A Food Transportation Framework for an Efﬁcient and Worker-friendly Fresh Food Physical Internet

-In this paper, we introduce a Physical Internet architecture for fresh food distribution networks, with the goal of meeting the key challenges of fresh product delivery and reduce waste. In particular, we explore fuel-efﬁcient delivery of fresh food among different stages in the logistics pipeline along with a worker-friendly delivery scheduling of the drivers. The important aspect of this proposal is the inclusion of a freshness metric and the heterogeneous, space-efﬁcient loading/unloading of different perishable goods onto the trucks depending on their delivery requirements. The paper also discusses mechanisms for reducing empty miles of trucks and the carbon footprint of the logistics by infrastructure sharing while reducing the driver’s away home time for long distance delivery. Via comprehensive simulations, the paper shows that the proposed architecture reduces the driver’s away home time by ∼ 93% whereas improves the food delivery freshness by ∼ 5%. The paper also shows a clear tradeoff between the transportation efﬁciency of the trucks and the delivery freshness of the food packages.


I. INTRODUCTION
The commodity distribution logistics has been undergoing rapid transformation in recent years, driven by a number of factors that include globalization of supply chains, automation, infusion of information technology, and mechanisms for better sharing of the transportation capacities.Unfortunately, the traditional transport logistics suffers from very low efficiencies (perhaps in the teens [1]) due to significant percentage of partially full or empty carriers (e.g., trucks, railcars, boats) and poor capacity use in distribution centers.An underlying reason for this is that large companies such as Walmart, Target, etc. continue to use private logistics, although smaller companies are increasingly making use of so called 3rd party logistics (3PL) or its variants [2].In 3PL, a separate logistics provider can work with individual resource providers (e.g., trucking company, distribution center owners, etc.) and thereby efficiently serve many logistics customers.Such a resource sharing has been key to the cyber Internet, and is likely to play a large role in logistics as companies see its benefits in significant cost, carbon footprint, and delivery time reductions.The other key reason is lack of standards that makes sharing and interoperability difficulty.However, there are developing standards such as GS1 standards for addressing and labelling of all the entities involved in the logistics [3] and the notion of π-containers [1] (as summarized in Table I and Fig. 1).Here too the cyber Internet sets the example by providing an extensive set of standards that make sharing and distribution of any type of content easy.
In their pioneering work [1], [4], [5] the authors have shown several similarities in between the logistics networks and cyber Internet, and proposed a Physical Internet (PI) model for an efficient, coordinated and well-structured supply chain network.The PI concept appears to be gaining traction in both the research community and industry, as evinced by recently held 3rd International Conference on this topic [6].In this paper, we specialize the notion of Physical Internet to perishable commodity logistics, which we call fresh food physical Internet (FFPI or F 2 π).Fresh food (including produce, edible fungus, dairy, seafood, meat, prepared but unpreserved foods, etc.) forms the dominant and increasing component of perishable commodities in terms of volume, carbon footprint, revenue, and importance.Customers increasingly demand freshest possible food at low prices.Other significant perishable commodities are blood for transfusion, short-life medicines, human organs for transplant, fresh flowers, etc. Perishable commodity distribution logistics tends to have even lower efficiency than distribution logistics in general because of the perishability related constraints.Unfortunately, a lot of fresh food is still discarded in the supply chain to the end customer either because of actual spoilage or because of being in less than perfect condition [7].There is a natural tradeoff between efficiency and freshness.The emerging notions of local sourcing of products attempt to reduce the waste, but result in significant additional complexity with respect of integration of local and nonlocal logistics.Thus, distribution mechanisms for perishable commodities that simultaneously achieve high efficiency and meet stringent quality of service requirements remain a substantial challenge [8].
The key characteristics in F 2 π is the constant deterioration of food quality as function of delay in the distribution pipeline and handling factors such as temperature, humidity, vibrations, etc.The deterioration process is unique to each product type, which makes shared handling of multiple types of products quite difficult.The modeling of fresh food logistics remains rather simplistic [8], largely concerns single products, and does not address the efficiency/freshness tradeoffs, particularly in the context of human factors such as driver friendliness.We believe that an integrated consideration of human factors is an essential component of intelligent transportation, since traditional logistics results in significant away-from-home time for drivers (from few days to several weeks), which causes high driver turn-over rate and consequent impact on service quality [1] which in tern results in driver shortage [9].This is depicted in Fig. 2(a)-(b).Fig. 2(a) shows that the truckload industry as a whole replaced the equivalent of 95% of their entire workforce of drivers by the end of 2014.In this paper we explore the idea of shared logistics to reduce trucker's Fig. 1. π-container architecture [1] time away from home, by dividing the long journey of a truck driver among multiple drivers.This requires rather close cooperation and interactions among the agents in the food pipeline particularly when we attempt to minimize food waste and try to achieve high transportation efficiency.
The paper shows through extensive simulations that the proposed F 2 π framework reduces the driver's away home time by ∼93% whereas improves the delivery freshness quality of the food packages by ∼5%.The simulation results also show an obvious tradeoff between the truck capacity utilization and loss of quality of perishable products; as a truck carries more packages to improve its transportation efficiency, the delivery time of its carried packages increases which reduces the delivery quality and vice versa.To the best of our knowledge, this is the first work to develop the truck scheduling, considering the environmental, economic as well as social aspects.Even if we address this in the context of fresh food logistics, our methodology is generic enough to be adapted to other logistics systems as well.
The outline of the paper is as follows.We first provide an overview of the F 2 π architecture in Section II-A.In section II-B we discuss the freshness quality metric using a timetemperature indicator, that is used for the packing, mixing and distribution of the the perishable products in the later sections.In section III we address the distribution and forwarding of the food packages among different distribution centers, along with a worker-friendly, fuel-efficient truck scheduling mechanism.Performance evaluations are reported in Section IV.The related works are summarized in section V. Section VI concludes the paper.

