Crowd logistics is a significant and fast expanding subset of crowdsourcing (Mladenow et al., 2015). Howe developed the phrase “crowd-sourcing” in 2006, defining it as outsourcing an activity usually performed by chosen agents such as employees to an unknown but considerable number of individuals through open recruiting (Howe, 2006). Crowdsourcing enables the public to do jobs that were previously performed solely by a few professionals (Huang et al., 2020). Crowdsourcing, when used properly, has the potential to benefit organizations of all sizes in a number of ways, including crowd-funding for capital, crowd-libraries, and crowd-clients for information sharing. Crowd-logistics is a new avenue for companies to provide value for their consumers at a lower cost (Mladenow et al., 2016).

Businesses have adopted crowd-logistics to implement logistical needs (Alnaggar et al., 2019); in 2015, Amazon launched a crowd-sourcing logistics service called Amazon Flex, which employs independent freelance drivers to deliver merchandise to clients along pre-planned routes. Amazon adopted Amazon fresh for time-sensitive items such as groceries, which guarantees a two-hour delivery window (Mehmann et al., 2015).

Additionally, Walmart began testing a crowd-sourcing logistics service called Spark Delivery in 2018; DHL also created MyWays to assist crowd-sourcing logistics by connecting end-consumers with the crowd (Kafle et al., 2017). For SME’s in developed nations, there has been an exodus of courier crowd-sourcing delivery platforms like DoorDash,Kanga, Roadie, PiggyBee, UberFreight, Truxx, and BuddyTruck, which act as a critical connection between SME’s and freelance drivers interested in delivering products for businesses (Alnaggar et al., 2021).

Research by (Mladenow et al., 2015) looked at the adoption of crowd logistics delivery platforms by business giants such as Amazon, Google, Wallmart, DHL and E-bay; they identified the need for disruptive business models, low cost structure and the immense power of the crowd as the reason for the rapid growth of crowd logistics platforms in developed economies. Focusing on the current growing industry of crowd logistics in the United States, (Alnaggar et al., 2021) reviewed different crowd sourced delivery platforms and concluded that crowd logistics platforms were here to stay and called for a more in-depth look at a variety mechanisms for its growth.

SME’s are considering using crowd-logistics because of its enormous potential to drive business-related operations, reduce costs, and provide customer value (Lin et al., 2020). Indeed, scholars are increasingly examining the possible implications of crowd-logistics. According to Alnaggar et al. (2019), contemporary industry trends are evolving toward more sustainable sources of delivery and logistics; he noted the necessity for crowd-logistics platforms to use efficient scheduling and routing approaches in order to expand their value chain. Since bikers and pedestrians are increasingly being considered “crowds,” it is commonly recognized (Kafle et al., 2017) that crowd-logistics, urban package delivery, and green logistics go hand in hand. SME’s, for example, may circumvent the lack or difficulty of recruiting skilled logistics teams and delivery services by engaging crowd services to transport items along route to their destination (Lin et al., 2020). Additionally, SME’s may promote their shared social responsibility by supporting green logistics, since crowd-logistics cuts emissions and pollutants produced by cargo vehicles by around 55% (Huang et al., 2020).

It is estimated that private vehicles and bikes are utilized by individuals less than 50% of the time (Li & Liu, 2021) leading to under-utilization of resources which could be otherwise used to generate income. As such various researchers have investigated how these underutilized resources could be used to create value for both businesses and owners of these resources (Buldeo Rai et al., 2017; Huo Bin, Feng Zhao, Guojie Xie, Lijuan Huang, HuanFang Wang, & Ruidong Zhu, 2020). But the adoption of crowd logistics platforms by both users and crowd has been shown to be reliant on a number of key issues. Research by (Alnaggar et al., 2021), shows that the allowed delivery time window, routing and monetary incentives were some key issues driving more users to adopt crowd logistics. However, this increase carries with it certain inconveniences for the suppliers of crowd services. According to Lin et al. (2020) packaging design, waiting time and route diversion are some key factors that inhibit the penetration of crowd-logistics. Table 1 summarizes key studies on this subject.

Finally, researches have stated that crowd-logistics provides value to all stakeholders involved; it helps SME’s to access a larger market and better customer interactions while also generating cash from otherwise underutilized resources for the community participating (Gong et al., 2021).

