety Ratio (High or Low) • The

class to which a PS belongs has a significant influence on how the PS is designed and managed.
Abhijit Gosavi, 2017 5
Missouri S & T Department of Engineering Management and Systems Engineering
Layout:
• The layout ≈ the arrangement of machines and offices in the production plant. • There are four types of layouts: 1. Product 2. Process 3. Cellular 4. Fixed-position •

The layout influences material-handling costs and sometimes influences how material is stored.
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Product Layout:
• Used in repetitive manufacturing with high volumes (flow-shop). • Material movement is more or less guided by one or two product types and is linear. • Machines are

laid out in a sequential manner so that the product visits each area, one right after the other. • Material-handling is reduced because of the flow in material

movement. • Reduced throughput times. • Conveyors, which are some of the cheapest material-handling equipment, are typically used.
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Missouri S & T Department of Engineering Management and Systems Engineering
Process Layout:
• Used when many different product types are being produced. • The production area is divided into “departments,” e.g., turning department, grinding department. •

Products, typically, visit a subset of the set of departments. • Material movement is non-linear and usually lacks flow. • Conveyors can rarely be used and one must use

a fork-lift truck or an AGV (Automated Guided Vehicles); both expensive! and lead to increased material-handling costs. • Usually, throughput times contain a great

deal of idle time.
Abhijit Gosavi, 2017 8
Missouri S & T Department of Engineering Management and Systems Engineering
Cellular Layout:
• Recommended as an alternative to process layouts; part of the philosophy of “Group Technology (GT).” • The facility is partioned into smaller “cells” or mini-

factories. • Each cell is dedicated to parts and machines that have high interaction. • In comparison to a process layout, a cellular layout requires lesser material-

handling and hence lower material-handling costs. • Many job-shops (plants in which many different types of products are produced) in North America have embraced GT,

and have obtained major cost reductions! • Examples of products: furniture, textiles.
Abhijit Gosavi, 2017 9
Missouri S & T Department of Engineering Management and Systems Engineering
Fixed-position Layout:
• Usually, the job (part being produced) is not moved much. • Production machines move around the job. • Used when jobs are extremely large. • Examples: airplanes and

ships. • Usually, profit per part has to be very high to justify a fixed-position layout. • Material-handling costs are high, but usually more than covered by the high

rate of returns.
Abhijit Gosavi, 2017 10
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Key Resources:
• Key resources in any PS are 1. Labor 2. Capital • Some PSs are labor-intensive while others are capital-intensive. • In capital-intensive PSs, machinery is

expensive, and usually automation plays a big role. • In labor-intensive PSs, machinery is cheap, but a great deal of labor is needed.
Abhijit Gosavi, 2017 11
Missouri S & T Department of Engineering Management and Systems Engineering
Capital-intensive:
• Large capital invested in expensive production equipment. Typical in semi-conductor manufacturing, precision manufacturing, and nano-manufacturing. • Resources have

to be used round the clock; multiple shifts used. • Little flexibility in varying capacity because machinery, e.g., semi-conductor fabs, CNC (computer-numerically-

controlled) machines, is expensive. • Typically, there is a bottleneck resource, which must be managed carefully, because it affects the production rate of the entire

plant. • Cannot react very easily to fluctation in demands.
Abhijit Gosavi, 2017 12
Missouri S & T Department of Engineering Management and Systems Engineering
Labor-intensive:
• Assembly and light manufacturing. • Lower end of manufacturing: turning, milling etc, which does not require high precision and can be done with cheap machines. •

Higher flexibility of production rates because labor can be varied by hiring, training, overtime (or unfortunately via layoffs when a downward change is needed). • Can

respond more easily to fluctuation in demands. • Preferred in countries where labor-costs are low — relatively speaking in the global context. • Equipment is not always

utilized highly.
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Missouri S & T Department of Engineering Management and Systems Engineering
Exercise:
Can you think of an organization which is labor-intensive and capital intensive? What kind of problems will it face?
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Product Nature:
• Parts are either manufactured in discrete mode or in continuous mode. • There is usually a time interval between manufacture of discrete parts, and there is none in

the case of continuous parts. • Examples of discrete parts: automobile parts, metallic products, electronics, textiles. • Discrete parts are said to be manufactured in

batches, i.e., a finite number of parts. • Examples of continuous parts: foods, pharmaceuticals, and chemicals. • Continuous parts are said to be manufactured in

