L’article intitulé « Integrating electric energy cost in lumber production planning » est inséré dans cette section du mémoire. Il a été soumis le 15 décembre 2017 à la conférence « MIM : Manufacturing Modeling, Management, and Control » et sera présenté à la 9e édition de cette conférence le 28 août 2019 à Berlin,
Résumé
Cet article présente un modèle de planification tactique, spécialement développé pour l’industrie du bois d’œuvre, intégrant le coût de l’énergie électrique dans le processus de décision afin de minimiser la consommation d’électricité. Le modèle calcule la consommation d'énergie en fonction de la puissance nominale de l'équipement, du moment auquel l'équipement est utilisé et d'un facteur de charge. Cela inclut également l'énergie utilisée pour chauffer ou refroidir les espaces de travail. En utilisant les données réelles d'une scierie nord-américaine recueillies d'août 2017 à juillet 2018, le modèle a montré qu'avec un facteur de charge calculé pour chaque mois et une bonne approximation de l'énergie de chauffage consommée, la consommation totale d'électricité calculée est proche de celle facturée par le fournisseur d'électricité. Ainsi, l’outil de planification tactique pourrait maintenant être exploité par toute scierie cherchant à intégrer le coût de l’énergie dans la planification de sa production.
Abstract
The arrival of digital technology in production systems represents a major challenge for manufacturers. The "4.0 Industrial Revolution" is pushing companies to review these same systems in order to develop decision-making tools that contribute to better capture any relevant opportunities while increasing profitability. In this context, this article shows a tactical planning model, specially developed for the lumber industry, integrating the electric energy cost in the decision process in order to minimize electric energy consumption. The model calculates the energy consumption based on equipment nominal power, the time at which the equipment is used, and a certain load factor. It also includes the energy used to heat or cool workspaces. Using real data from a North American sawmill collected from August 2017 to July 2018, the model showed that with a load factor calculated for each month and a good approximation of the heating energy consumed, the total energy consumption calculated is close to the one billed by the electricity supplier. Hence, the tactical planning tool could now be exploited by any sawmill aiming to integrate energy cost as a decision variable in its production planning.
Introduction
The manufacturing sector is one of the largest energy consumers in the world. In the last fifty years, its consumption has increased drastically and it now consumes about half of the world’s total energy produced (Liu et al., 2014). Most of the time, the sources of energy used are not renewable (Andruleit et al., 2013). Thus, in order to reduce their ecological footprint, several companies put in place various decision-making tools integrating the energy facet, which allows them to maintain better control over it.
In Canada, the lumber manufacturing sector is an important energy consumer, with more than 126,009,913 GJ consumed each year (Government of Canada, 2018). In the Province of Quebec, Canada, there are more than 194 sawmills in operation (Government of Québec, 2017) and they play a major role in the economy of the Province (Transition énergétique Québec, 2017). In 2013, their energy supply during the manufacturing process was divided as follows: 55% came from wood (in the form of biomass to supply steam to the dryers), 22.6% from electricity, 17.2% from natural gas and 5.1% from other sources (Government of Canada, 2017). The energy cost for this industrial sector is particularly significant and could certainly be reduced by taking it into account during the production planning phase.
Furthermore, with the advent of the 4.0 industrial revolution, companies are looking for more efficient and smart ways to optimize their production planning processes. In many cases, companies achieve their goal by developing agile, distributed, and reconfigurable production systems (CRISI de l’Université Laval, 2017). Hence, the aim of the article is to integrate the electric energy cost in a lumber production planning model, in order to get an efficient production plan while optimizing the energy management. Linear programming models are often interesting avenues to solve this kind of problem. The sales and operations planning linear model developed by Marier et al. (2014a) to plan lumber production was therefore chosen and adapted to include energy-intensive production processes, the calculation of the energy consumed by these processes, and the costs generated by this consumption. Hence, this new tool allows operation planning in a sawmill integrating the energy facet.
The article is divided as follows. Section 2 first presents a literature review to summarize how companies can include energy consumption in their production planning as well as the existing planning tools for the lumber industry. The problem investigated in this article is explained in Section 3. Section 4 introduces the results obtained when integrating energy consumption in the production planning for lumber production. Finally, a brief conclusion is presented in Section 5.