II. OVERVIEW OF A SHARED F 2 π ARCHITECTURE
The basic diagram of a food logistic is shown in Fig. 3. Foods from farmlands are taken to the packing centers where they are sorted and packed for delivery to any of the nearest distribution centers (DCs) and retailers.If the quality of some products deteriorate significantly at any stage of the food pipeline, they are sent to the food banks [11] where they are consumed at lower cost or at free to the people who need them.By distributing the food products that otherwise would be wasted to the food banks, the food loss in the chain can be drastically reduced.The entire process is fairly complicated, due to the inter-dependencies of several issues, ranging from environmental to social, or from economical to food freshness.

A. From Private Logistics to Shared Logistics
In the traditional supply chain, the trucks often go empty for a variety of reasons besides lack of sharing.It is reported that in USA the trailers are approximately 60% full in the distribution process.The global transport efficiency is recently estimated to be lower than 10% [1].The effect is not just merely efficiency related.This results in more number of truck runs, which increases its environmental impact as well as the transportation costs.Also higher truck runs turn the drivers to become modern cowboys [1], which results in driver shortage and higher turnover rate.The biggest reason for this inefficiency is that in traditional supply chain different vendors use their own private network/trucks for product delivery and do not frequently coordinate with each other.For an example Walmart and Target use their own food network as well as their trucks in the delivery process which reduces the transportation efficiency.Other reasons include: (a) the need to return the truck and product containers back to the source so that they will be available quickly to handle the next shipment, and (b) lack of demand or unavailability of suitable product or its containers to fill the truck on is backwards journey.
To overcome this, in a shared F 2 π, the responsibilities of the distribution companies and the shipping companies are first separated.In F 2 π the trucks are not owned by the distribution companies.Rather the trucks are owned by some shipping companies (similar to UPS, FedEX etc) that take delivery orders from different DCs and deliver them to the corresponding destination DCs.This separation serves two key purposes.First, if the truck journeys are scheduled properly, their space can be shared to deliver the demands of different distribution companies.This reduces the empty miles, improves transportation efficiency as well as reduces carbon footprint and transportation costs.On the other hand reducing empty miles reduces the driving burden of the drivers too.Second, in such a model, the containers can be provided by the shipping companies.Thus in a truck's journey, the containers move with the truck, loaded-unloaded with the packages that are to be delivered in between the DCs.In this model returning the empty containers back to the source is not needed.Such a shared model is promising for improving the overall efficiency of the logistics system, however brings some new challenges.Scheduling the truck in this shared model needs to account for several factors such as: (a) transportation efficiency, (b) driver's away home time, (c) delivery freshness of the food packages, and (d) road congestion especially in city areas at peak hours.Some of these objectives are contradictory; for example, as the trucks are shared among the DCs, there is always a tradeoff between capacity utilization and loss of quality of perishable products due to additional delays in waiting for product to carry and loading/unloading.These distribution decisions are taken by consulting with the 3PL operators to ensure collaborative logistics, instead of private logistics decisions taken by the individual companies.Fig. 4. Impact of temperature on the appearance of "Killarney" red raspberries during a storage period of 7 days [12].