pounds, i.e.,
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some unit of weight. • Discrete parts can be usually stored easily in between production operations. • Usually, continuous parts, because of their nature, cannot be

stored for long intervals of time because they may get damaged. As a result, usually, there are severe restrictions on how continuous parts can be stored in between

processes.
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Missouri S & T Department of Engineering Management and Systems Engineering
Push or Pull:
• Some systems are operated according to the so-called Push philosophy. • In Push systems, a high-level production planning system authorizes machines to produce. This

was the traditional control system for moving material for many years. (Chapter 8) • In Pull systems, jobs are made when an authorization comes from the next station.

(Chapter 7)
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Missouri S & T Department of Engineering Management and Systems Engineering
Types of Inventory:
• Raw materials (includes spare parts for machines that need frequent repairs) • Finished goods (or products): goods sitting in warehouses and at retailers (if the

retail outlet is owned by the manufacturer). • Work-in-Process (or Work-in-Progress): Semi-finished goods. • Pipeline: goods in transit from suppliers to manufacturers

and goods in transit from manufacturers to retailers.
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Missouri S & T Department of Engineering Management and Systems Engineering
Inventory Turns:
• This is a term you will hear a lot in analysis, even on radio or TV (PBS Nighly Business Report), of companies. • It is the following ratio. Cost of goods sold

annually Cost of inventory in stock at year end . • Example: A company that sells goods that cost them $20 million and has $5 million in inventory at the year end is

said to have 20/5 = 4 inventory turns. • Clearly, a healthy company will have a large value for this ratio. • In the years past, even 1 was considered an acceptable

number, but nowadays, companies are shooting for ratios as high as 40.
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The Role of Inventory:
• Inventory “consists of physical items moving through the production system.” • Carrying inventory can amount to 20% or more of the manufacturing costs, and is hence

an important issue that we cannot ignore. • It’s like fat in the system; if you want to improve your health, can you ignore the fat you carry? • There are three

important principles of inventory management, and there is an important tradeoff involved here: 1. There is a minimum level of inventory needed — a level needed to

ensure smooth production operations. (if there is insufficient inventory, machines starve and waste time doing
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Missouri S & T Department of Engineering Management and Systems Engineering
nothing. 2. Too much inventory costs money. 3. When you place an order or set up a machine for production, it is the cost of ordering or time for set up that

determines what the size of the batch, Q, should be. The size of the batch determines how much inventory you carry in your system.
Abhijit Gosavi, 2017 21
Missouri S & T Department of Engineering Management and Systems Engineering
Batch Sizes, Order Sizes, Inventory, and Safety Stocks:
• The batch (lot) size is the number of items released on the shop floor. • The order size is the number of items ordered from a supplier. • Inventory = Inventory in

stock (work-in-progress & finished products) + On order (raw materials) – Backorders (products) • Safety stock is the number of units of inventory (raw material or

finished product) that we plan to have on hand when an order arrives.
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Missouri S & T Department of Engineering Management and Systems Engineering
Lead time and Cycle time:
The two are not the same, although they’re used interchangeably.
In the context of production: • Lead time is the time between the starting of the manufacturing process and the delivery to the customer for a given batch. • Cycle

time is the time for producing a batch on a given machine.
In the context of ordering raw material: • Lead time is the time between placing an order and the time the order is realized. • Cycle time is the time between placing

successive orders.
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Calculation of Cycle time, Lead Time, Lot Sizes and Transfer Batches:
• Cycle time of a batch on a machine = (Set-up time + (Batch size × Unit Production time)). • Oftentimes, the batch is split into several transfer batches. This can

oftentimes reduce the lead time of the batch in the entire system. • When a lot is split, which is called lot-splitting, the lead time of the batch in the shop floor is

the time elapsed since the first transfer batch enters the shop floor until the final transfer batch exits the shop-floor.
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Is holding inventory justified?
• Randomness causes us to keep inventory for three reasons 1. Demand from customer is random, and since our production cycle times are never zero, in case of higher-

than-predicted demand, without inventory we lose the customer. 2. Machines break down, and if we do not have sufficient finished-goods inventory, our competition can take

advantage of that. 3. Suppliers can be variable and erratic. • Moreover, one often gets price breaks out of ordering larger order sizes, and this can cause inventory