Literature review
This literature review focuses on ways to introduce energy cost in a production planning model and on planning models developed during the past years for the lumber industry. The articles considered were extracted from the Engineering Village database using keywords related to lumber industry, operation planning, energy, and methods to calculate energy consumption. This database was chosen because it allows access to high level scientific research in engineering.
Optimization models minimizing energy consumption
This section describes optimization planning models aiming to minimize the energy consumption in production systems. Two models are presented since both of them have the same objective as the one pursued by our research: minimizing energy consumption while maximizing the number of produced outputs.
Choi and Xirouchakis (2014) developed a holistic approach based on a multi-criteria objective function to minimize the energy consumption of certain departments in a factory while maximizing the number of outputs produced. They showed that a perfect multi-objective solution that simultaneously optimizes each objective function is almost impossible. This is why they created nine scenarios and compared them with each other in order to prove the necessity and the practical applicability of the developed approach. Each scenario represents a system configuration consisting of machine tools, automated material handling devices, load/unload stations, and pallets.
Liu et al. (2014) proposed to minimize the energy consumption and the total weighted tardiness in job shops. Results showed that with the use of their model and the multi-objective optimisation algorithm NSGA-II, the energy consumption decreases greatly, but at the sacrifice of its performance on the total weighted tardiness objective up to a certain level. However, the model developed is still useful in cases where it is possible to relax the part concerning the tardiness (as in a real workshop).
In both models, energy consumption is calculated according to the method proposed by Thiede et al. (2012). They proposed a methodology focusing on the energy consumption of each piece of equipment involved in the production process. It encompasses three main steps. The first two steps consist in generating a list of all the equipment needed to manufacture the products (step 1) in order to determine their nominal power (step 2). These data can be found in all technical books provided by the supplier of the equipment. Nominal power is known to be higher than the power consumed during the production process, but it serves as a basis when it is impossible to use more accurate measuring devices. Step 3 requires determining the operating time of each
equipment depending on the product manufactured. Once the data are collected, it becomes possible to evaluate the energy consumption (kWh) of each equipment for each of the products manufactured by using (2):
(2)
where NP is the nominal power of the machine (kW) and t is the operating time of the machine (hours).
The Ministry of Natural Resources Canada (2004)pointed out that when the motors used have a high efficiency, as is the case for the lumber industry, the energy consumption approximation should include a load factor between 60% and 75% and then be calculated by using (3):
(3)
where LF is a load factor (%).
Existing planning model in the lumber industry
The lumber production process is described as divergent: one log will systematically lead to the production of several products, some of them being associated with a demand while some others having to be kept in stock for possible upcoming orders. For this reason, various authors have proposed mathematical models that facilitate the tactical and operational planning of lumber production.
For example, Marier et al. (2015) developed an integer programming model for lumber drying that dynamically generates loading patterns respecting the capacity of the dryers. The model identifies, for a particular dryer, which drying process will be used, how many bundles of different lengths will be placed on each row of each rail, etc. Marier et al. (2014b) proposed a mixed-integer programming model for lumber planing. The goal is to propose a production plan that minimizes inventory costs, order delays, maintenance and production costs.
Marier et al. (2014a) furthermore developed a tactical planning model to define which unit or group of business units of a same company should be responsible for the execution of the different lumber production operations and which resources or groups of resources in those business units should be used. It also specifies the constraints to be respected in terms of production and distribution deadlines, lot sizing, and inventory policies, while taking into account the lumber selling price fluctuation on the market. Any sawmill using such a model may
W
=
NP t
However, the model does not take into account the energy consumption cost associated with the production process. The next section introduces how such a model has been adapted to integrate the energy facet.
Problem definition and mathematical model
In this section, a description of the problem investigated is first given, followed by a description of the model developed and the hypotheses made.
Problem definition
In the forest products industry, energy is typically perceived as a cost that cannot be managed. Operations planning is therefore conducted without taking into account the energy associated with the production process. In the Province of Québec, Hydro-Québec, a publicly owned utility, has been offering a demand response (DR) program since 2016 for small and medium commercial and industrial customers who are able to reduce their load between 6h-9h AM and 16h-20h PM in the winter season. A financial compensation of 70 Can-$/kW-year is offered to program participants. Without any knowledge of how to include the energy as a decision variable in their production planning, it is difficult for forest products companies to evaluate the opportunities of participating in the DR program of their local utility. In this context, this article focuses on the adaptation of a planning model for lumber production in order to integrate the energy consumption. Since developed a lumber production planning model adapted to the Quebec sawmills’ reality, this linear programing model has been selected and modified so as to integrate the most energy-intensive processes, the energy consumption associated with the production processes, the one related to workspace heating and the energy costs as a decision variable. Since Marier et al. (2014a) developed a lumber production planning model adapted to the Quebec sawmills’ reality, this linear programing model has been selected and modified so as to integrate the most energy-intensive processes, the energy consumption associated with the production processes, the one related to workspace heating and the energy costs as a decision variable. The following subsections show how the main objective was achieved.