B. Modeling the Perishability Metric
Traditional supply chain logistics are researched more towards reducing the transportation cost in the delivery process.In F 2 π, one of the important factors is the food freshness, that needs to be integrated with the tradition logistics.Fresh food packages deteriorate in quality over time according to complex biochemical processes that depend on the food type, initial quality, temperature, humidity, vibrations, bacterial level, and bruises during storage/transportation.For example, Fig. 4 shows the impact of storage temperature on the appearance of raspberries during a storage period of 7 days.At any certain environmental conditions (temperature, humidity etc.) the food quality deterioration as a function of time t can be described by a non-decreasing function that is henceforth denoted as ζ(t).The deterioration of food products are nothing but biochemical reactions, thus ζ(t) can be modeled as a function of some measurable parameters related to the reaction that determines the quality loss.
We describe a metric for estimating the degradation of a measurable parameter of a food product using its timetemperature indicator.Like any other biochemical reactions, in food products as well, certain parameter A gets converted to another, say B over time.As the reaction proceeds, the concentration of A decreases, whereas that of B increases.The concentration loss (of A) or gain (of B) of a particular ingredient at any instance can be described by the following equation: where C is the concentration of the ingredient, k is the rate of degradation that depends on temperature and other factors, and n is the order of reaction that is either 0 (zero order) or 1 (first order) for most of the food products.Food products like fruits or vegetables generally follow zero-order degradation or linear decay, whereas products like meat or fish follow first-order degradation of exponential decay.Thus the quality can be measured by checking the concentration of certain ingredients in the food products.For example concentration of Vitamin C or sulfur can be the quality indicators for different fruits or vegetables, whereas the concentration of bacterias like Mesophiles, Psychrotrophs, Lactobacilli, Enterococci, Coliforms etc can be the quality indicators for meat products.The rate of concentration loss or gain k at different temperatures can be modeled using Arrhenious equation as follows where k 0 is a constant, E a is the activation energy, R and Γ are gas constant and absolute temperature respectively.Thus if a food product goes through multiple phases i = 1, 2, ..., m with time t i at i-th stage and rate k i (based on temperature Γ i ), then the end concentration of an ingradient With these, we can scale a perishability function of a food product ζ(t) from the level of concentration of some measurable parameters.It suffices to assume that ζ belongs to the real range [0, 1] where 1 means that the product so far has not suffered any quality loss and 0 means that product has no value.Thus if we know the storage time and temperature of the chain in different stages, we can estimate the delivery quality of a product using the above approach.In reality because of different disturbance in the food chain (vibrations, change in temperature or humidity etc) the quality deteriorates faster or slower than the theoretical expected rate.

III. PRODUCT DISTRIBUTION AND TRUCK SCHEDULING
With these we next formulate our truck scheduling problem with the vision of sharing the truck space to deliver food packages among multiple distribution companies.As mentioned earlier, one of the concerns of traditional logistics is the long driving time of the truck drivers, that makes them stay away from home for days and sometimes for weeks.To cope with this, in F 2 π the delivery of food packages are made using shorter hops among the distribution facilities.Making shorter trips reduce the driver's away home time, which improve the quality of their personal, social and family life and at the same time reduce their turnover rates [17].An ideal case of this is shown in Fig. 6 where the trucks have their certain coverage areas/domains within which they distribute food products among different DCs.The long driving distance in between DC s and DC d is divided into shorter hops, that are determined by interdomain delivery strategies.When a truck gets order to deliver something from one DC to multiple other DCs, it checks whether the nearby DCs have to deliver food packages among

Intra-domain strategy
Inter-domain strategy Fig. 6.Inter and intra-domain schemes between the DCs. each other.It then makes its schedule accordingly so that its fuel efficiency or delivery freshness is maximized and at the same time the driver can return to the starting point (DC s ) within his scheduled hours.The appropriate scheduling of the trucks within their coverage domains bring the need for developing smart intra-domain distribution strategy (IntraDS).Proper integration of inter and intra-domain strategies need considerations of storage/traveling time of the individual food packages as well as their delivery requirements, while improving the transportation efficiency of the trucks and their driver-friendly schedules.We discuss the routing and scheduling strategies in these two domains in the following subsections.

A. Inter-domain strategy
The inter-domain strategy depends on the coverage areas of the trucks.By using the coverage areas of the trucks, as well as the availability of the other transportation modes (rail, river etc.), the shipping company generates the connectivity graph among the DCs and then implement a routing scheme on this connectivity graph.The routing scheme is similar to the shortest-path routing [18] in computer networks, where the cost function may be a function of a number of factors, like (a) expected delay (waiting time in the DC + travel time), (b) end-to-end delivery quality, (c) the environmental impacts etc.In F 2 π the shipping companies need to pay extra carbon taxes [19] for using road transportation, and to prefer river/rail transportation wherever available.Imposing carbon taxes will encourage the shipping companies to use transportation modes that are more environment friendly.
Notice that some of these DCs can be considered as πtransit, π-switch, π-bridge, π-gateway, π-hub [1] etc depending on their role in the distribution logistics.For example Fig. 7 shows a scenario that integrates the local and long-distance logistics.In this figure the local and regional packages are brought at the π-hubs for long-distance delivery which is the distribution of packages in between different regions.The local distribution can be done by small trucks or trailers, whereas the large trucks (18 wheelers) are used for the delivery in between the hubs.