to increase.
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Inventory-carrying (holding) costs:
• There are several sources to this: 1. It takes up space that has to be rented, and heated or cooled. 2. One has to keep track of where it lies, and so there are

administrative costs. 3. Taxes and insurance costs are often based on how much inventory is carried. 4. Damage • Remember that with time, value of money goes down, and

there is a lot of capital tied up in inventory that could earn interest. • Usually, inventory is calculated as a percentage of the total cost of the material.
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Costs related to inventory strategies:
• Associated with ordering material, there exist fixed costs, usually, due to transportation. The ordering costs also depend on how much is ordered, and as discussed

previously, often fall with an increased size of order. This drives us to order large quantities. • Usually, it takes some time (and hence money) to set up a machine

for a new product. This cost drives us to use increased batch sizes.
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EOQ:
• The Economic ordering quantity. • Let h denote the holding cost per unit time per unit of inventory. • Let Q denote the size of the order. • Let A denote the

ordering cost, which is a fixed cost per batch. • Let D denote the demand for the item in unit time. • The inventory will change from Q to 0 over a time interval, and

hence the average inventory will be Q/2. • Then the inventory carrying cost calculated per unit time is hQ/2. • Clearly, if Q items are depleted in a time interval

when the rate
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Missouri S & T Department of Engineering Management and Systems Engineering
is D per unit time, the time interval is of length Q/D. • Then the ordering cost calculated per unit time is A/(Q/D) = AD/Q. • Then the total cost per unit time for

the system, TC, is hQ/2 + AD/Q. • Differentiating TC with respect to Q and setting the first derivative to 0, one obtains the optimal quantity Q∗ to be Q∗ =√2AD h
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Missouri S & T Department of Engineering Management and Systems Engineering
Tradeoff between stock-outs and finished product inventory:
• The EOQ considers raw material inventory; now we turn to finished product (f.p.) inventory. • Low amounts of f.p. inventory increase the probability of shortage

thereby raising shortage costs and hence total costs. • High amounts of f.p. inventory cause not only cause inventory-holding costs to be high (which in turn causes

total costs to rise), but also pose a serious risk in that a part of the f.p. inventory may never sell at the price it is supposed to.
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The role of information:
• Information cannot be used as a substitute for inventory, but it sure helps in reducing inventory! • A PS which has detailed information about the demand

requirements at its retailers has a reduced need for keeping safety stock. Hence, a PS equipped with a good information system is bound to have lower shortage costs. •

A more transparent system is easier to manage.
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Missouri S & T Department of Engineering Management and Systems Engineering
Guiding principles of PSs:
• 1. Learning curves: with time production times and costs go down. Usually, the first prototype costs more money. Learning from past experience helps. • 2. Product

life cycle: all products have a finite life. When a product is new, the demand is small, but it grows with time, and then finally, it starts declining. All PSs must

recognize this fact, and adjust themselves to changes (reversed bath tub curve and profit margins). • 3. Set up time defines variety: A PS with huge set up times

(changeover times) cannot afford to produce jobs with a great deal of variety. Huge set up time also raises inventory. Modern mantra is to reduce set-up time and

increase variety in products.
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Missouri S & T Department of Engineering Management and Systems Engineering
Guiding Principles (contd.):
• 4. Inventory is a necessary evil. It cannot be avoided totally, but it must be minimized to the extent possible for excessive amounts of inventory form a major

source of risk to the system. • 5. Little’s Law: I = λT, where I denotes the average inventory in the system, λ denotes the rate of demand (or rate of arrival of parts

into the system), and T denotes the average lead time. If inventory increases, so does lead time. Increased lead times imply reduced flexibility to changes in customer

demands and market fluctuations. (You may have seen Little’s rule in the following symbols: L = λW).
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Missouri S & T Department of Engineering Management and Systems Engineering
Modeling:
• A model is a mathematical equation (EOQ formula) or a computer program (simulation programs) that imitates the actual system in some way. • We can play around with

the model to predict how the system will behave without tampering with the actual system. • Hence models can be used to improve system behavior and to improve decision

making.
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Missouri S & T Department of Engineering Management and Systems Engineering
A systems perspective:
• IEs like to adopt a “systems” perspective (the big picture) when analyzing the PS. • Such a perspective would recognize that the PS is a part of the supply chain,

and that the supply chain contains suppliers of raw materials, retailers who sell the products, the customers, and the warehouses needed in intermediate storage. •

