Operations & Logistics Management Summary (Final Exam)
Week 1; Introduction to operations and logistics management
Introduction section
Operations is the activity of managing the resources and processes that produce and deliver goods and
services. Transformation lies at the core of all operational activities.
Examples of transformation;
Factory; transforms raw materials into final products that the consumer buys
Barber; the input is a customer that wants their hair cut, the transformation process is the
cutting process, the output is a satisfied, short haired customer.
Operations management refers to the design, operations and improvement of the system that creates
and delivers the firm’s primary goods/services. This concept is all about making the system more
effective (doing the right things to create the most value) and efficient (doing something with the
lowest possible input).
There are five key performance indicators (competitive priorities) most of the time you cannot be
good at everything and there needs to be a trade-off notion of trade-offs ;
Cost
Quality; performance quality (basic operating characteristics), conformance quality (made to
specifications), reliability quality (working life).
Delivery; delivery speed (how quickly can a need be fulfilled), delivery reliability (deliver
products when promised consistently)
Flexibility; mix flexibility (wide variety of products), changeover flexibility (produce a new
product, with little changeover time), volume flexibility (produce a wide range of volumes)
Sustainability; environmental sustainability (energy use, waste), social responsibility (labor
protection, addressing societal issues)
Process section
In this course two different models are used; stochastic and deterministic. Stochastic is under uncertain
circumstances, different outcomes can occur on average is a good example, since then there is
variation between the processes. Deterministic refers to the model where everything is known in
advance, ‘’the arrival rate is 3 per hour exactly’’, this happens every time, no matter the circumstances.
Important is that in deterministic models we ignore waiting line effects, even with batch production.
Capacity of a system refers to the amount of output that a specific system is capable of achieving over
a certain period of time. The period of time is essential of course, since otherwise the number would
not tell us anything about the production process.
The arrival rate is the number of products that arrive at the process per unit of time. If the inter-
arrival time is 20 minutes, the arrival rate will be 60/20 = 3 per hour or 3*24 = 72 per day. The
throughput time is the time that passes from the moment of entry and the moment at which the process
is finished.
The deterministic throughput time can simply be calculated as the sum of all the individual processing
times. If the whole production process has multiple paths, we calculate the throughput time of each
path and then multiply them by the probability that each path will be followed, then we sum this up, to
get the total throughput time.
,Design capacity is the theoretical maximum output of a system or process in a given period of time.
While, the effective capacity of a system refers to the actual capacity of a system. If a machine is 10%
of the time in maintenance, the design capacity includes this 10%, while the effective capacity
excludes the 10%.
The bottleneck of a system is the process within a system that limits the output of the system. If none
of the individual processes is the bottleneck, the arrival rate must be the bottleneck. The departure rate
will therefore always be the same as the capacity of the bottleneck.
The utilization rate is the fraction of the total time in which a machine is used for a product or service.
Utilization rate = total operating time / total time (OR) = arrival rate λ / (n)*production rate μ, n is the
amount of parallel operators.
Efficiency = actual output / effective capacity
Work in progress is the number of products that have been taken into production, but not yet been
finished. We can calculate using Little’s Law; L = λ*W (throughput time). Other estimation is as
follows; WIP = Σρi*Xi, where X refers to batch size, ρ to the utilization rate, and Σ to the sum of all the
processes within the system.
Week 2; Service processes and queuing models
Services
Every service needs a service package to be properly executed. A service package is a bundle of
tangible and intangible resources that is provided in a certain environment. Such as, supporting
facilities, facilitating goods, information, explicit services (observable), implicit services (vaguely
perceivable).
Queuing models
There are different types of queuing models; single server and single line, multi-server and multi line,
and multi-server and single line. Often the queue discipline of first come first served is used (only one
used in this course), priority is another example of a queue discipline. When observing a queue
consumers can behave differently than just standing in line;
- Balking; when a customer observes the queue and decides to leave straight away.
- Jockeying; when a customer switch between queues if they think they will get served faster.
- Reneging; when a customer enters the queue but at some point decides to leave the queue.
We discuss two different models in this course, which are the following M/M/1 and M/D/1, in both
cases there is one server. The difference between the two is the service process, for M/D/1 this is
deterministic, or known in advance. For M/M/1, this is random (negatively exponential) or stochastic.
It is important to know how to identify which model is relevant, since the formulas differ.