In Africa there exists a huge gap of limited available crowd logistics platforms

for businesses. As shown by our review, little attention to date has been given to the question of whether the African market is amenable to crowd-logistics and the associated instruments. As per (Denis Benoit, 2021), it is clear that the digital economy in Africa is growing quickly and will soon become a major force in global economic growth as a whole. In recent times, more people are incorporating technology into their daily lives and technological advancements are gaining popularity throughout Africa (Azmeh & Foster, 2018). As such, studying the factors that affect the adoption of crowd-logistics by the African market has significance as Africa possess a huge market potential for crowd logistics platform.

Additionally, existing research focuses mostly on crowd-logistics for big firms and e-commerce, with little or no attention on SMEs and their usage of crowd-logistics. As a result, this article tackles the aforementioned two gaps by adapting TAM to evaluate the link between SMEs and crowd-logistics and then testing the model in the African environment.

The Technology Acceptability Model (TAM), established by Davis in 1989 (Davis et al., 1989), can forecast the acceptance and utilization of Crowd-logistics platforms. Although various theories, such as the Theory of planned behavior (TPB) (Ajzen, 1991) have been developed to examine and forecast system acceptance, the TAM model is the most frequently recognized model because it is seen to be more parsimonious, predictive, and resilient than the other models. Various academics in the field of information systems have used it to examine the effect (Liao et al., 2018; Salman & Abd.Aziz, 2015).

TAM is a collection of external variables that track the influence of external factors on two major user perceptions: Perceived Ease of Use (PEOU) and Perceived Usefulness (PU) (PU). These perceptions influence users’ favorable or negative attitudes toward technology. One’s attitude about utilizing technology effects one’s behavioral intention to use and, ultimately, defines the technology’s actual use.

The most essential variables in the technology adoption model are perceived ease of use and perceived usefulness. Perceived Ease of Use is defined as “the degree to which a person feels that utilizing a certain system would be devoid of effort.” The definition of perceived usefulness is “the degree to which a person feels that employing a certain system will improve his or her performance.” Both of these characteristics are impacted by external influences in the TAM model. As a result, including these external elements in the TMA model is critical for describing technology adoption behavior (Davis et al., 1989).

Additionally, Davis et al. (1989) contended that TAM without external factors provides only general information about users’ perceptions of a system and does not provide particular information that may help drive system development. TAM with defined external factors not only forecasts technology utilization but also explains why a specific system may be accepted, allowing researchers and practitioners to take suitable corrective measures (Davis, 1989).

As a result, several studies have expanded TAM with other external components to support a range of issues (Abdullah & Ward, 2016; Sorce & Issa, 2021). Researchers that study the extension of TAM are primarily concerned with the interactions between external influences and the two core dimensions of TAM (PEOU and PU). This research adopts the TAM model as discussed by (Davis et al., 1989) and is presented in Figure 1 below.

Self-Efficacy is the first external component evaluated in TAM in the context of crowd-logistics platform utilization. Self-Efficacy (SE) refers to an individual’s judgment of his or her own capability to perform a specific task (Bandura, 1982). In the context of computer usage, “Computer Self-Efficacy” (CSE) refers to a person’s confidence in his or her ability to complete a task with a computer (Karsten et al., 2012). CSE can affect people’s behavioral intentions to use computers, because people who consider computers too complex and believe that they do not have the ability to use computers will avoid them (John, 2013; Karsten et al., 2012; Loar, 2018). In contrast, “the higher the individual’s computer Self-Efficacy, the greater his/her usage of computers” (Teo et al., 2010). Research shows that SE has a significant impact on how a user perceives the usability of a new platform or technology (John, 2013; Karsten et al., 2012; Romero et al., 2009). This shows that SME owners with greater Self-Efficacy are more inclined to use crowd-logistics platforms (Romero et al., 2009; John, 2013), whereas SME owners with lower Self-Efficacy may avoid utilizing it.

Based on existing literature (Schmid, 2022; Paucar et al., 2021; Liao et al., 2018) this study adopts the Bayesian inference using Markov Chain Monte Carlo (MCMC) approach to analysis the data. Monte Carlo method provides a numerical approach for solving complicated functions. According to Pooley and Marion (2018), the use of Bayesian inference for statistical models enlarges the range of usable models for formulation of more complex statistical models, it also allows non-deterministic knowledge that are difficult to describe with logic

to be represented as a prior distribution and explicitly reflects it in evaluation of explanations (Ishihata et al., 2011). Markov Chain Monte Carlo (MCMC) is particularly useful in Bayesian interference. Thus, to generate a sample from P ( y ) , given we know f ( y ) but not K . As such, we do not know P ( y ) , which can be expressed as;

P ( y ) = f ( y ) K (1)