B. Intra-domain strategy
After getting the delivery orders from the DCs, the shipping companies schedule their trucks for fulfilling the delivery orders, after consulting with the 3PL operators.Each truck driver maintains his maximum continuous driving time and within that time he tries to serve as many orders as he can to maximize the design objectives.The Intra-domain routing strategy of the trucks is similar to the traveling salesman problem (TSP) [20], pickup and delivery problem [21] and ride-sharing problem [22], but have a number of differences.First most of the schemes proposed for the above-mentioned problems try to minimize the overall travel time of the vehicles, whereas our objective is to maximize the fuel-efficiency, reduce the empty-miles and at the same time fresh delivery of the food products to their destinations.Second the abovementioned problems do not have any maximum delay bound, whereas our scheme has to consider the maximum driver's away home time, which puts an upper limit of the travel time of the trucks.Third in the above related problems, a vehicle needs to go at every location at least once and serves their requirements, whereas in our scheme a truck driver may skip fulfilling the demands of some DCs within its coverage area, if the maximum time-limit cannot be maintained or if visiting few DCs effectively reduce the performance objectives.Those skipped packages will be delivered by other trucks.Also contrary to the previous works, in our scheme the truck driver may visit the DCs more than once, which makes the problem more complicated.Also notice that there may be multiple roads (channels) corresponding to one hop.It may happen that some roads are busy in day time, but not in evening hours, so taking those roads at evening time is better, whereas in daytime other roads are preferred.While scheduling the trucks, the scheduler considers only the road that takes minimum transit time.Notice that the proposed truck scheduling can be applied for distributing packages in both local and longdistance logistics.We next model the optimization problem and then discuss the complexity of IntraDS in the following subsections.Time when the truck delivers at DC j in the -th transit-segment Decision Variables Whether or not the truck goes from DC i to DC j at the -th transit-segment

1) Problem formulation of IntraDS:
The objective of In-traDS is mainly twofold.First is to maximize the efficiency of the transportation, which we define as the amount of product delivery per miles/time.Second is to maximize the cumulative delivery quality of all the packages, which we define as the product of the delivery quality and the delivery amount.Thus our objective function is to Here Q t ij is the initial average Vitamin C content (or other indicators) of the t-th type packages from DC i to DC j and k is the quality decay rate at the truck temperature.The term i j t d t ij i j x ij .Tij is defined as the efficiency-factor, whereas ji is defined as the quality-factor.A and B are the weights of the efficiency-factor and the quality-factor respectively.Equation(4) assumed linear decay, however exponential decay can be modeled similar to equation(3).Notice that the efficiency-factor is basically the package delivery rate of a truck (for example the numbers of packages delivered per miles), whereas the quality-factor is a product of the delivery quality and the amount delivered.
The necessary variables are listed in Fig. II, where the term transit-segment is defined as follows.If a truck goes from DC 1 →DC 2 →DC 3 →DC 1 , then the first transit-segment starts at DC 1 and ends at DC 2 , the second segment starts at DC 2 and ends at DC 3 and so on.The maximum number of transit-segments allowed for a truck is assumed to be T.The source of a truck is denoted as .The constraints are defined as follows.
Continuity constraint: If the truck comes at point j at transitsegment , then it needs to leave from j at transit-segment +1, i.e.
Also a truck loads and unloads goods at DC i only when it is at the DC i , i.e.
where M is at least as high as the maximum amount of objects that can be picked-up/delivered at any particular DC.The amount of goods that is loaded is less than the corresponding delivery requests.Also the cumulative amount of loading and unloading is equal.The trucks need to deliver all the packages that they have loaded before ending their journey.These give rise to the following set of constraints Truck-load constraint: The truck-load at any transit-segment is equal to the truck-load at its previous transit-segment and the difference of the amount that is loaded and unloaded at .Also the truck-load at any is less than the truck capacity C.
where V t is the volume of the container type t.Constraint(8) simply assumes that multiple containers of different sizes always fit within a truck as far as their cumulative volume is less than the truck's capacity.This is an over-estimation of the packing ability of the containers.However in reality this over-estimated amount of packages can be passed to a loading module that loads a fraction of the assigned packages by solving typical 3D-bin packing [23].The remaining packages can be carried by other trucks while they are scheduled.Notice that due to the use of modular containers or π-containers [1], the error due to this over-estimation is limited.
Travel time constraint: The total travel time is bounded by the minimum and maximum driving time allowed, i.e.
Also the delivery time at the DCs are recorded as follows: where w j is assumed be the time for pickup/delivery at the delivery point j.

