The proposed optimization model has been applied to the design of a R-AS/RS for frozen palletized food to be maintained at −23 °C, located in the province of Pordenone in north-eastern Italy (latitude 45.8°, longitude 8.6°). The required storage capacity is 4800 unit loads (on standard ISO1 pallets) with a throughput of 45 units/h.
In the following
Section 4.1 results of coupling the R-AS/RS with a PV system for the reference case are assessed, when the objective function to be minimized is the yearly total cost of the facility. In
Section 4.2 the minimization of energy withdrawal from the national grid is, instead, discussed. Finally, in
Section 4.3 the impact of supply chain decision variables on configuration and performance of the R-AS/RS is derived, to trigger a virtuous cycle towards the sustainability of the whole cold chain.
4.1. The Reference Case: Minimising Yearly Total Cost
Table 3 reports the design characteristics and performance of the optimal configuration that minimizes the yearly total cost of the refrigerated warehouse with and without a PV plant. The introduction of the PV system does not affect rack configuration of the R-AS/RS. The same number of columns, levels, aisles, and lane depth are selected. The trade-off between increasing the available PV surface to enhance power generation and compacting the storage volume is highly affected by the high investment cost of vertical elements (rack frames and cranes, especially), leading to the same vertical height and one aisle in both configurations. The introduction of the PV plant affects positively the yearly cost, which is reduced by 1.3%, and allows a reduction of the electricity demand from the grid of 16.4%. Thus, PV adoption increases the sustainability of the refrigerated facility, positively affecting both economic and environmental performance.
Considering the yearly cost structure of the optimal warehouse configuration without a PV plant reported in
Figure 3a, it can be noticed that the energy costs account for 31.2% of yearly total cost, with refrigeration requirements playing the major role (see
Figure 4a). The refrigeration plant results to be the most expensive component, accounting for 30.9% of the yearly total cost. The costs of AS/RS (i.e., rack, cranes, and satellites) and building are similar, being 16.7% and 16% of the yearly total cost, respectively. Finally, maintenance and land costs play a minor role accounting just for 2.4% and 2.8% of the yearly total cost, respectively.
The impact of the introduction of the PV plant on the yearly total cost can be observed in
Figure 3b. It is worth noting that the energy cost is reduced from 31.2 to 26.4%, while the maintenance cost is increased from 2.4 to 2.8%. The cost of the PV plant accounts for 3.5% of the yearly total cost. The remaining costs are slightly increased.
Figure 4a shows the structure of the electricity demand for the optimal solution of the reference case. The refrigeration equipment absorbs 79.2% of the electricity demand, thus representing the most energy intensive component of the refrigerated warehouse. The auxiliary equipment (i.e., fans) and the movement equipment (i.e., cranes, satellites, and trucks) use 10.1% and 8% of the electric energy demand, respectively. Electricity demand of lighting accounts just for 2.8% of the total energy required. The refrigeration load structure is reported in
Figure 4b; we can observe that the product cooling covers nearly half refrigeration load, while transmission load and infiltration load represent 23.7% and 19.3%, respectively.
Figure 5a shows the typical daily profile of the grid power demand of each month when the PV is not installed, ranging from a minimum value of 69.9 kW to a maximum value of 95.9 kW. The impact of the PV plant is shown in
Figure 5b; the grid power demand is always positive, meaning that the power generated by the PV plant is entirely absorbed by the warehouse. During the peak hours of the summer months (i.e., from 11 a.m. to 1 p.m. local time), the PV plant can reduce the grid power demand up to 66.9%, while during winter months the reduction of energy withdrawal from the grid can achieve 30.7%. These savings can be related to the similar pattern of refrigeration requirements and PV-based power generation, both increasing with high outdoor temperatures and sunny conditions. Therefore, PV generation can cover a significant portion of energy requirements during peak hours, thus positively contributing not only to the facility energy self-sufficiency, but also to grid balance and associated GHG emission reduction. With regards to the overall electric energy withdrawal from the grid, the decrease due to PV installation varies from the minimum value of 8.8%, reached in January, to the maximum value of 20.4%, achieved in July, while the average reduction of grid electricity demand is about 16.4%.
