Mathematical Optimization of Product Pricing and Inventory in China Vending Machine Market

Abstract

The rapid expansion of automated retail has made vending machines an increasingly important channel for convenient consumer services in China. However, operators face a joint decision problem involving product pricing, inventory allocation, replenishment, and uncertain demand. This paper develops a mathematical optimization framework for product pricing and inventory management in the Chinese vending machine market. A demand function is constructed to capture the effects of price, location, time, product characteristics, and random demand fluctuations. The model integrates expected sales revenue, purchasing cost, holding cost, shortage cost, and waste or expiration cost into a unified profit objective. A constrained optimization problem is then formulated to determine product-level prices and inventory quantities under capacity, budget, service-level, and operational constraints. The analysis shows that optimal decisions should balance price sensitivity against inventory availability rather than maximize sales volume alone. Products with high demand uncertainty require more flexible safety-stock policies, while products with relatively stable demand can be managed with tighter inventory levels. Location-specific pricing and differentiated inventory policies can improve profitability when consumer demand varies substantially across sites. The paper provides an analytical basis for vending machine operators to coordinate pricing and inventory decisions and identifies directions for incorporating real-time data and machine-learning forecasting into future optimization models.