Delivery constraint:
The delivered packages should ensure its required freshness limit , i.e.
This constraint assumes linear decay, whereas exponential decay can be modeled in a similar fashion.
Other constraints: Also the truck should start and end at the starting point.To keep the problem simple, we assume that the truck does not visit a point more than η.For our simulations, we keep η to be 2 for simplicity.These give rise to the following constraints We next define two instances of IntraDS, based on the values of A and B in equation ( 4).When (A, B) = (1, 0), the problem becomes efficiency-factor maximization problem, named E-IntraDS, whereas (A, B) = (0, 1) makes it quality-factor maximization problem which we call Q-IntraDS.
2) Complexity of IntraDS: The IntraDS can be proven to be NP-complete as shown in the following theorem.
Theorem 1.The problem IntraDS is NP-complete.
Proof: We first introduce a decision version of IntraDS as follows: determine whether there exists a feasible route and loading-unloading schedule such that the objective function of equation( 4) is more then a constant U. Clearly, given a route and loading-unloading schedule, the problem is verifiable in polynomial time, i.e.IntraDS ∈ NP.Now we reduce the TSP to the IntraDS problem.We define an instance of the IntraDS problem as follows: we assume that there is no intermediate pickup.Thus the truck loads all the products at the origin and after delivery, it returns to the origin.We also assume that A = 1 and B = 0 in equation( 4).The total amount of packages loaded at the origin is one unit.This reduction transforms a TSP instance into a IntraDS instance.Thus there exists a feasible solution of IntraDS such that the objective function is more than U if and only if TSP has a route at cost less than 1 U .Thus IntraDS is verifiable in polynomial time and there exists a polynomial time reduction of TSP to IntraDS.This completes the proof.

IV. PERFORMANCE EVALUATION A. Performance of Inter-domain forwarding
We consider a truck that carries broccolis that have the Vitamin C content of 99.9 mg/100 g initially.We assume that the broccolis are maintained at two types of environment, one is a chilled environment of 2 • C. In another case they are carried at 20 • C. Also at 2 • C, k = 0.0408 mg/100 g in an hour, where at 20 • C, k = 0.1375 mg/100 g in an hour [13], [25], [26], [27].
Effect on driver's driving time: We first demonstrate the advantage of using short hops for delivery among the DCs.We consider a scenario where a truck needs to deliver certain amount of packages to a DC that requires 48 hours of driving time.A driver drives 12 hours continuously, takes rest for 12 hours and then starts driving again.The maximum driving time of 12 hours is estimated according to the Federal Motor Carrier Safety Administration (FMCSA) regulations [28]; also the chance of road accidents due to driver fatigue is found to be below 10% within this limit as observed from Fig. 8(a).If this job needs to be done by a single driver (one hop scenario), then it takes almost 84 hours for the driver to reach at the destination, deliver the packages and then returning back at the starting point takes another 96 hours.This long trip time deteriorates the overall quality of the products as well as increase the driver's time away from home.In case of two hops, the driver needs to unload the packages at the halfway point (a DC that is 24 hours apart), from where another driver loads the packages and delivers them to the ultimate destination DC.This reduces the trip time of each driver as seen from Fig. 8.As seen from Fig. 8(b), by introducing 8 hops in between the DCs, the trip time is reduced by ∼93%.Also whenever a driver reaches in a delivery point, it needs to wait for the workers to load/unload the packages to/from the truck, which we vary from 0-3 hours in Fig. 8. Obviously the trip time increases due to additional waiting time due to additional loading-unloading.
Reducing the continuous driving time also reduces the chance of driver fatigue and road accidents, as seen from Fig. 8(a).Thus using shorter intermediate hops not only reduces the away-home time of the truckers, but also reduces the chance of accidents as observed from Fig. 8(b).
Effect on delivery freshness: Also notice that increasing the number of intermediate hops improves the delivery freshness.From Fig. 8(c) we can observe that at 20 • C, by introducing 8 hops, the Vitamin C content in the delivered broccolis are improved by ∼5%, when the waiting time for loading/unloading is assumed to be zero.With the increase in intermediate loading-unloading, the Vitamin C content starts decreasing.With 8 intermediate hops, the Vitamin C content decreases by ∼3% when the loading-unloading time increasing from 0 to 3 hours.Fig. 8 clearly shows the benefits of using multiple hops for building a worker-friendly fresh food delivery chain.From Fig. 8(c) we can also observe that the broccolis retain their Vitamin contents higher in a chilled atmosphere; the Vitamin contents drops by ∼5% if the temperature increases from 2 • C to 20 • C. Because of additional loading/unloading time in the intermediate points, deciding the number of intermediate delivery hops is an important choice for determining the delivery of fresh quality food, as well as forming a workerfriendly food logistics.