Adopting a system’s perspective can make dramatic changes in how a business is carried out. • Example: Dell Computers: eliminated holding costs by using expensive

transportation; resulted from looking at the big picture!
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Missouri S & T Department of Engineering Management and Systems Engineering
Lot splitting example:
• Lot splitting can reduce lead times and WIP. The following example shows how. • A batch of material must visit 5 workstations in series to be converted into finished

product. Each batch is made up of 100 units. The processing time of each unit on each workstation is 2 minutes. The set-up time is one hour. Assuming no time is lost

in waiting for machines, determine the lead time of the batch. Now, if the batch is split into 10 transfer batches, where each transfer batch has a size of 10,

recompute the lead time. Calculate the reduction in lead time and inventory achieved by the lot-splitting.
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Missouri S & T Department of Engineering Management and Systems Engineering
Chapter 3
Notes prepared by Abhijit Gosavi Missouri S & T Rolla, MO 65409
Abhijit Gosavi, Feb 7, 2017 1
Missouri S & T Department of Engineering Management and Systems Engineering
Study Plan:
• Section 3.1 • Section 3.2 (exclude 3.2.2, 3.2.3, 3.2.4, and 3.2.5) • Section 3.3 (exclude Sections 3.3.1.2, 3.3.1.3, and 3.3.2) • Note: Sections 3.4 and 3.5 will be

covered briefly.
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Missouri S & T Department of Engineering Management and Systems Engineering
Forecasting:
• The science underlying the prediction of demand for the next year or a pre-specified time horizon. • A common approach is to examine past demand and then extrapolate

any trend forward. • Requires a thorough understanding of markets and customer behavior. • There are dangers in extrapolation. • Several mathematical techniques are

available for the analysis of past demand and trends.
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Missouri S & T Department of Engineering Management and Systems Engineering
Why is forecasting needed?
• Strategic planning: – Deciding which product(s) to produce in subsequent years. – Should new machines be purchased? – Should one invest in new technology for

production? • Tactical and operational planning in MTS: – How much raw material to order. (Tactical issue) – When to release material on shop floor. (Operational issue)
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Missouri S & T Department of Engineering Management and Systems Engineering
Errors in forecasting:
No forecast is ever perfect; some errors always exist. • If a forecast strays far from how much demand is realized, either a new method should be selected or else the

cause has to be identified. The causes could potentially be: 1. Falling product attractiveness → lost demand for product 2. At times catastrophic events can occur

(e.g., 9/11), which change overall demand • Other factors to be considered to avoid errors: 1. Economic metrics, e.g., unemployment levels, change in salaries
2. Advertisement, which can affect demands, and if not accounted for can lead to errors
Abhijit Gosavi, Feb 7, 2017 5
Missouri S & T Department of Engineering Management and Systems Engineering
Forecasting is necessary!
• In the MTS scenario, good forecasting is critical. (Discussed). • In the MTO scenario, also, forecasts are necessary to determine resource requirements. • Finally,

forecasts are always helpful tools but should be used as guidelines especially in a volatile market.
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Missouri S & T Department of Engineering Management and Systems Engineering
Heirarchical forecasting:
• Top-down: Forecast total number of products and separately forecast proportion of each category. • Bottom-up: Forecast each category separately, and sum the amounts

in each category to produce the total forecast for a product. • The total forecast is what is essentially required for ordering raw material.
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Missouri S & T Department of Engineering Management and Systems Engineering
Building models for forecasts
• Identifying target variables. • Collect data (from market surveys, expert predictions, and historical data). • Build models, i.e., hypothesize parameters.
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Missouri S & T Department of Engineering Management and Systems Engineering
Checking models
• et = Dt −Ft • Dt is the actual demand in time period t • Ft is the forecasted demand for time period t • ¯ e =∑T t=1 et T • σ2 =∑T t=1 (et−¯ e)2 T−1 • SSE =∑T t=1

(et)2
Abhijit Gosavi, Feb 7, 2017 9
Missouri S & T Department of Engineering Management and Systems Engineering
Expo. smoothie. model
• St = αDt + (1−α)St−1, where • St denotes the estimation of the expected demand from the start until (and including) t. • Dt is the actual demand in time period t. •