4.2. The Reference Case: Minimizing Energy Demand from the Electric Grid
Table 4 reports the optimal configuration of the R-AS/RS with and without a PV plant, when energy demand from the electric grid is minimized. In this case, the introduction of the PV plant greatly affects the configuration of the refrigerated warehouse. In particular, the number of levels is halved, moving from 10 to 5, while the number of aisles is doubled. When PV is not adopted, vertical space is fully exploited, taking advantage both from crane movements and reduction of lost space refrigeration due to compact rack (maximum depth, one aisle). Since the cost of rack vertical frames and cranes increasing with rack height is not taken into account by the energy-based objective function, the selected configuration presents more levels than the minimum cost one (see
Table 4), moving from 6 to 10 levels. The need to enhance PV power generation to counterbalance energy requirements, instead, leads to extend the available surface on the roof for PV panels installation by adopting two aisles (and two cranes), disregarding the related high investment costs. This PV minimum energy solution is characterized by a yearly total cost increase of 11.9% with respect to the R-AS/RS without PV plant, while energy withdrawal from the grid is reduced by 13.1%. In the case of minimum energy consumption, the introduction of PV generation highly affects the environmental performance of the refrigerated facility, but from the economic point of view energy savings are not able to counterbalance the higher investments on AS/RS rack and machines needed to extend roof surface, as in the minimum cost one.
The yearly cost structure of the optimal solution minimizing the grid electricity demand when a PV plant is not installed is shown in
Figure 6a. In this case, the energy costs account for 29.5% of yearly total cost, with refrigeration requirements playing the major role (see
Figure 6a). The refrigeration plant results to be the most expensive component, accounting for 30.8% of the yearly total cost. Compared to the optimal solution minimizing total costs, in the optimal solution minimizing the grid electricity demand the costs of AS/RS equipment (i.e., cranes, satellites and trucks) and building have a major impact, being respectively 19.3% and 16.4% of the yearly total cost. On the contrary, maintenance and land costs further reduce their impact reaching 2.2% and 1.9% of the yearly total cost, respectively.
The yearly cost structure of the optimal solution minimizing the grid electricity demand when using a PV plant is shown in
Figure 6b. In this case, the shares of energy and refrigeration plant costs are reduced to 21.7% and 29.7%, respectively, while the other cost shares are increased. In particular, the impact of the AS/RS equipment costs moves from 19.3 to 21.7% of the yearly total cost. This significant cost increase is mainly due the additional crane required to serve the second aisle.
Figure 7a shows the structure of the electricity demand for the optimal solution minimizing grid electricity and using a PV plant. Compared to the optimal solution minimizing total cost and adopting PV power generation, the share of the AS/RS equipment energy is lower, passing from 8% to 6%. The shares of the refrigeration and lighting energy are slightly increased, moving from 79.2% to 80.3% and from 2.8% to 3.4%, respectively. From the structure of the refrigeration load showed in
Figure 7b it is worth noting that the share of the transmission load increases from 23.7% of the optimal solution minimizing cost and using PV (see
Figure 3b) to 26.5%. This increase in the transmission load is due to the extended surface of heat exchange, which moves from 5412 m
2 of the optimal solution minimizing cost to 6239 m
2 needed to fully exploit PV generation in the minimum energy configuration one.
The typical daily profile of the grid power demand of each month of the optimal solution minimizing the grid electricity demand without PV is shown in
Figure 8a. In this solution, the minimum and maximum values of the grid power demand range from 65.3 kW to 90.1 kW; these values are slightly lower than the respective values of the optimal solution of minimum yearly total cost without PV adoption.
In
Figure 8b grid power demand is always positive, meaning that the electricity produced by the PV plant is entirely absorbed by the warehouse facilities. By comparing the optimal solutions minimizing the grid electricity demand without and with the PV plant, it can be highlighted how PV generation can reduce the grid power demand up to 75% during the peak hours of the spring months and 43% during winter months. With regards to the demand of electric energy from the grid, the reduction associated with the installation of the PV plant varies from a minimum value of 10.7%, reached in January, to a maximum value of 24.7%, achieved in July, with an average value of 13.1% along the year.