B. Performance of Intra-domain forwarding
We next compare our proposed Intra-domain delivery schemes E-IntraDS and Q-IntraDS using a small network consists of five DCs.The travel time in between the DCs are shown in Table IV where the DCs are denoted as A to E. We ignore the pickup/delivery time for simplicity.We use AMPL solver [29] for solving the optimization problem.We consider two types of packages with raspberries and broccolis.We assume that the containers ensure that the packages are kept at 2 • C, which corresponds to the deterioration rates of 0.0229 mg/100 g and 0.0408 mg/100 g per hour respectively.Their initial Vitamin C content is assumed to be 27 and 99.9

TABLE III. ORDER MATRIX
mg/100 g.We have normalized these decay rates by assuming the delivery thresholds of strawberries and broccolis to be 25 and 95 mg/100 g respectively, thus their percent deteriorations are 1.15% and 0.83% per hour respectively.is assumed to be 0.85.The demand matrix of each one of these two types of food packages among the DCs as shown in Table III.In Table III X is a variable, which is varied from 10 to 200 for our simulations.We assume all the packages are of same size of unit volume.The truck has a volume of 100, i.e. its capacity limit is of 100 packages.Also the T min is assumed to be 6 hours, whereas T max is varied in between 6 to 12 hours.Effect on transportation efficiency: Fig. 9(a) compares the efficiency-factor of E-IntraDS with increasing X.From Fig. 9(a) we can observe that the transportation efficiency starts increasing with the increase in X.This is because with higher X, the truck is loaded with more packages, which increase its efficiency.But after a certain point, the efficiency saturates.Interestingly, this point is almost similar to all (T min , T max ) values, which is X ∼50 in Fig. 9(a).Also we can observe that by increasing T max from 6 hours to 12 hours increase the efficiency by ∼80%-200%.This is because with higher T max , the truck gets more time to schedule its route to improve its efficiency, which is limited for lower T max .
Effect on delivery quality: Fig. 9(b) shows the qualityfactor of Q-IntraDS with varying X.The quality-factor increases by 3-5 times with the increase in X from 10 to 100, as more number of packages are transported and delivered.But after X = 100, this factor starts saturating.Similar to Fig. 9(a), the saturation point is similar for all (T min , T max ) values.We can also observe that the quality-factor increases by 4 times, as T max is increases from 6 hours to 12 hours.This is because with higher T max , the truck's travel time increases as well as the number of loading-unloading, which increase the qualityfactor.
Fig. 9(c) shows the delivery quality of the packages with different (T min , T max ) pairs.We can observe that the delivery quality decreases with the increase in T max .This is because the higher travel time results in more waiting time of the packages within the truck, which increases their average spoilage.Comparing Fig. 9(a) and Fig. 9(c) show a clear tradeoff in between the transportation efficiency and delivery quality.As we increase the T max the efficiency factor increases whereas the average delivery quality reduces.This is because as T max increases the truck delivers more packages to improve its delivery rate, which indeed increases the delivery time and results in quality loss.
Effect on product priority: Fig. 9(d) shows the effect of Q-IntraDS in product mixing.When the demand is low, i.e.X is less compared to the truck capacity, both strawberries and broccolis are carried and delivered.Whereas with the increase in X, more number of broccolis are transported.This  is because the percent decay rate of broccolis is much less than that of strawberries, thus delivering more amount of broccolis improve the quality factor, compared to carrying strawberries.We can also observe that the amount of broccolis increase by ∼4 times, when T max is increased from 6 hours to 12 hours.This is obvious because of the higher number of carried packages with increased travel time.In Fig. 9(d) the number of broccolis delivered is always higher than raspberries, as the spoilage rate of broccolis is lesser.With such an objective function, the products that are more perishable is always given lower preference.To overcome this limitation, the objective function can be modified as .
In this objective function, the first factor is identical to the objective function of Q-IntraDS, whereas the second factor gives preference to the products that are close to their spoilage limit.Fig. 9(e) shows the effect of the perishable food transportation with the modified objective function, where α is assumed to be 0.5.From Fig. 9(e) we can observe that the raspberries are given more priority while mixing, due to their higher spoilage rate compared to broccolis.