α is the learning rate. • Ft,t+τ denotes the forecast for time period t + τ given the information (history) until (and including) t. • Hence Ft,t+τ = St for a simple

expo. smoothie. model. • The expo. smoothie. model ignores seasonal variations.
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Missouri S & T Department of Engineering Management and Systems Engineering
Expo. smoothie. model: Example 1
Data: t = 33;S32 = 56.8;D33 = 58;α = 0.2.
F33,34 =?;F33,35 =?. Since St = αDt + (1−α)St−1, we have S33 = 0.2(58) + 0.8(56.8) = 57.04 = F33,34 = F33,35.
Abhijit Gosavi, Feb 7, 2017 11
Missouri S & T Department of Engineering Management and Systems Engineering
Expo. smoothie. model: Example 2
Demand data for 5 months: D1 = 65;D2 = 63;D3 = 72;D4 = 79;D5 = 81. α = 0.1.
S1 = D1 = 65.
S2 = 0.1(63) + 0.9(65) = 64.8.
S3 = 0.1(72) + 0.9(64.8) = 65.52.
S4 = 0.1(79) + 0.9(65.52) = 66.868.
S5 = 0.1(81) + 0.9(66.868) = 68.2812.
Note that the forecast for the future is 68.2812 though the recent demand has been 81. I.e., this model adapts slowly to changes in the market and is hence likely to

not overestimate!
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Missouri S & T Department of Engineering Management and Systems Engineering
Moving Average Models
• The idea here is to average past demand to predict the future. • When demand is averaged from the past w periods, the result is a simple moving average or w-moving

average. • When demand is averaged from all the past periods, the result is a cumulative moving average. • In Example 2 above, if we let w = 2, then simple moving

averages would lead to: F3 = 64;F4 = 67.5;F5 = 75.5 and so on. • In Example 2 above, cumulative moving averages would lead to: F2 = 65;F3 = 64;F4 = 66.67;F5 = 69.75

and so on.
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Missouri S & T Department of Engineering Management and Systems Engineering
Regression models
• When time is an independent variable, we have what is called a time-series model. • With time-series models, one generally extrapolates. • Regression is not a good

technique for extrapolation; regression is preferably performed over variables other than time. • Usually, data from many other variables are available in conjunction

with the historical sales, e.g., economic indicators, advertising costs etc. These data can be used in the regression model for forecasting.
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Missouri S & T Department of Engineering Management and Systems Engineering
Regression computations
• We will use x to denote our independent variable and y to denote the dependent variable (e.g., sales). • Thus far, we have used D to denote y; thus Dt ≡ yt. •

Minimize SSE of the forecast error; SSE =∑T t=1(et)2. • y = β0 + β1x + ϵ. • We will use Ft+1 = β0 + β1xt+1 to predict, where xt+1 is the independent variable predicted

for the next time interval, (t + 1). • Example for x here could be an economic indicator.
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Missouri S & T Department of Engineering Management and Systems Engineering
Regression computations: R2
• Ft = β0 + β1xt; e2 t = (Ft −yt)2; SSE =∑T t=1 e2 t. • ¯ y =(∑T t=1 yt)/T; SST =∑T t=1(yt − ¯ y)2. Then R2 = 1− SSE SST . If there is a single variable (x) in the

regression and if R2 > 0.5, the model is considered to be adequate, i.e., it explains the variation well. If R2 is less than 0.5, this is not the case. If there is

more than one x variable, the value of R2 may not be a good indicator of whether the model is adequate; an adjusted R2 is used to determine whether the model is

adequate. Most statistical software provide the values of R2 and adjusted R2.
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Missouri S & T Department of Engineering Management and Systems Engineering
Regression computations: contd.
The underlying linear equations are:
T ∑
t=1
yt = Tβ0 + β1
T ∑
t=1
xt (1)
T ∑
t=1
xtyt = β0
T ∑
t=1
xt + β1
T ∑
t=1
(xt)2. (2)
Example: For the data given below, develop a forecast for the sales for the next year in which the economic indicator is expected to have a value of 2.9.
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Missouri S & T Department of Engineering Management and Systems Engineering
Economic Indicator (xt) Sales (yt) (yt −Ft)2 (yt − ¯ y)2 1.1 65 0.083 57.76 2.4 71 0.0142 2.56 1.9 67 2.7272 31.36 3.4 79 8.6729 40.96 4.7 81 2.1652 70.56
Total ¯ y = 72.6 13.6679 203.2
Using Equations (1) and (2), we have ∑x = 13.5;∑x2 = 44.23;∑xy = 1018.5;∑y = 363. Solving the equations, we obtain: β0 = 59.27 and β1 = 4.9357. Then, since xT+1 = 2.9,