Adapting an existing model and gathering equipment nominal electric power data
The initial planning model of Marier et al. (2014a) took into account sawing, drying and planing operations for lumber production. It was possible to note that certain energy-consuming activities were not part of the model, such as debarking and shredding. These activities were added to the model. By looking into the reference books associated with the equipment performing these operations, it was therefore possible to find their nominal electric power consumption. The sawmill considered for the study encompasses one debarker (~530 kW), one shredder (~190 kW), one sawing line (~2900 kW), five dryers (between ~40 kW and ~260 kW) and one planing line (~1165
kW). The sawmill considered manufactures nearly 300 different types of product per year, which explains the necessity of a production line like the one mentioned above.
Once these data were collected, it was possible to add the electric energy facet into the model. Different sets, subsets, parameters and variables were therefore defined to calculate energy consumption and cost. The list below summarizes these additions to the model (bolded terms) and the terms that are important to understand the aim of the model.
Set and subset: N Mills n. n ∈ N;
S Supply sources s. s ∈ S;
Sn Supply sources s of mill n. s ∈ Sn;
P Products p. p ∈ P;
A Production activities a. a ∈A;
An Production activities a of mill n. a ∈ An;
M Market m. m ∈ M; K Transport mode k. k ∈ K;
Rok,p Possible roads of the product p by transport mode k between mills n and n’.(n,n’) ∈ Rok,p;
MO Months of the year mo.mo ∈ MO;
SMO Subset associating each period t to a specific month of the year mo. (t, mo) ∈ SMO.
Parameters:
T Number of periods t included in the planning horizon; αm,p,t Selling price of a product p to a market m at a period t;
𝐶𝑠,𝑛,𝑡𝑎𝑝𝑝 Supply cost from source s to node n in the period t; 𝐶𝑎,𝑛,𝑡𝑝𝑟𝑜 Production cost of activity a ∈ An in the period t; 𝐶𝑚,𝑝,𝑡𝑖𝑚𝑚 Inventory holding cost of product p at mill n in period t;
𝐶𝑛,𝑛𝑡𝑟𝑎′,𝑘,𝑝,𝑡Transport cost of a product p through a road (n, n’) ∈ Rok,p by a transport mode k at the period t;
δe,a,n Resource capacity used by activity a ∈ An;
NPe Nominal electric power of resource type e;
LFmo Load Factor per month mo;
CECt Electric energy consumed to heat the workspaces at period t;
C1 Energy cost beyond 210,000 kWh (0.037 Can-$/kWh);
BigM Big Number (10,000,000).
Variables:
Vm,p,t Quantity of product p sold from mill n to market m at period t;
Rs,n,t Quantity received from source s to mill n in period t;
La,n,t Number of times that the activity a is launched in period t;
In,p,t Inventory of product p at mill n at the end of period t;
Tn,n’,k,p,t Quantity of product p transported by mode k through road (n,n’) ∈ Rok,p in period t;
CTmo Total electric energy consumption per month mo;
CMmo The consumption gap to reach LE per month mo;
CPmo The consumption portion beyond LE per month mo;
Zmo 1, If CTmo is beyond the threshold per month mo
0, Otherwise;
𝑪𝒎𝒐𝒆𝒏𝒆𝒓 Energy cost per month mo.
The adapted lumber production planning model aims to maximize the profit. Thus, it considers sales revenue as well as supply, production, inventory, transportation and energy costs (4).
(4)
The model is subject to various constraints namely production and distribution deadlines, lot sizing, supply and transportation limits, inventory policies and product flow balance. The mathematical equations of the basic model are presented in Marier et al. (2014a)’s paper.
