This document presents two models for visualizing and understanding production in complex process facilities: the production flow network (PFN) and the production flow map (PFM). The PFN models the physical flow of materials through units like reactors, tanks, and pipelines. The PFM complements the PFN by explicitly mapping the connections between input and output ports throughout the production chain, making it easier to follow individual stock flows. Both views represent units, operations, and stocks as the basic elements of any production system and can help planners, operators and managers better understand and optimize complex multimodal production operations.

1. Production Modeling for Multimodal Operations
Jeffrey Dean Kelly1
1
Industrial Algorithms LLC., 15 St. Andrews Road, Toronto, Ontario, Canada, M1P 4C3
E-mail: jdkelly@industrialgorithms.ca

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Introduction
Understanding and modeling the production inside complex process industry facilities can be a difficult task at the best of times. In
part I we described the formulation of nonlinear planning models required to optimize production and some of the fine-points on its
mathematical modeling. The focus of part II is to highlight two views of production called the production flow network (PFN) and the
production flow map (PFM) which can help to clarify the complexities surrounding the production of any process industry facility.
There are already several techniques and devices available to aid in this endeavor however relatively little attention has been paid to
modeling the details of production when several operating modes, production activities or processing tasks exist for any given
production or processing-unit across multiple stages of production. As mentioned, the purpose of this article is to present two distinct
and complementary views of the production system in context with both the physical and functional aspects of the production or
manufacturing. These new views engage the spatial framework or the material-flow-path of the production as opposed to its
hierarchical decision-making (i.e., planning, scheduling and control) and its temporal dimensions (i.e., years to months to weeks to
days, etc.).
Any manufacturing or production environment can be modeled using three fundamental objects or constructs and they are units,
operations and stocks. Units represent the physical equipment which support the production and includes such objects as reactors,
fractionators, heat exchangers, tanks, spheres, warehouses, pipelines, cranes, pumps and compressors. Units are considered to be
renewable resources which may also include manpower and tools or even catalysts. Operations are the functional activities, tasks or
instructions performed by the units. Every unit must be assigned to at least one operation over its life-time else it is considered to be
redundant. Stocks are the feedstock, intermediate, work-in-progress and product materials being either mixed, separated and/or
transformed inside the units in a particular operation. Stocks are considered to be non-renewable resources because they are consumed
and produced by the unit-operations. Other examples of stocks include chemicals and utilities such as caustic soda, corrosion
inhibitors, flow improvers, air, water, steam, electrical power and fuel. Effluents and emissions of hazardous materials or by-products
are also considered as stocks but are dealt with in different ways (i.e., incinerated, treated, scrubbed, etc.)
From the perspective of modeling the complete production scenario inside a process industry facility, several tools and methodologies
are available which involve all aspects of the facility’s life-cycle from its conception, design and construction to its planned, scheduled
and controlled operation. These include the well-known practices of critical path methods (CPM), program evaluation and review
techniques (PERT) (Rardin, 1998), process flow diagrams (PFD) (or flow-sheets), piping and instrumentation diagrams (P&ID),
Gantt (or time-line) charts, disjunctive graphs, throughput charts (Pinedo, 1995), schedule-graphs (Sanmarti et. al., 1998), string
diagrams (Newman et. al. 2002), recipe networks (Mauderli and Rippin, 1979 and Wang et. al., 1997), state-task network (STN)