M/M/1 formulas and their meanings (formulas are given);
- Ls = λ / (μ − λ); Average number of customers in the system
- Ws = 1 / (μ − λ); Average time spent in the system
- Lq = λ² / [ μ(μ − λ) ]; Average number of customers waiting in line
- Wq = λ / [ μ(μ − λ) ]; Average time spent waiting in line
- P(n > k) = (λ / μ)^(k + 1); Probability of more than k customers in the system
M/D/1 formulas and their meanings (formulas are given);
, - Ls = λ(2μ − λ) / [ 2μ(μ − λ) ]; Average number of customers in the system
- Ws = (2μ − λ) / [ 2μ(μ − λ) ]; Average time spent in the system
- Lq = λ² / [ 2μ(μ − λ) ]; Average number of customers waiting in line
- Wq = λ / [ 2μ(μ − λ) ]; Average time spent waiting in line
In each formula λ refers to the arrival rate, and μ refers to the service rate (customers / hr). In most
cases the following relationship holds; Ls = λ*Ws and Lq = λ*Wq.
Week 2; First Training Session (Questions + Answers)
Question 1)
Consider the service process depicted below. What is the utilisation rate of this process?
Answer; λ = 6 per hour, μ = (60/8)*3 = 22.5 per hour Utilization rate = λ/μ = 6/22.5 = 0.27
Question 2)
Customers arrive at a ticket office staffed by only one employee. The mean arrival rate of customers is
3 per minute. The average service rate is 4 customers per minute. The arrivals follow a Poisson
distribution and the service time follows a negative exponential distribution. What is the probability of
having exactly one customer in the system?
Answer; λ = 3 per minute, μ = 4 per minute, since we know that the arrivals follow a poison
distribution and service time is random M/M/1 system relevant formula is; P(n > k) = (λ / μ)^(k
+ 1). Since this is the probability of having more than k customers in the system we can apply the
following formula; P(n > 0) – P (n>1) = P(n = 1) 0.75 – (0.75)^2 = 0.1875
Question 3)
Consider the process at an administration office where customer orders are processed. Every 3.9
minutes an order arrives. An incoming order is first reviewed in Arrival rate: 6 customers per hour
Workstation with 3 parallel employees. One employee can serve a customer in exactly 8 minutes
Training #1 Questions 2 12.4 minutes by an employee to check whether all products are available
(which can be seen as Activity 1). There are three of these employees and each order is checked by
one of them. Next, the order goes to one of three parallel operating bookkeepers to check whether the
customer has paid all past bills(Activity 2). It takes a bookkeeper 7.2 minutes to check a customer’s
payment record. Finally, the order goes to a clerk who enters the order into the company’s computer
system in 9.5 minutes (Activity 3). There are two clerks available, who work in parallel.
What is the utilization rate of the clerks at Activity 3? Support your answer with calculations.
Answer;
Week 1; Introduction to operations and logistics management
Introduction section
Operations is the activity of managing the resources and processes that produce and deliver goods and
services. Transformation lies at the core of all operational activities.
Examples of transformation;
Factory; transforms raw materials into final products that the consumer buys
Barber; the input is a customer that wants their hair cut, the transformation process is the
cutting process, the output is a satisfied, short haired customer.
Operations management refers to the design, operations and improvement of the system that creates
and delivers the firm’s primary goods/services. This concept is all about making the system more
effective (doing the right things to create the most value) and efficient (doing something with the
lowest possible input).
There are five key performance indicators (competitive priorities) most of the time you cannot be
good at everything and there needs to be a trade-off notion of trade-offs ;
Cost
Quality; performance quality (basic operating characteristics), conformance quality (made to
specifications), reliability quality (working life).
Delivery; delivery speed (how quickly can a need be fulfilled), delivery reliability (deliver
products when promised consistently)
Flexibility; mix flexibility (wide variety of products), changeover flexibility (produce a new
product, with little changeover time), volume flexibility (produce a wide range of volumes)
Sustainability; environmental sustainability (energy use, waste), social responsibility (labor
protection, addressing societal issues)
Process section
In this course two different models are used; stochastic and deterministic. Stochastic is under uncertain
circumstances, different outcomes can occur on average is a good example, since then there is
variation between the processes. Deterministic refers to the model where everything is known in
advance, ‘’the arrival rate is 3 per hour exactly’’, this happens every time, no matter the circumstances.
Important is that in deterministic models we ignore waiting line effects, even with batch production.
Capacity of a system refers to the amount of output that a specific system is capable of achieving over
a certain period of time. The period of time is essential of course, since otherwise the number would
not tell us anything about the production process.
The arrival rate is the number of products that arrive at the process per unit of time. If the inter-
arrival time is 20 minutes, the arrival rate will be 60/20 = 3 per hour or 3*24 = 72 per day. The
throughput time is the time that passes from the moment of entry and the moment at which the process
is finished.
The deterministic throughput time can simply be calculated as the sum of all the individual processing
times. If the whole production process has multiple paths, we calculate the throughput time of each
path and then multiply them by the probability that each path will be followed, then we sum this up, to
get the total throughput time.
,Design capacity is the theoretical maximum output of a system or process in a given period of time.