Finally, we can conclude that coupling a R-AS/RS with PV power generation by adopting a cost minimization perspective leads to enhance the sustainability of the refrigerated facility embracing both the economic and energy saving dimensions. Introducing PV generation in the cost minimization perspective leads to better performance than just minimizing energy requirements without renewables. Comparing results in column 2 of
Table 3 with results in column 1 of
Table 4 it can be highlighted a cost reduction of 2.8% and an energy demand decrease of 10.8% gained by the min cost solution with PV installation with respect to the min energy solution without renewables. Thus, fostering renewables into storage phases reveals to be an effective way to enhance overall sustainability of the whole cold chain.
Otherwise, adopting PV from the energy requirements minimization perspective leads to further 2.6% of relative energy savings with respect to the cost minimization configuration (compare column 2 of
Table 3 and
Table 4) but with a relative yearly total cost increase of 15.1% due to higher investments. However, this cost increase could be sustained by public institutions to achieve SE4All objectives. In this case, the proposed model can be used by policy makers to properly quantify subventions.
4.3. Sensitivity Analysis on the Reference Case: Energy Price Impact
The impact of electricity price on the warehouse costs has been assessed by varying the reference price of 0.148 €/kWh [
39] up to ±50% and considering three different operating time windows per day at a constant pace of 45 cycles per hour: 24, 16 and 12 h.
The relative difference between the yearly total cost of a refrigerated warehouse with PV (
) and one without renewables introduction (
) is calculated as in Equation (12) and reported in
Figure 9a. It is worth noting that when the electricity price variation is about −25% (i.e., 0.111 €/kWh), the economic advantage of installing a PV plant is almost voided. In addition, by reducing the operating hours of the refrigerated warehouse, the difference on yearly total cost becomes more sensible to electricity price variation, since PV power generation covers an increasing proportion of energy requirements.
Figure 9b reports how the yearly total cost of a warehouse with a PV plant varies with the electricity price. It is possible to observe that the yearly total cost has a maximum variation of ±13%, when the warehouse operates 24 h/day, and a minimum variation of ±7%, when the warehouse operates 12 h/day.
In the case of daily hours operating only, in fact, PV integration can significantly reduce energy withdrawal from the grid. When the warehouse operates continuously over the 24 h, instead, nightly requirements cannot be counterbalanced by PV generation.
4.4. Sensitivity Analysis and Discussion on Food Supply Chain Decision Variables
To explore the capability of the proposed optimization model to act as a decision support tool, the impact of food supply chain decision variables on storage facility cost, energy use, and greenhouse gas emissions has been investigated. Since the introduction of a PV plant has been proved to increase the overall sustainability of a refrigerated warehouse when the yearly total cost is selected as the objective function (see
Section 4.1), the following simulations regards a PV integrated R-AS/RS with minimum cost optimization and input parameters as in the reference case.
Referring to the framework of
Figure 1, supply chain decisions able to impact on the configuration and performance of a R-AS/RS integrated with a PV plant are: (1) the storage temperature; (2) the temperature of incoming products; (3) the system throughput; (4) the batch size; (5) the facility location.
Regarding storage temperature, a sensitivity analysis has been performed by varying from −21 °C to −29 °C with respect to the basic value of −23 °C of the reference case (see the previous
Section 4.1). The cell temperature impacts on the main components of the refrigeration load (i.e., transmission, infiltration, and product load) and therefore it is expected to have a significant impact on performance. Results are reported in
Figure 10. The electricity consumption (see
Figure 10a) increases up to 67.9% with respect to the reference value of −23 °C when a storage temperature of −29 °C is used, while it decreases by −19.1% when reaching −21 °C for a PV integrated facility. The yearly total cost shows a lower but significant sensibility to the storage temperature variation (see
Figure 10b), ranging between +18.3% at −29 °C and −5.1% at −21 °C for a PV integrated facility; the R-AS/RS configuration, in fact, is unchanged, but energy costs impact on the yearly total one. If absolute values of a PV integrated R-AS/RS (see green-colored features in
Figure 10a,b) are compared to those achieved by a refrigerated warehouse with no renewables introduction (see red-colored features in
Figure 10a,b), it can be appreciated how PV adoption contributes to counterbalance energy requirements for severe cell temperatures that can be required to preserve food quality along the whole cold chain, thus offering the supply chain manager more opportunities for an overall optimization than solution not including renewables.
Regarding the temperature of the products entering the refrigerated warehouse, which depends on the upstream stages of the cold chain, the reference value of −15 °C has been lowered to assess possible energy savings.
