Extended Abstract

Introduction and purpose: The growth of e-commerce and rising costs in the final stage of the supply chain have prompted postal and logistics companies to seek solutions that increase productivity and reduce costs. These developments have caused policymakers in the supply chain to pay special attention to the final stage of goods delivery. This stage is considered one of the critical factors in increasing intra-city traffic and has a direct impact on the performance of urban logistics. One relatively new logistics solution is the use of smart delivery lockers as an alternative to home delivery. Using these lockers reduces the need for additional trips and optimises transportation in the final stage of distribution, although costs arising from customers travelling to the lockers may also be imposed on the system. The location of these lockers and the price of this service affect customer choice and preference for home delivery. The present study therefore aims to develop an integrated location-pricing model for urban smart lockers.

Methodology: This study develops an integrated location-pricing model for smart lockers in an urban distribution network, modelling locker location decisions and delivery service pricing simultaneously and at the same level. This approach is primarily driven by the interdependence of these decisions in final delivery networks. The location of lockers directly impacts customer reach, demand coverage and capacity utilisation levels, while service pricing determines demand and the profitability of each location. Therefore, making these decisions separately can result in suboptimal economic and operational solutions. Consequently, decisions regarding the selection of locker installation locations, the determination of service prices at each site and the allocation of customer demand are made simultaneously to accurately reflect the interaction between the spatial and economic aspects of the network. In the proposed model, demand is price-sensitive in order to examine the direct effect of pricing policies on customer behaviour and demand absorption. The price of each service is set within a controlled range and a price deviation constraint is applied between sites to maintain coordination at the network level. Constraints related to locker type capacity, service capability, demand coverage and flow balance are also included in the model to ensure operational decisions remain consistent. The model can be applied over multiple time periods, with each customer using only one of the active lockers in their area. The installation and operating costs of each locker type are fixed and transportation costs are calculated in proportion to geographical distance. A logistics company manages all lockers, making location, pricing and demand allocation decisions centrally with the aim of maximising total profit over a multi-period horizon. The developed mathematical model is a mixed-integer non-linear mathematical programming. To ensure that the model can be solved in a reasonable amount of time, some nonlinear relationships have been rewritten using linearisation transformations and the definition of combined variables.

Findings: Computational findings show that permissible price limits and price deviation constraints between sites play a decisive role in forming the spatial pattern, allocating demand and determining the final profit of the network under study. The most important managerial outcome of the proposed model is that locker capacity is the most important profit driver. However, increasing capacity to the optimal level sharply increases profit, and after reaching saturation point, further capacity increases only create costs and do not increase efficiency. Additionally, locker installation costs are the most critical cost factor and cause the greatest profit reduction. Controlling the initial investment cost is more important than controlling other costs. Additionally, the results showed that network expansion should be targeted, as increasing potential locations or demand points does not necessarily increase profits. In many cases, due to high costs or low demand, network profit decreases. Analysis of the results shows that the proposed model can be used as a decision-making tool by managers and policymakers in urban logistics, providing an optimal platform for decision-making and helping to reduce costs and increase customer satisfaction in urban delivery networks.

Conclusion: In addition to theoretical aspects, this research includes valuable management results for logistics companies, locker users, and urban policymakers. The analyses show that the optimal design of a smart locker network is a multidimensional decision with economic, operational, and social impacts.