FT+1 = β0 + β1xT+1 = 59.27 + 4.9357(2.9) = 73.58. R2 = 1− SSE SST = 1− 13.67 203.3 = 0.9327. Since R2 is above 0.5 and this is a linear model with just one variable,

this is an acceptable model.
Abhijit Gosavi, Feb 7, 2017 18
Missouri S & T Department of Engineering Management and Systems Engineering
Regression models (contd.)
• Non-linear regression models used where a linear fit is not evident from visual inspection. • Minimize MSE of the forecast error. • Dt = β0 + β1t + β2t2 + ϵ. •

Equations can be worked out via calculus.
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Missouri S & T Department of Engineering Management and Systems Engineering
Judgmental Forecasting
• Delphi Method • Market Surveys
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Missouri S & T Department of Engineering Management and Systems Engineering
Combining Forecasts
• We have two forecasts whose variances (in error) are known from historical performance. • Let θ be the weight associated with forecast 1, whose variance is σ2 1. •

Let (1−θ) be the weight for forecast 2, whose variance is σ2 2. The combined forecast is: θF1 + (1−θ)F2. • Then, the optimal value of θ, to be denoted by θ∗, is: θ∗ =

σ2 2 σ2 1 + σ2 2 . • The variance of the combined forecast is θ2σ2 1 + (1−θ)2σ2 2.
Abhijit Gosavi, Feb 7, 2017 21

Missouri S & T Department of Engineering Management
Chapter 4
Notes prepared by Abhijit Gosavi Missouri S & T Rolla, MO
Abhijit Gosavi 1
Missouri S & T Department of Engineering Management
Study Plan:
• All sections excepting for 4.1.2.3, 4.1.2.4, and 4.2.6. • Main ideas 1. Strategic Planning 2. Role of the supply chain in a PS with special emphasis on the bull-whip

effect.
Abhijit Gosavi 2
Missouri S & T Department of Engineering Management
Strategic planning:
• A strategic plan provides a view of where the company is headed and how to get there! • Development of the strategic plan requires an understanding of 1. Core

competencies of the organization 2. Customer markets 3. The need for integration 4. Flexibility
Abhijit Gosavi 3
Missouri S & T Department of Engineering Management
Core competencies:
• The measures of competitiveness are good candidates. • Rapid delivery could be a core competency.
Abhijit Gosavi 4
Missouri S & T Department of Engineering Management
Market identification:
• Conducting surveys can help. • Sometimes you can create markets by creating a great product.
Abhijit Gosavi 5
Missouri S & T Department of Engineering Management
Integration:
• How many of the production stages should be integrated within the organization? • When you own some parts of the production stages, you integrate vertically. • How

many stages in production should be allowed to be outsourced (not necessarily to other countries but other companies)? • Requires analysis of manufacturing costs.
Abhijit Gosavi 6
Missouri S & T Department of Engineering Management
Flexibility
• An important decision to be made is: how flexible do you want your organization to be in terms of 1. the variety of products it can produce 2. adapting to changes in

volumes 3. adapting to changes in routes of material in the shop floor. • A more flexible organization has higher chances of survival in the long run!
Abhijit Gosavi 7
Missouri S & T Department of Engineering Management
Some decisions to be made by strategic planners:
• Make or Buy • MTO or MTS • What kind of technologies to invest in.
Abhijit Gosavi 8
Missouri S & T Department of Engineering Management
Make or buy
• Let c1 be the cost of buying a unit from a vendor. • let c2 be the variable cost of producing it in-house and C be the fixed cost. • Then produce in-house if C + c2X

