The inventory system components of resupply and storage affect performance through the factors of cost and carbon emissions, respectively. This duality between sustainability measures is extended in this section to a deeper level of detail for both cost and emission performance factors of the inventory. In particular, the factor categories of resupply and storage are each affected by different drivers. Achieving holistic decision making at the inventory level necessitates not only a consideration of various sustainability perspectives but also an accurate modeling of the associated inventory performance factors. This section is dedicated to presenting the considered drivers and the modeling of their components based on the inventory system characteristics.
4.1. Driver Identification
As highlighted previously, the main inventory aspects that affect performance are related to reordering and storage. Firstly, the factor of resupply encompasses both costs and emissions of order issue and transport. The former is related to the organizational effort needed for issuing an order to the supplier, which is enabled by costs such as personnel, software, and additional overheads. Correspondingly, carbon emissions are generated by the energy consumption in office spaces during the procurement process, constituting a fixed factor for reorder costs or emissions. On the other hand, a variable contribution to resupply emissions and costs is given by the transport driver. Freight is often a major focus within environmental sustainability, as vehicles are often highly polluting elements of the supply chain. In particular, costs and emissions depend both on the supply route and the vehicle used. Specifically, the fuel consumption of the vehicle is influenced by both the shipment size and the vehicle type, with fuel consumption hinging also on the weight of the shipment. Furthermore, the supply route impacts both the cost and emission factors for transport, influenced by factors such as travel distance and speed, which introduces another dimension to performance considerations.
Regarding the other key factor influencing inventory system performance, namely, storage, both costs and emissions are connected to operational energy usage. This portion of the storage factor encompasses drivers such as energy needed for lighting, heating, and air conditioning for ensuring favorable working conditions. Such drivers are highly dependent on different warehouse parameters and correct modeling can help identify the most impactful components on inventory performance and decisions. Furthermore, storage costs are notably affected by warehouse and material handling depreciation, stemming from the initial installation costs. This paper asserts that this holds true from an environmental standpoint as well, as carbon emissions are also a result of the warehouse installation phase. Such carbon emissions are commonly categorized under the embodied carbon measure, closely linked to the material characterization of building components. Moreover, such costs or emissions are incurred specifically for inventory, and their effect on inventory decisions needs to be considered for assessing the impact of different strategic decisions on tactical aspects like inventory control. Another closely related aspect tied to building components is the thermal characteristics of the warehouse structure, given their direct impact on the operational energy requirements for space heating.
The contribution of the presented drivers to each performance factor is summarized in
Figure 1, where the categorization is valid for both economic and environmental perspectives. This hierarchy is also followed in
Section 4.2 for the formulation of both cost and emission performance factors, which takes into considerations different components for each driver.
4.2. Factor Modeling
Based on the above discussion of inventory factors for economic and environmental performance, this section presents the proposed modeling approach for the related drivers. The aim in this portion of the formulation is to consider all the determinants for costs and emissions that are relevant for inventory decisions, with a focus on different driver components and how to estimate them.
Regarding the economic perspective, the cost factor for resupply
is modeled following the previously presented identification as a function of the reorder quantity
Q. This factor measures the cost related to each reorder, which encompasses both order issue, with a fixed contribution
, and transport. The latter (
) depends on the reorder quantity. The resulting formulation for cost per reorder
, incurred at each inventory cycle, is
The contribution of the decision variable of reorder quantity relates to the transport driver category and it is twofold. Firstly, larger order sizes might need multiple shipments depending on vehicle capacity. Secondly, transport efficiency is affected by the weight cost factor per unit distance. More specifically, the transport component is affected directly by freight characteristics as follows:
where
D is the travel distance for a single shipment,
the cost weight factor, and
the capacity of items per shipment. Additionally, the freight route has an additional impact other than distance: the travel speed. This affects the baseline cost per unit distance parameter
.
In particular, the parameter
can be estimated as being proportional to the fuel consumption via the cost per fuel volume. Following the formulation of [
34], the fuel consumption per unit distance is estimated as follows:
where
is the power required depending on vehicle speed, estimated as in Equation (
13), assuming a constant travel speed and null road angle. The other parameters are reported in
Table 2.