Figure 11a shows that the electricity demand from the grid can be reduced up to 37.3% when products enter a PV integrated storage facility at −21 °C, for a yearly total cost reduction of 10% (
Figure 11b). If no PV plant is installed, instead (see red-colored features in
Figure 11a,b) any variation at supply chain level required to preserve product quality leads to greater efforts both from economic and environmental perspectives.
Figure 12a shows how the system throughput affects the grid electricity demand when yearly total cost is minimized, and a PV plant is used. System throughput affects the infiltration load due to the different number of door openings to bring unit loads into the storage space, the product load due to different number of products whose temperature has to be increased to the storage one, and energy requirements for movement equipment (i.e., cranes, satellites, and trucks, with related internal load also). It is worth noting that the variation of the grid electricity demand is not linear but shows a sudden increase between 51 and 52 cycles per hour and then a rapid decrease between 56 and 57 cycles per hour. A similar behavior occurs in the yearly cost shown in
Figure 12b, with the difference that the rapid variations lead always to increasing costs. Such patterns can be explained by analyzing the rack configuration of the optimized storage facility reported in
Table 5. When varying the system throughput, the CP solver finds basically three warehouse configurations. The first configuration, which ranges from 15 to 51 cycles per hour, is composed by 25 columns, 6 levels, 16 lane depth, and 1 aisle. The second configuration occupies a narrow range (i.e., 52–56 cycles per hour) and presents a major number of columns (i.e., 43) and levels (i.e., 7), while the lane depth is halved; the number of aisles remains the same. Finally, the third configuration, which ranges from 57 to 75, has the same number of columns and levels of the first configuration, but the number of aisles is doubled, while lane depth is halved. These changes in rack configuration should be ascribed to the need of lowering the total cycle time of the AS/RS machine, moving horizontally along the aisle and vertically to reach the desired level, plus the satellite, moving along the lane in depth. When the throughput grows, satellite cycle time is decreased by reducing the lane depth while preserving selectivity for retrieval operations (i.e., halving the lane so that incoming lots can be split into two sublots to be assigned to one lane each), thus leading to a reduced rooftop surface and less PV modules (see the last column in
Table 5). The AS/RS cycle time is then adjusted moving towards higher racks until the pace is so stringent to be satisfied only with parallelism by inserting two aisles and two aisle-captive cranes, consequently.
Finally, another important decision variable of the cold supply chain is the location of the refrigerated warehouse. To have a better understanding on how the location affects the warehouse configuration and performance, the optimal solution obtained for the reference site of Pordenone in north-eastern Italy has been compared with the optimal solution of the locations reported in
Table 6, which present different climate conditions as well as electricity price and carbon intensities. Specific features of the European cities are provided in [
39,
40], while Singapore’s carbon intensity and electricity price are provided by the Energy Market Authority of Singapore ([
41,
42]). Different outdoor temperatures impact on refrigeration load, while the latitude affects radiance and PV panels inclination, thus modifying PV power generation.
The electrical energy demand from the grid for each considered location is reported in
Figure 13a when the refrigerated warehouse is integrated with a PV plant (green-colored bars) or not (blue-colored bars). It is possible to observe how the impact of PV integration increases moving from the northernmost city (i.e., Helsinki) to the southernmost ones (i.e., Siracusa and Singapore), which can better exploit PV generation due to higher radiance and sunny hours per day.
Figure 13b highlights how the yearly total cost depends not only from the climate conditions of the location as power demand, but also from the related electricity price. Singapore, which presents quite the same cost than Siracusa for a storage facility without PV integration and similar PV generation potential, can benefit less than Siracusa from PV installation due to its lower price for energy withdrawal from the grid. Helsinki, which can rely on a very low price for energy withdrawal from the grid and poor climate conditions for PV generation (low solar irradiance), has no economic benefit for PV integration. In this case, PV installation leads to a higher yearly total cost (see
Figure 13b) due to investment costs not sufficiently counterbalanced by energy cost savings. Attention is also deserved by a supply chain manager to avoid GHG emissions, when assessing the environmental impact of the cold chain. Due to different national mixes of energy sources, for similar amount of energy savings from the grid, avoided emissions (see orange bars in
Figure 13a) are higher for cities whose power needs are mainly satisfied by fossil fuels (e.g., Hamburg) than those where renewables have high penetration (e.g., Helsinki).