MCMC allows us to estimate P ( y ) even if we do not know the distribution by utilizing a function f ( y ) that is proportional to the target distribution P ( y ) . We focus on stochastic models that contain parameters θ and latent variables y . As such the Bayes theorem is given as follows:

p ( θ | y ) = p ( y | θ ) p ( θ ) p ( y ) = p ( y | θ ) p ( θ ) ∫ p ( y | θ ) p ( θ ) d θ (2)

To clearly demonstrate how the Bayesian approach functions (Ishihata et al., 2011), in order to calculate the posterior p ( θ | y ) , we need to calculate the product of the likelihood P ( Y | θ ) and the prior p ( θ ) over a normalizing factor (the evidence). As the integral term for the normalizing factor is often complicated and unknown; but the posterior is proportional to the product of the likelihood and prior. For numerical stability during computational simulation, we utilize the log function to transform our data samples and as such calculate the log of the unnormalized posteriror. Hence the posterior distribution is propositional to the likelihood multiplied by the prior distribution as follows:

ln p ( θ | y ) ∝ ln p ( y | θ ) p ( θ ) (3)

We first initialize to some values of θ , for t = 1 , 2 , 3 , ⋯ , N we propose θ based on a proposal distribution q . Then we calculate for the acceptance ratio r and acceptance probability A (Ishihata et al., 2011; Zhang & Mahadevan, 2003).

r ( θ * , θ ( t ) ) = exp ( ln f ( θ * | y ) ln f ( θ ( t ) | y ) ) q ( θ ( t ) | θ * ) q ( θ * | θ ( t ) ) (4)

= exp ( ln f ( θ * | y ) − ln f ( θ ( t ) | y ) ) q ( θ ( t ) | θ * ) q ( θ * | θ ( t ) ) (5)

Finally, we accept the new θ according to acceptance probability A . Here we are defining f as the unnormalized posterior, where,

f ( θ | y ) = p ( y | θ ) p ( θ ) (6)

To know if MCMC has converged we examine the trace that is, the plot of θ over iterations. As the newly proposed θ is dependent on the current θ we expect some auto-correlation in the Markov chain as the samples are not completely independent. As such it can be shown that the error of the estimation in MCMC is,

σ 2 ≈ τ N V a r p ( θ | y ) [ θ | y ] (7)

where τ is the integrated auto-correlation time of the chain and represents the steps needed before it is no longer dependent. We use an effective sample size N τ to account for the auto-correlation. Thus, to minimize error we reduce the

auto-correlation and increased the number of samples. Our approach to reducing auto-correlation is via thinning, that is, taking the nth sample after convergence for constructing the distribution. For further studies on Bayesian Inference using MCMC you can refer to, (van Ravenzwaaij et al., 2018).

To ensure the reliability of the study scales of all variables are referenced from previous research. The six antecedent variables, including: perceived experience, subjective norms, enjoyment, computer anxiety and self efficacy are adapted from (Abdullah & Ward, 2016; Sorce & Issa, 2021). With respect to the antecedent perceived risked, we measured it with the scale used by (Chin et al., 2015; Lai, 2017). The 7-point Likert scale was employed; with scores ranging from strongly disagree to strongly agree. As a result, we created a questionnaire with 32 items to examine the essential factors in this investigation. Table 2 presents the survey items and sources.

This study employed the purposive sampling approach where participants were chosen based on their characteristics and aims of the investigation. As such, our research selected SME owners across Africa who had at least received a high school diploma. These SME owners were supposed to have been in operations for at least a year. An online poll was sent across Africa through their social media groups on Facebook, WhatsApp and Telegram. A population size of 1000 group members was supplied with a URL link to the survey to answer the questionnaire individually at their convenience. Follow up reminders were issued frequently over a one-month period. To guarantee privacy all the questions were gathered anonymously. For each portion of the questionnaire; the researcher offered specific instructions to assist participants answer individual questions truthfully. Table 3 presents a descriptive statistics of the respondents of this research.

A filter question was used to identify persons who owned SME’s and had some awareness of crowd-logistics platforms. These individuals are more likely to be current on logistics and delivery trends while also having some understanding of how these platforms work. Finally, while 135 replies were received, only 130 were complete and could be analyzed. This data set is sufficient to run a Bayesian inference model on (Paucar et al., 2021).

