2.4
This satises all the assumptions of the EOQ model. The only nicky thing is to keep the units
consistent.
G0
D = 60 units: wk x52 wklyr = 3120unitslyr
l: I it: = 0.25fy1' X $0.02 = $0.005I'y1'
A = $12
. 'ZAD 2x12><3120
Q = = =3869.SSE3370
it 0.005
The
Additional sample questions solution:
1) Assuming task 1 is producing item 1, task 2 is producing item 4, task 3 is producing item
5, task 4 is producing item 6, task 5 is producing item 7.
Big bucket:
Minimize z t 1 i 1 cit Qit Ait Yit t 1 r 1 hrt I rt
T
Inventory Pooling
1
Distributed versus Pooled Inventory
Distribution center 1
Versus
Assembly factory
Assembly factory
Consolidated
distribution center
Distribution center 2
Retailers
2
Retailers
Examples of Inventory Pooling
Centralized warehousing (phy
The EOQ Model with
Planned Backorders
1
Demand does not have to be satisfied immediately
(from on-hand inventory).
Customers are willing to wait.
A penalty cost b is incurred per unit backordered per
unit time.
Orders are received L units of time afte
The Base Stock Model
1
Assumptions
Demand occurs continuously over time
Times between consecutive orders are stochastic but
independent and identically distributed with the exponential
distribution (i.e., the demand is a Poisson process)
Inventory is r
Inventory Control
1
Lecture Topics
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Introduction to Production Planning and
Inventory Control
Inventory Control Deterministic
Demand
Inventory Control Stochastic Demand
Inventory Control Stochastic Demand
Inv
The (Q, r) Model
1
Assumptions
Demand occurs continuously over time
Times between consecutive orders are stochastic but
independent and identically distributed with the exponential
distribution (i.e., the demand process is Poisson)
Inventory is reviewe
Inventory Control with
Stochastic Demand
1
Lecture Topics
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Introduction to Production Planning and
Inventory Control
Inventory Control Deterministic
Demand
Inventory Control Stochastic Demand
Inventory Contro
Inventory Control with
Time-Varying Demand
1
Lecture Topics
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Introduction to Production Planning and
Inventory Control
Inventory Control Deterministic
Demand
Inventory Control Stochastic Demand
Inventory Cont
IE 5551 - Production Planning and
Inventory Control
Saif Benjaafar
Department of Industrial & Systems Engineering
University of Minnesota
1
Course Objectives
Introduction to methods for managing production,
inventory, and distribution systems
Topics cover
IE 5522 Spring 2017 Homework 1
Instructions:
This homework is due in class on Jan 31 at the beginning of class.
Print your name and student ID number on the front of the homework.
You must turn in a hard copy at the beginning of class.
Your work must be l
IE 5551 Spring 2017
Assignment # 1
Due Date: February 2, 2017
1. Read Chapter 2 from Factory Physics
2. Problems 4 and 5 from Chapter 2 (Factory Physics).
3. In a system with planned backorders, suppose the parameters are: D = 1800, A = 80, h
= 0.76, b =
Solutions to Example Problems
Problem 1
Let
+
x =
x if x > 0;
0 otherwise.
(a). The random variable of unsold units is (Q X)+ , and E[(Q X)+ ] =
R
RQ
(Q x)+ f (x) dx = 0 (Q x)+ f (x) dx.
0
(b). The random variable of sold units is min(Q, X), and E[min(Q,
The Economic Production Quantity
(EPQ) Model
1
Similar assumptions to the EOQ model, except that
production/delivery is not instantaneous
Units are produced and delivered one unit at a time
Production capacity is finite with a finite production
rate P
2.4
This satises all the assumptions of the EOQ model. The only nicky thing is to keep the units
consistent.
G0
D = 60 units: wk x52 wklyr = 3120unitslyr
l: I it: = 0.25fy1' X $0.02 = $0.005I'y1'
A = $12
. 'ZAD 2x12><3120
Q = = =3869.SSE3370
it 0.005
The
Name:
IE 5551
Final Sample
1) What are the key principles advocated in the book Lean Thinking? (10 points)
2) What is the major lesson you learned about managing factories from reading the book
The Goal. (10 points)
Name:
3) The arrival rate to a machinin
IE 5551 Midterm Sample
1 Describe causes of the causes of the Bullwhip eect. How could they be addressed? Which type of rms is particularly vulnerable to the bullwhip eect? (10 points) 2 When is postponement (delayed product dierentiation) particularly us
IE 5551 Midterm Solution
4)
FFTFFFFFT
5a)
We want to find the smallest Q s.t. P( D Q) 0.85.
Since demand D is equally like distributed among 31, 32, , 50, we have
P( D x)
5b)
1
, for 31 x 50. Therefore we get Q 47.
20
Now, P( D Q ') 0.95 Q ' 49.
Q Q ' Q
8.1
(a) The mean is 5 and the variance is Ill The coefcient ol'variation is also zero. These preeess times
eotdd be from a highly automated maehine dodieatod to one product type.
{b} The mean is 5, the standard deviation is DJ 15 and the CV is 11.023. The
IE 5551
HW 3
1. Problem 15, 17 Chapter 2 (Factory Physics).
2. Solve question (a) of Problem 9, Chapter 2 (Factory Physics); use holding cost ht = 1.
3. Formulate problem 9 as a mixed integer linear program (MILP).
4. Draw the corresponding network and co
Name:
IE 5551 Production and Inventory Control
Assignment # 2
Due Date: February 16, 2017
1) Consider a perishable product whose daily demand can range from a low of 31 to a high of 50.
Demand is uniformly distributed over this range, so that sales of the