Moreover, the coefficients related to the transported weight for each shipment
are estimated as proportional to the contribution to fuel consumption per unit distance of every product of mass
, given by
Regarding the cost performance factor for storage
, the cost per unit time for each product stored is modeled taking into consideration the various drivers that allow for maintaining an inventory in a warehouse. These drivers make cost factors dependent on problem characteristics such as warehouse location, building characterization, and warehouse system requirements. Firstly, a warehouse needs to maintain a working environment in terms of temperature. Another operational driver considered in the storage performance factors is lighting, needed for keeping a warehouse operational. While these drivers are linked to operational aspects of the warehouse, installation costs also need to be considered through depreciation of the building and its material handling systems. The resulting cost for storage is modeled as
where
,
, and
are the overall energy requirements per unit of time for heating, air conditioning, and lighting, respectively. These contributions, linked to costs with the factors of cost per electricity
and gas
, together with installation and management costs per unit of time
, are repartitioned for a product with unit volume
v per unit over the available storage space usable for that product
V.
Regarding the first drivers for the operational category, the technique of degree days is used to estimate the energy requirements for heating a building and for air conditioning for temperature control. Degree days are defined as the sum of temperature differences between a set-point and reference temperatures [
35], and are dependent on building location due to temperature variations. CIBSE [
36] underline how the heat loss of a building, and thus, the required energy for the considered period, is directly proportional to this difference. Regarding heating, they link energy requirements via the heating degree days (HDDs) with the building heat loss coefficient
as follows:
On the other hand, for air conditioning they formulate energy requirements as proportional to the air flow rate
and air specific heat
via the cooling degree days (CDDs):
Specifically,
and
are the efficiency coefficients for the heating system and the air conditioning, respectively, and
t the total operative hours per unit time.
Moreover, according to [
36], the overall heat loss coefficient is the result of the thermal characterization of the building elements (i.e., floor, roof, walls), and the air infiltration rate
N:
In particular, each building element’s thermal conductance is given by its surface
A and its thermal transmittance
U.
Additionally, as different warehouses and inventory systems may require different lighting conditions [
37], it is important to consider this driver for the performance of the inventory in terms of both costs and emissions. In particular, the resulting energy required for a lighting system is modeled as
which links the lighting requirements of the warehousing system via required illuminance
L to the related estimated energy needs, considering a floor area
A and a luminous efficacy for the lighting system
F.
Paired with the operating cost components, the installation costs and additional management costs are another driver category. The drivers related to installation costs
are related to construction, land purchasing, permission fees, and forklift flee purchasing [
38], and are related to facility lifetime
p. Additionally, management costs
can be incurred in the considered time horizon, thus contributing to total cost per unit time:
Emission factors share similar drivers as the cost components. In particular, emissions for each resupply cycle
are again influenced by a fixed (
) and a transport component (
):
Specifically,
is the emission per unit distance, which is a function of average travel speed, and
, the weight factor that influences transport emissions. In particular, as mentioned previously, the variable of reorder quantity affects the transport emissions because of the number of required shipments, but also due to the degradation in performance related to increasing transported weight. These emission parameters for transport are estimated as proportional to the fuel consumption estimations of Equation (
12) and Equation (
14), respectively, via the carbon emissions incurred per fuel volume.
From the operating phase perspective, a warehouse contributes to the emissions of storage via the required energy for keeping it operational (i.e., for heating, air conditioning, and lighting) as follows:
where facility embodied carbon
defines the emissions per unit time related to construction and installation, and the operational drivers are related to the previously defined energy consumption of heating and air conditioning, lighting, and cold rooms via the emission factors for electricity
and gas
.
More specifically, total embodied carbon refers to the contribution of each warehouse building element
i to embodied carbon
, since each building element is constituted of different materials and quantities. The resulting contribution of this driver to the storage emissions is
where the embodied carbon of each building element depends on the related material characterization. Through the identification of the constitutuent materials of each building element, both thermal and embodied carbon characterization can be performed for the warehouse building.