Purpose Being the final end of the logistic distribution, attended home delivery (AHD) plays an important role in the distribution network. AHD typically refers to the service provided by the distribution service provider to the recipient's doorstep. Researchers have always identified AHD as a bottleneck for last-mile delivery. This paper addresses a real-life stochastic multi-objective AHD problem in the context of the Indian public distribution system (PDS). Design/methodology/approach Two multi-objective models are proposed. Initially, the problem is formulated in a deterministic environment, and later on, it is extended to a multi-objective AHD model with stochastic travel and response time. This stochastic AHD model is used to extensively analyze the impact of stochastic travel time and customer response time on the total expected cost and time-window violation. Due to the NP-hard nature of the problem, an ant colony optimization (ACO) algorithm, tuned via response surface methodology (RSM), is proposed to solve the problem. Findings Experimental results show that a change in travel time and response time does not significantly alter the service level of an AHD problem. However, it is strongly correlated with the planning horizon and an increase in the planning horizon reduces the time-window violation drastically. It is also observed that a relatively longer planning horizon has a lower expected cost per delivery associated. Research limitations/implications The paper does not consider the uncertainty of supply from the warehouse. Also, stochastic delivery failure probabilities and randomness in customer behavior have not been taken into consideration in this study. Practical implications In this paper, the role of uncertainty in an AHD problem is extensively studied through a case of the Indian PDS. The paper analyzes the role of uncertain travel time and response time over different planning horizons in an AHD system. Further, the impact of the delivery planning horizon, travel time and response time on the overall cost and service level of an AHD system is also investigated. Social implications This paper investigates a unique and practical AHD problem in the context of Indian PDS. In the present context of AHD, this study is highly relevant for real-world applications and can help build a more efficient delivery system. The findings of this study will be of particular interest to the policy-makers to build a more robust PDS in India. Originality/value The most challenging part of an AHD problem is the requirement of the presence of customers during the time of delivery, due to which the probability of failed delivery drastically increases if the delivery deviates from the customer's preferred time slot. The paper modelled an AHD system to incorporate uncertainties to attain higher overall performance and explore the role of uncertainty in travel and response time with respect to the planning horizon in an AHD, which has not been considered by any other literature.