C. Performance evaluation with larger number of DCs
As the proposed Intra-domain forwarding is NP-complete, we have used a genetic algorithm based meta-heuristics [30] to evaluate its performance in large network scenario.We first assume that there are 50 distribution points that are positioned uniformly in an area of 100×100 sq. unit.The source-destination pairs are generated uniformly randomly with a probability of 10%.Each source-destination pair has to ship some objects that are uniformly generated from (0, r).We assume two types of objects, one has higher priority than the other one.T min and T max are assume to be of 50 units and 500 units respectively.
Comparison with different truck size: Fig. 10 shows the achieved transportation efficiency with the variation in truck size.From Fig. 10 we can observe that the the transportation efficiency improves by ∼2 times with the increase in r from 100 to 500.This is because with more package arrival, the truck space is better utilized which improves the transportation efficiency and reduces the empty miles.The efficiency also increases by ∼2 times while the truck size increases from 100 to 500 as the trucks can transport more objects in their journey.
Effects of item waiting time on delivery quality: We now show the effect of object waiting time on delivery quality.We assume that the objects wait at the distribution points before an truck arrives, picks them up and delivers them in their successive destinations.This entire delay results in quality loss or spoilage which we model as linear and exponential function with spoilage rate k of 0.005 and 0.05 per unit time respectively.A fresh item is assumed to have a quality of 100.Fig. 11 shows the variation of delivery quality with different item waiting time and spoilage rates.From this figure we can observe that the delivery quality drops drastically with exponential decay model, with k = 0.005 and 0.05 the delivery quality drops down by ∼40% and <5% respectively when the waiting time becomes 100 units.Intuitively this motivates the necessity of just-in-time supply of objects with respect to the truck arrival time at the distribution points, rather than keeping the objects waiting for longer periods.

A. Related Works
Modeling of fresh food spoilage has been considered extensively in the literature.A very recent literature is [31], where the authors have modeled the shelf life of the elegant lady peaches using the time-temperature data, over a linear pipeline of four stages: harvesting, warehousing, transportation, and retailing.Similar approaches for shelf life modeling is discussed in [32] for chicken breast meat, [33] for ground beef, [34] for mushrooms etc.
On the other hand, different planning models for agrifood supply chain, starting from farming, harvesting, storing and distribution, is also well-mined.[35] provides a thorough review of the state of the art in the area of planning models for the different components of agri-food supply chains for both perishable and non-perishable food products.The perishable food literature, which is of primary interest here, is quite recent and often focuses on specific types of produce.Interestingly as reported in this survey [35], the number of works devoted for production-distribution decisions for perishable argi-food supply chain are relatively sparse.In [36], an integrated production-distribution plan is developed for the seedling supply chain of a Finish nursery company.The main objective of this model is to minimize the total cost of production and transportation while meeting the customer demands as well the capacity related constraints.Authors in [37] discuss about the post-harvest handling of fresh vegetables.The purpose of this research is to maximize the expected profit considering the food preservation facilities, under the conditions of uncertain production and demand.These models typically are optimization models and try to maximize profit or revenue.Reference [38] presents a conceptual model of supply chain and identifies a number of parameters to quantify the performance of the supply chain network.However, the paper is mostly about defining the metrics and then collecting data for a few case studies.The metrics are classified into four categories that include efficiency, flexibility, responsiveness, and food quality.Efficiency metrics relate to things that the network principals care about (e.g., profit, inventory needs, etc.), flexibility metrics are about how easily the network can adapt to changing environment, responsiveness and food quality mostly deal with customer satisfaction.Some very recent related works are reported in [39], [5], [40], [41], [42] on physical Internet, that proposes the idea of imitating the cyber Internet architecture in physical supply chain.[43], [44] introduced a mathematical model to select a requisite number of modular containers to pack a set of products to maximize space utilization.In [45], [46], [47] the authors have shown that considerable synergies exist between information networks carrying time-sensitive information and perishable commodity distribution networks, and have proposed a five-layer network model to unify the two.Various traceability related issues for contamination detection in logistics system are reported in [48], [49], [50].To ease traceability in large logistics, the industry has undertaken a Produce Traceability Initiative (PTI), which is already implemented by several large food retailers (including Walmart and Whole Foods), and is being adopted by others (See www.producetraceability.org/).The traceability is ensured by diligently implementing two tasks.The first one is to assign unique IDs (barcodes or RFIDs) to each and every entity in the network, and second is to maintain the logs for every individual product that is handled by all the agents.However, these papers talked about some important points regarding reducing empty miles and drivers driving time, standardization of the containers, transportation efficiency, package tracking and traceability etc. while the food quality and freshness have not been discussed.