Monte-Carlo is a mathematical term that refers to the method of estimating posterior parameters using random sampling in order to analyze the acquired parameters. The MCMC sampling technique is carried out by combining the well-established and dependable Metropolis-Hastings algorithm with the No-U-Turn Sampler (NUST) on the data. The NUST is especially advantageous for sampling from models with a large number of continuous parameters. And the

Metropolis-Hastings algorithm samples randomly from a posterior distribution in order to estimate the properties of its parameters across a large number of repetitions using a specific algorithm to successively generate a Markov Chain for a number of underlying components. PyMC3 is a Python library for Bayesian statistical modeling and Probabilistic Machine Learning, with a particular emphasis on advanced Markov chain Monte Carlo (MCMC) and variational inference (Salvatier et al., 2016).

The Bayesian Cronbach’s alpha is used to determine the reliability and validity of the method. It was calculated using the Python pingouin module. Table 4 contains the data. We present a normality test focused on the endogenous variables of our research respondents in Figure 3 below.

As a pre-requisite for the validity of the model, reliability analysis in Table 4 has been conducted. The Cronbach’s Alpha values were calculated for each construct. The TMA model indicated a satisfactory fit. Cronbach’s alpha values range from 0.8728 to 0.9849 indicating high overall internal consistency among the items under each of the constructs, which is greater than the acceptable criterion of 0.70 (Thorndike, 2016) confirming the measurement model’s dependability.

Prior to evaluating the fitness of the conceptual model described in Table 4, it is

important to compare the scale value of the technology acceptance model that the participating SME owners showed regarding the adoption of crowd logistics platforms and its corresponding technology. The data was analyzed using a Bayesian repeated-measure ANOVA (Schmid & Stanton, 2019). In terms of their prior odds, all hypotheses are considered to be equally likely. Thus, the default Microsoft Excel prior for fixed effects with alpha (α) = 0.5. was used in the study. Results from the Bayesian ANOVA are summarized in Table 5. Hypotheses were tested against the null model in order to see how well they predicted outcomes. The seven latent variables served as categorical predictors. All possible models were considered, but we ruled out any that had substantial evidence for their existence (H₀). Because they’re considered implausible, we also excluded models with interactions but no main effects. As can be seen in Table 6, the models that have been left over provide at least some support for the hypothesis that the combined effects are real. Table 5 provides a summary of our results.

A one-way repeated ANOVA was conducted to examine the adoption of crowd logistics platforms for SME’s in Africa. The F test statistic is 95.57407 and the corresponding p-value is 0.0000199. Since the p-value is less than 0.005, we reject the null hypothesis and conclude that there is a statistically significant mean between our constructs. These results show substantial evidence for the acceptance of these logistical platforms by SME owners to be high and confirms the robustness of these results against changes in the priors.

To derive posterior estimates for the model’s unknown variables, we investigate locating the Maximum Posteriori (MAP) point and producing summary statistics using MCMC sampling methods, which is presented in Table 7 below.

The maximum a posteriori (MAP) estimates for a model are the mode of the posterior distribution and are often determined using numerical optimization techniques. While this is frequently a quick and simple procedure, it simply provides a point estimate for the parameters and might be misleading if the mode does not represent the distribution. PyMC3’s find MAP function implements this feature (Salvatier et al., 2016). Figure 4 presents the posterior samples of degrees of freedom (mu) and scale (sigma) parameters of TAM model. Each plotted line represents a single independent chain in parallel.

Because the syntax is comparable to statistical notation, specifying this model in PyMC3 is simple. Each line of Python code, for the most part, corresponds to a line in the model notation. We import the necessary components from PyMC3 and run the model. This is the model statement that describes the priors and likelihood. In this case, mu is defined as a stochastic variable (we want a chain of sampled values for it), and we offer a prior distribution and hyper-parameters for it. The Normal likelihood function is used, with one parameter to be estimated (mu) and one known (denoted as sigma). Our “dependent variable” is defined as observed=data, where data is collected from respondents. The research has an acceptance rate of 0.872115 and the auto-correlate of degrees of freedom (mu) and scale (sigma) parameters of the model is displayed in Figure 5.

The data run through the PyMC3 model and the results indicate a good fit to the

model. We plot the distribution of the model by plotting many of our sampled volatility paths on the same graph. Each is rendered partially transparent as such the regions where many paths overlap are shaded more darkly.

As can be seen the model correctly infers the relationship between perceived risk, perceived experience, subjective norms, enjoyment, computer anxiety and self efficacy and the perceived usefulness of the model. In addition, the results indicate that perceived risk is a strong factor that affects SME owner’s willingness to adopt crowd logistics platforms. In other words, SME owner’s are more likely to use crowd logistics platforms if they feel the inherent perceived risk can be mitigated and they will benefit from using the platform. The normality test of our data (Figure 3) showed that our data is normally distribution and all hypothesized relations were strong.