To calculate the electric energy consumption for production activities, it is necessary to determine the operating time of machinery. This time can be calculated by multiplying the parameter δe,a,n with the variable La,n,t. It is also
important to note that the air conditioning and workspace heating of the plant also rely on electricity, so these costs need to be included as well. Hence, with this data, it is possible to calculate the energy consumption per month (5). (5) , , , , , , , , , , , , , 1 1 1 , , , , , ', , , , ', , , 1 1 ( , ') n n k p T T T app pro m p t m p t s n t s n t a n t a n t t p P m M t n Ns S t n Na A T T
imm tra ener
n p t n p t n n k p t n n k p t mo t p P n N t p P k K n n Ro mo MO Maximize
V
C
R
C
L
C
I
C
T
C
= = = = = −
−
−
−
−
, , , ,(
(
))
n mo mo e e a n a n t t e E n N t SMOa A t SMOCT
LF NP
L
CEC
=
+
moMOIn Quebec, sawmills are charged for electricity under a specific tariff option (i.e. M-type tariff). This tariff for the April 1rst 2018 – March 31th 2019 period stipulates that the first 210,000 kWh consumed each month must be
billed at 0.0499CAD-$/kWh and the remainder at 0.0370CAD-$/kWh. Customers are also billed for power, i.e. they must pay either 90% of the apparent average power or the power peak achieved (real) during the month depending on the maximum between these two values. However, for the sake of simplicity, problem modeling was limited to energy consumption cost and cost associated to the monthly peak power demand was neglected.
In this case, two situations can occur: one where the total monthly consumption is below 210,000 kWh (i.e., Case 1 in Figure 6) and one where it exceeds it (i.e., Case 2 in Figure 6).
Figure 6: Energy cost versus energy consumption for a M-type tariff option
From a mathematical point of view, this relation can be expressed by (6), as shown in Figure 6. On one hand, if the total energy consumption is higher than LEmo (~210,000 kWh), the difference CPmo must be added. On the other hand, if the total energy consumption is less than LEmo, CMmo must be subtracted.
(6) Equation (7) forces the Zmo decision variable to be one in the case where the total energy consumption is greater than the threshold. Equations (8) and (9) ensure that when CPmo takes a value, CMmo equals zero and the opposite. (7) (8) (9) mo mo mo mo
CT
=LE
+CP
−CM
moMO(
)
mo mo moCT
LE
+
BigM Z
moMO mo mo CP BigM Z moMO (1 ) mo mo mo CM LE −Z moMO(10) In this way, the electric energy cost may become a part of the planning process for lumber production. However, some assumptions had to be made to calculate the total energy consumed by the production process. The next subsection summarizes the hypotheses made.
Hypotheses
Since Hydro-Québec has implemented the communicating meter, commercial and industrial customers can now download their own energy data through a secure and personalized web portal called “Business customer space”. Within the agreement of the industrial partners of the project, 15-minute energy consumption data were retrieved from this portal from August 2017 to September 2018. The first hypothesis concerns the electricity consumption for heating workspaces. This data was separated into two categories, the production days and the non-production days. The production days, for the sawmill considered, are the weekdays excluding Friday. The non-production days include Fridays, weekends, holidays and annual vacation days. It is worth mentioning that in the case of production days, the break and dinner hours were removed in order to have a more realistic energy portrait since the model does not take into account these hours. Thus, two graphics were obtained (Figure 7, Figure 8). Standardized values were calculated by using (11):
(11) where x are the observations, and are the mean and the standard deviation of all observations.
Figure 7: Standardized electricity data obtained for production days 1 2 ( ) ener mo mo mo mo C =C CT +C LE −CM moMO
(
)
Standardized Value
x
−
=
Figure 8: Standardized electricity data obtained for non- production days
Based on these figures, it is possible to calculate polynomial regression curves which give a good approximation of the electricity consumption for the mill according to the temperature. In both cases, the heating electric energy is calculated using the area below the curves. Thus, based on an average temperature for the last years measured near the sawmill, it is possible, for each day of the year, to approximate the electric energy consumption caused by workspace heating. Thus, based on an average temperature for the last years measured near the sawmill (Simulation énergétique des bâtiments, 2018), it is possible, for each day of the year, to approximate the electric energy consumption caused by workspace heating.
The second hypothesis concerns the load factor. Usually, the electricity supplier approximates the load factor around 75%. However, according to Natural Resources Canada (2004), the load factor can vary between 60% and 75%. After some tests for a couple of months, using a constant 75% load factor and another one of 60%, significant differences were observed between the theoretical energy consumed and the energy charged by the electricity supplier. As a result, for each month of the year, the load factor was adjusted in order to get as close