< c1X, i.e., if X >
C c1 −c2
.
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Missouri S & T Department of Engineering Management
MTO Vs MTS
• Items which have small order sizes are best made to order. • Typically, high volume parts are made to stock. • MTS increases risk; but increasingly, managers are

using delayed differentiation strategies, wherever possible, to minimize risk. • When items have a high risk of becoming obsolete, it makes more sense to MTO or use

delayed differentiation. • MTO requires small production lead time; if production lead time is huge, MTO is infeasible. • Most companies are striving to reduce

production lead time by using lean manufacturing so that they can either use MTO or use delayed product differentiation.
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Missouri S & T Department of Engineering Management
Simple math. model to determine whether to MTO or to MTS
• Assumption: 1. Demand rate is constant and non-random. 2. Set-up costs (A) are identical in both production modes (i.e., MTS and MTO). 3. π denotes the cost of

backorder which is incurred under MTO. 4. Cs denotes cost of monitoring inventory in MTS, which is a significant cost under MTS. 5. QMTO denotes the average order

quantity under MTO.
Abhijit Gosavi 11
Missouri S & T Department of Engineering Management
• We MTS if: √2ADh + Cs < (A + π)D QMTO . • The above follows from the fact that the LHS is the cost in MTS and the RHS is the cost in MTO. • Note that D QMTO denotes the average number of orders received under MTO. Abhijit Gosavi 12 Missouri S & T Department of Engineering Management Supply chain concepts • Logistics • Bull-whip effect • Vendor managed inventory • Relationship with vendors • Cross-docking Abhijit Gosavi 13 Missouri S & T Department of Engineering Management Logistics • Packing, loading, transporting, unloading at intermediate stages is collectively called logistics. • Usually, items are shipped to regional distribution centers (RDCs) before being shipped to local wholesalers or retailers. • Road, rail, air, ships are used for transportation. • Logistics have acquired a global dimension because 1. Customers are located all over the world 2. Production plants are located in many parts of the world; companies try to use beneficial exchange rates to their advantage in allocating production targets. Abhijit Gosavi 14 Missouri S & T Department of Engineering Management Bull-whip effect (BWE) Defn: The phenomenon in which the orders to supplier tend to have larger fluctuations (variance) than the sales to buyers; this distortion subsequently propagates upstream to higher levels of the supply chain in an amplified form. In other words, there is a tendency to order more than you need. A small increase in the sales at the retailer can trigger a bigger increase in the production quantities in the production plant, which causes an even bigger increase in the size of the raw material orders. Abhijit Gosavi 15 Missouri S & T Department of Engineering Management Bull-whip effect (contd.) • Thus the BWE leads to: 1. Excessive production at the production plant. 2. Major variations in raw material orders placed. • BWE is a result of information myopia and panic of shortages. • If we analyze the causes further we find three reasons for this panic: 1. Non-zero lead times (ordering issue). 2. Order batching reduces costs; there is a non-zero fixed cost per order (ordering issue). 3. There is a non-zero set-up time on machines (production issue). Abhijit Gosavi 16 Missouri S & T Department of Engineering Management Solutions to BWE • A more effective information-sharing strategy that allows each stage in the supply chain to have information about demands (orders placed) at other stages. • VMI (Vendor-Managed Inventory). Abhijit Gosavi 17 Missouri S & T Department of Engineering Management Vendor-managed inventory (VMI) • VMI is a philosophy in which the vendor is responsible for the inventory control at the production plants (and retailers). • The vendor monitors the inventory at each production plant, and delivers raw material. • The production plant is not responsible for placing orders. • This usually leads to less stock-outs at the production plant because the vendor is able to coordinate its activities better; it does not receive all its orders at roughly the same time (start of month or week), which is typical of traditional inventory systems. • It also reduces inventory carrying costs for the production plant. • Because of better information sharing, it reduces the BWE. Abhijit Gosavi 18 Missouri S & T Department of Engineering Management Vendor relationship • An issue involved in supply chain management is: how many and which vendors should be used and which production stages should be vertically integrated. • Some important factors in selecting vendors are: cost, delivery speed, and quality. • Measures can be taken to strengthen the relationship with vendors for a long life. Abhijit Gosavi 19 Missouri S & T Department of Engineering Management Cross-docking • The idea is to meet all demand with minimal storage at intermediate points. • Goods received are directly shipped to customers / retailers/ wholesalers without intermediate storage in RDCs. • The major difference with traditional policy is that one has to coordinate products arriving from different sources and get them ready to be sent directly to the customer. Traditionally, production systems dispatched their products to RDCs, and goods sat in the RDC warehouse for a long time (costing money) before they were assembled and shipped. • Requires a satellite-based inventory tracking system for retailers like Walmart. Abhijit Gosavi 20