B. Discussions
The overall proposed scheme is a culmination of several factors that are inspired by the cyber Internet concepts along with the inclusion of physical entities like trucks and drivers.For example, the integration of local and long-distance logistics along with the use of π-hubs in Fig. 7 is a direct imitation of the hierarchical cyber Internet architecture (i.e.access or regional area networks, metropolitan area networks, core networks etc.) in the physical space.Intuitively this results in the package consolidation at the π-hubs from different neighboring DCs for long-distance transportation, which results in more truck load for long-distance large trucks and reduces the longdistance empty miles.On the other hand in computer networks time-sensitive packets (like video, audio packets etc.) are given higher priorities compared to typical data packets, which can also be imitated by tuning the objective function of problem(4) as done in Fig. 9(e).
On the other hand the physical logistics has certain differences compared to the cyber space: the main difference is the presence of the carriers and their drivers.Redundant carrier transportation results in higher transportation costs as well as green-house gas emissions.The drivers have their own preferences of shorter driving hours, which is also addressed in this paper.Thus the proposed architecture is bringing the cyber Internet concepts along with the incorporation of the physical entities (trucks, drivers etc.) into an integrated optimization framework to improve the overall efficiency, costs, environmental and social impacts of the logistics drivers, which indeed complements the recent Physical Internet initiatives.

VI. CONCLUSIONS
In this paper, we introduced the notion of worker-friendly, F 2 π architecture and explored the mixing, packaging and delivery of food packages in different parts of the food pipeline.
The key characteristics of this proposed architecture is the use of (a) a freshness quality parameter for efficient loading of multiple food products on the trucks and schedule food trucks according to the delivery requirements of individual packages, and (b) infrastructure sharing and efficient transportation to improve the driver's away home time, while maintaining an end-to-end fresh delivery of the food packages.We believe that the proposed F 2 π architecture will complement the existing efforts of emulating the digital Internet into the traditional logistics networks.However the proposed F 2 π model requires sharing of various resources (trucks, drivers, warehouses) among different competitive entities/companies, which brings the concern of security, privacy and fairness.In future we want to address the privacy concerns that may arise in such a collaborative and competitive framework.

Fig. 2 .
Fig. 2. One key concern of todays logistics is the long driving and away-home time of truck drivers which results in (a) higher turnover rate [10] and (b) driver shortage [9].

Fig. 5 .
Fig. 5. (a) Vitamin C degradation in different vegetables at 20 • C (data obtained from [13]).(b) Changes in vitamin C content of cucumber grown at control or high temperatures during their storage at 10 or 20 • C [14].(c) Bacterial content in chicken meat at 2 • C (data obtained from [15]).(d) Changes in sensory quality of iced cod (0 • C) [16].

RΓ
for zero-order C = C 0 .e± m i=1 k0.ti.e − Ea RΓ for first-order (3) where C 0 is the initial concentration of the ingredient.The parameter k can also be obtained from experimental results at different temperatures.In equation(3) the ± sign represents the loss or gain of concentration depending on the type of the measurable parameter.For example, the Vitamin concentrations of fruits or vegetables decay over time, whereas the bacterial growths on meat products adds up with time.Fig. 5(a) shows the Vitamin C degradation of different vegetables over time at 20 • C which shows the linear decay, thus k's are the slopes of the graphs.Fig. 5(b) shows the effect of storage temperature on Vitamin C degradation on cucumber.Also the exponential growth of certain bacterias on meat substances are shown in Fig. 5(c)-(d) where ln(k)'s are the slopes.

Fig. 7 .
Fig. 7. Integration of local and long-distance food logistics.

2 °CFig. 8 .
Fig. 8. (a) Percentage of accident due to fatigue as a function of hours of driving [24].Variation of (b) the trip time of the drivers, and (c) Vitamin C content at delivery with the number of hops.The waiting time is the time taken a each intermediate hop to load-unload the packages in between different trucks.

Fig. 9 .
Fig. 9. Variation of (a) efficiency-factor, (b) quality-factor, (c) average delivered quality, and (d), (e) number of delivered packages, with different X.In the legends R(a, b) and B(a, b) denote raspberries and broccolis, and a and b are T min and Tmax respectively.

Fig. 10 .
Fig. 10.Variation of efficiency factor with different demand rates.

Fig. 11 .
Fig. 11.Effect of package waiting time on delivery quality.

TABLE II .
Amount of type t loaded at DC i for delivery at DC j at the -th transit-segment d t ij Amount of type t unloaded at DC i from DC j at the -th transit-segment R t ij Amount of type t that are on the truck for delivery at DC i from DC j at the -th transit-segment L tTruck load of type t at transit-segment S t ij Delivery request from DC i to DC j of type t T ij Time of travel from DC i to DC j B j TABLE OF NOTATIONS Indices i, j Index for distribution centers (1, ..., N) that are within the coverage areas of the trucks Index for transit-segments of the trucks (1, ..., T) t Index for types of products (1, ..., T )