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(Kondili et. al., 1993), resource-task network (RTN) (Pantelides, 1994) and the state-equipment network (SEN) (Yoemans and
Grossmann, 1999). All of these methods can in some degree be applied to both continuous and semi-continuous (CSC) and batch and
semi-batch (BSB) type processes including processes which have convergent and divergent material-flow-paths. CSC processes are
characterized by continuous (concurrent, simultaneous) and non-accumulating flow of material through their boundaries whereas BSB
processes have batch (consecutive, sequential) flow implying some level of flow accumulation to occur. Convergent or Leontief
processes have many input or feed streams and only one output or product stream (i.e., co-feeds, mono-product) whereas divergent
processes have one feed stream and many product streams (i.e., mono-feed, co, joint and by-products). Obviously hybrid processes
involving both convergent and divergent flows can also be easily accommodated. The next two sections to follow detail the PFN and
PFM which are intended to provide distinct and informative views on the production.
Production Flow Network (PFN)
The first view to describe is the PFN. An example of a small process industry plant is shown in Figure 1. There are several distinctive
unit objects drawn which are the parcel (inverted triangle), pool (triangle), continuous process (vertical rectangle), batch process
(vertical rectangle partially filled), perimeter (diamond) and pipeline-units (horizontal rectangle). The collection of all units,
operations and stocks is known as the plant. The continuous and batch process-units are flow consumers and producers where batch
process-units, parcel-units and pool-units all contain inventory or hold-up and are the flow accumulators of the production. Pipeline-
units are assumed to always be full so flow accumulation is not expected which implies no change in the total amount of transit-stock
although parcel-unit inventory can affect the transit-stock position. The notions of safety and cycle-stock then apply to the batch
process-units and pool-units only. The bolded arrows denote external streams which can only be connected by what are known as inlet
and outlet port-units (circles); these are the flow interfaces to and from other units. The smaller arrows attached to the other units are
referred to as internal streams whereby process yields can be attached for example when modeling the behavior and effects of the
processes on the product stocks. Both external and internal streams carry the flow of stocks.

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Parcel
Port with
Internal Stream Pool Continuous Process PerimeterBatch Process Pipeline
Multi-Process
Multi-Product
Multi-Plex
External Stream
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
B
A
B
C
D
E
A
AA
A
B
Figure 1. Production Flow Network for a Small Plant Example.

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The PFN is very similar in spirit to the PFD and in the chemical engineering literature this is sometimes referred to as a superstructure
as opposed to a network given the temporal intermittent nature of the unit-operations. However in the PFN, explicit representation of
the operations are shown which is absent in the PFD. We decompose the operations into three functions and they are called modes,
materials and moves. Modes are operations in or on process-units and perimeter-units and can be both productive and non-productive
activities. These modes are used to effectively discretize the operating region of the units as a function of feed and product quantity
and quality and processing conditions such as temperatures and pressures; within any given mode, the yields of products for example
are assumed to be relatively constant or interpolate linearly in a base plus delta fashion. Materials are operations in or on parcel-units,
pool-units, pipeline-units and port-units such as the material-service of a swing tank. Moves are the transfer or movement operations
between an outlet port-unit and an inlet port-unit. Each of the operations also have transitioning details associated such as sequencing,
start-up, stand-by, switch-over and shut-down events. There can also be ramp-down and ramp-up operations just before a unit-
operation is shut-down and just after it has started-up which effectively turns-down the flows in and out of the equipment in order to
lessen the impact or disruption of the production event on downstream units or utility providers.
The dotted-line boxes surrounding selected units indicate that a particular unit is multi-purpose. Multi-purpose means that it can swing
from one operation to another although if the renewable resource is not of the shared-type then it can only perform one operation at a
time (i.e., unary or single-use); an example of a shared resources is a parcel-unit which represents a marine-vessel with multiple holds
or compartments. Process-units which are multi-purpose are called multi-process meaning that they have multiple modes. Pool-units
are said to be multi-product if they can store more than one product but not at the same time. It should be noted that the logic or
operating rule when swinging-over any material-service on a tank for example must ensure that the heel inventory is below a certain
threshold quantity specified for safety and contamination reasons. Outlet ports can be of the multi-plexed type if one or more
concurrent flows can be accommodated at any given time; inlet ports can also be multi-plexers. The objects contained inside the
dotted-line boxes become what are known as unit-operation pairs or tuples. They represent the virtual, logical or implicit views of
either the meta-physical or meta-functional dimension of the production. The prefix “meta” is used to describe the metaphor or image
that the physical objects can co-exit at least notionally with their meta-physical (or meta-functional) counter-parts. It should be pointed
out that if a particular unit-operation is not scheduled or operated, then all of the external stream flows in and out are forced to zero.
In contrast to the recipe and state-task networks which are used quite extensively in the batch processing industries for planning,
scheduling and executing production for specialty chemicals, pharmaceuticals and other relatively low-volume but high-valued
products, the PFN should be considered as a complement in the sense that it views production more along the lines of the equipment
units and material flow and not strictly from the point view of the recipe or process structure. In recipe networks, equipment or units
are not explicitly shown until a final control recipe is derived (ISA, 1995). Instead the sequence of functional operations (sometimes