While, the effective capacity of a system refers to the actual capacity of a system. If a machine is 10%
of the time in maintenance, the design capacity includes this 10%, while the effective capacity
excludes the 10%.
The bottleneck of a system is the process within a system that limits the output of the system. If none
of the individual processes is the bottleneck, the arrival rate must be the bottleneck. The departure rate
will therefore always be the same as the capacity of the bottleneck.
The utilization rate is the fraction of the total time in which a machine is used for a product or service.
Utilization rate = total operating time / total time (OR) = arrival rate λ / (n)*production rate μ, n is the
amount of parallel operators.
Efficiency = actual output / effective capacity
Work in progress is the number of products that have been taken into production, but not yet been
finished. We can calculate using Little’s Law; L = λ*W (throughput time). Other estimation is as
follows; WIP = Σρi*Xi, where X refers to batch size, ρ to the utilization rate, and Σ to the sum of all the
processes within the system.
Week 2; Service processes and queuing models
Services
Every service needs a service package to be properly executed. A service package is a bundle of
tangible and intangible resources that is provided in a certain environment. Such as, supporting
facilities, facilitating goods, information, explicit services (observable), implicit services (vaguely
perceivable).
Queuing models
There are different types of queuing models; single server and single line, multi-server and multi line,
and multi-server and single line. Often the queue discipline of first come first served is used (only one
used in this course), priority is another example of a queue discipline. When observing a queue
consumers can behave differently than just standing in line;
- Balking; when a customer observes the queue and decides to leave straight away.
- Jockeying; when a customer switch between queues if they think they will get served faster.
- Reneging; when a customer enters the queue but at some point decides to leave the queue.
We discuss two different models in this course, which are the following M/M/1 and M/D/1, in both
cases there is one server. The difference between the two is the service process, for M/D/1 this is
deterministic, or known in advance. For M/M/1, this is random (negatively exponential) or stochastic.
It is important to know how to identify which model is relevant, since the formulas differ.
M/M/1 formulas and their meanings (formulas are given);
- Ls = λ / (μ − λ); Average number of customers in the system
- Ws = 1 / (μ − λ); Average time spent in the system
- Lq = λ² / [ μ(μ − λ) ]; Average number of customers waiting in line
- Wq = λ / [ μ(μ − λ) ]; Average time spent waiting in line
- P(n > k) = (λ / μ)^(k + 1); Probability of more than k customers in the system
M/D/1 formulas and their meanings (formulas are given);
, - Ls = λ(2μ − λ) / [ 2μ(μ − λ) ]; Average number of customers in the system
- Ws = (2μ − λ) / [ 2μ(μ − λ) ]; Average time spent in the system
- Lq = λ² / [ 2μ(μ − λ) ]; Average number of customers waiting in line
- Wq = λ / [ 2μ(μ − λ) ]; Average time spent waiting in line
In each formula λ refers to the arrival rate, and μ refers to the service rate (customers / hr). In most
cases the following relationship holds; Ls = λ*Ws and Lq = λ*Wq.
Week 2; First Training Session (Questions + Answers)
Question 1)
Consider the service process depicted below. What is the utilisation rate of this process?
Answer; λ = 6 per hour, μ = (60/8)*3 = 22.5 per hour Utilization rate = λ/μ = 6/22.5 = 0.27
Question 2)
Customers arrive at a ticket office staffed by only one employee. The mean arrival rate of customers is
3 per minute. The average service rate is 4 customers per minute. The arrivals follow a Poisson
distribution and the service time follows a negative exponential distribution. What is the probability of
having exactly one customer in the system?
Answer; λ = 3 per minute, μ = 4 per minute, since we know that the arrivals follow a poison
distribution and service time is random M/M/1 system relevant formula is; P(n > k) = (λ / μ)^(k
+ 1). Since this is the probability of having more than k customers in the system we can apply the
following formula; P(n > 0) – P (n>1) = P(n = 1) 0.75 – (0.75)^2 = 0.1875
Question 3)
Consider the process at an administration office where customer orders are processed. Every 3.9
minutes an order arrives. An incoming order is first reviewed in Arrival rate: 6 customers per hour
Workstation with 3 parallel employees. One employee can serve a customer in exactly 8 minutes
Training #1 Questions 2 12.4 minutes by an employee to check whether all products are available
(which can be seen as Activity 1). There are three of these employees and each order is checked by
one of them. Next, the order goes to one of three parallel operating bookkeepers to check whether the
customer has paid all past bills(Activity 2). It takes a bookkeeper 7.2 minutes to check a customer’s
payment record. Finally, the order goes to a clerk who enters the order into the company’s computer
system in 9.5 minutes (Activity 3). There are two clerks available, who work in parallel.
What is the utilization rate of the clerks at Activity 3? Support your answer with calculations.
Answer;
