Manufacturing
Planning and Control
MPC 6th Edition
Chapter 4a
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
Advanced Sales and
Operations Planning
Within the Sales and Operations
Planning (SOP) process, modeling
procedures can be used to
establish overall production and
inventory plans.
The basic issue is what levels of
resources should be provided in
each period. Powerful and easily
accessible tools are available for
solving these models.
4a-2
Agenda
What is advanced SOP?
Mathematical programming
Linear programming
Mixed integer programming
Lawn King example
Principles
4a-3
Linear Programming
Hiring Costs
m
Minim ize
 C
t 1
H
Firing Costs
Labor Costs
Overtime
Costs
H t  CF Ft  CR X t  COOt  CI I t  CUU t 
Inventory
Costs
subject to
I t 1  X t  Ot  I t  Dt
I t  Bt
Inventory
Constraints
X t  A1tWt  U t  0
Regular Production Constraint
Ot  A2tWt  St  0
Overtime Production Constraint
Wt  Wt 1  H t  Ft  0
Idle Time
Costs
Workforce Change Constraint
W0  A3
I 0  A4
Wm  A5
Initializing
Constraints
4a-4
LP Assumptions
Item
Value
Regular-time cost per employee per month
$1,828
Overtime cost/unit
$33.04
Inventory carrying cost per unit per month
$1.77
Hiring cost/employee
$800
Firing cost/employee
$1,500
Regular-time productivity (units per month per 83
employee)
Maximum overtime units/month
17
Ending inventory
≥ 2,000 units
August inventory
16,460 units
August employees
72
4a-5
LP Model and Solution
Changing
cells (decision
variables)
4a-6
LP Settings and Options
Minimize total costs
Constraints
•Ending workforce = actual (72)
•Reg. production <= capacity
•OT production <= capacity
•Monthly inventory >= 2,000
•Ending inventory (August) = actual (16,460)
•Hires/Fires must be integers
4a-7
Principles
To ensure credibility, the match between the
real world and the model should be as close as
possible.
 Relatively homogeneous product lines (or
portions of lines) allows for a closer match
between model and reality.
 Before the potential of advance techniques can
be realized, the firm must invest in training,
enhance data, improve basic MPC practices,
and determine clear objectives.

4a-8
Principles
Management must realize that significant efforts
in model formulation, understanding, testing,
and explanation are important to successful
applications.
 Advance techniques must be built on a
foundation of good basic practices.
 Spreadsheet-based models offer executives a
better choice.

4a-9
Quiz – Chapter 4a





The objective of a Linear Programming planning approach is
to ___________.
Microsoft Excel has both Linear Programming and Mixed
Integer Programming capabilities. (True/False)
A key step in the modeling process is to identify assumptions.
(True/False)
Determination of inventory holding costs is generally a simple
process with few assumptions. (True/False)
The Advanced Sales and Operations process can be
implemented as soon as a firm starts using Sales and
Operations Planning. (True/False)
4a-10