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referred to as a process) is charted with specific ingredient amounts or intensities attached where necessary when material flow is
represented. Hence, recipe networks are more functional than physical. On the other hand, the PFN shows the production from the
perspective of the meta-physical or unit-operations also in the context with the flow of stocks. Moreover, in contrast with the job-shop
or flow-shop scheduling found in the discrete-parts manufacturing industries (Pinedo, 1995) which utilize disjunctive graphs, the PFN
as mentioned shows the flow of materials explicitly. Disjunctive graphs on the other hand, albeit are meta-physical in the sense that
they show both the operations (jobs) and units (machines) on one diagram, do not depict the flow of the parts being manufactured or
operated on.
Production Flow Map (PFM)
The second view is the production flow map which is almost identical to the PFN in terms of information yet it can be a little easier to
navigate and modify (or augment) than the PFN especially for large production instances which may also include not just the
production-chain but also the other supply and demand-chain physical and functional objects. Figure 2 provides the PFM for the same
small but representative plant example.
Feed or Inlet-Side
Product or Outlet-Side
1 2
3
4
5
7
6
8 10
11
12
13
14
159
A B A B
A B
A
C D E
A A
EDCA
BA
BA
Figure 2. Production Flow Map for the Small Plant Example.
The same objects are used except that the unit-operation tuples are split into their feed and product-sides. Product-sides have attached
the outlet ports whereas feed-sides have the connected inlet ports. The idea is to present each of the sides on opposite ends of the view
where it is equally valid to have the products on the left and the feeds on the right and visa-versa. Furthermore, the order of the
product-sides and feed-sides in terms of the meta-physical object placement can also be arbitrary (i.e., the order or sequence of unit-

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operations inside the respective feed or product-sides can be specified). The PFM is useful because there is no retention of a spatial
material-flow-path concept or structure as in the PFN. The PFM’s prime objective is to show the explicit mapping of outlet ports to
inlet ports throughout the entire production-chain setting clearly and succinctly. This is of value when it is necessary to focus on a
particular stock or related set of stocks when in the PFN the stream flows can be very far apart spatially in the network making
graphical navigation cumbersome. Consequently, the PFM should be considered as more of a stock-specific or focused view whereas
the PFN is more of a unit-operation-specific view (thus the complementary relationship between them). To make this more evident
consider an oil-refinery where the production is sometimes demarcated along the lines of clean or white-oil product versus dirty or
dark-oil product, then the PFM could be used as a helpful tool to model and monitor the daily stock flows for both related oils in the
plant separately in different views or in the same view just positioned at different locations in the map. The PFM can also be used to
represent certain distributed products inside a supply or demand-chain whereby the product-side can represent the supply-side
producers or suppliers and the feed-side can represent the demand-side consumers or customers. This would enable the individual
product-lines (or groups of stocks) for a particular market to be shown easily. Without the PFM, a large flow network view can be
constructed with the unavoidable result of many overlapping and crossing flow lines making the picture somewhat difficult to trace
what supplier is delivering what material to what customer. This is mostly avoided in the PFM because there is a single assignment or
association of one supplier flow of stock to one customer where the spatial representation of the material flow context is abstracted.
Summary
Presented in this brief article are some of the fine-points around the production details found in all process industry plants. The focus
of this paper has been to delineate several of the most fundamental concepts underlying production and manufacturing. Two novel
views, the production flow network and the production flow map are shown which can aid any planner, scheduler, process engineer,
operator and manager in more effectively understanding, formulating and stewarding his or her production responsibilities.
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