Market demand in today's global environment is highly dynamic, shaped by globalization, evolving consumer preferences, and shifting priorities. To address these challenges, firms increasingly adopt dual-channel supply chain systems that integrate both online and offline channels. The integration of sales data across these channels provides valuable insights into consumer behavior, enabling effective resource allocation during peak seasons and periods of demand uncertainty. In this study, an integrated dual-channel supply chain model is developed under a stochastic lead time and variable demand, incorporating investment in lead time reduction and setup costs reduction. Demand is considered as a function of the selling price, the advertisement cost, and the consumer service cost for both channels. The model allows shortages and treats the reorder point as a decision variable, jointly determining the optimal selling price, order quantity, reorder point, lead time, machine failure rate, and cost allocations. A global solution is obtained analytically, and an iterative algorithm provides optimal numerical results. The analytical results show that dual-channel facilities significantly boost profitability. Profit decreases by 62.90% and 43.18% when the offline and online facilities are absent, respectively. Consumer service facilities are also critical, as profit declines by 10.99% without them. Similarly, profit decreases by 7.65% in the absence of advertisement facilities and by 3.70% when setup costs reduction is not considered. The findings also indicate that the absence of free delivery reduces profit by 2.25%.
Citation: Nandita Barman, Adrijit Goswami, Biswajit Sarkar, Mitali Sarkar. Service oriented dual channel supply chain system with stochastic lead time and variable demand[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 716-753. doi: 10.3934/jimo.2026026
Market demand in today's global environment is highly dynamic, shaped by globalization, evolving consumer preferences, and shifting priorities. To address these challenges, firms increasingly adopt dual-channel supply chain systems that integrate both online and offline channels. The integration of sales data across these channels provides valuable insights into consumer behavior, enabling effective resource allocation during peak seasons and periods of demand uncertainty. In this study, an integrated dual-channel supply chain model is developed under a stochastic lead time and variable demand, incorporating investment in lead time reduction and setup costs reduction. Demand is considered as a function of the selling price, the advertisement cost, and the consumer service cost for both channels. The model allows shortages and treats the reorder point as a decision variable, jointly determining the optimal selling price, order quantity, reorder point, lead time, machine failure rate, and cost allocations. A global solution is obtained analytically, and an iterative algorithm provides optimal numerical results. The analytical results show that dual-channel facilities significantly boost profitability. Profit decreases by 62.90% and 43.18% when the offline and online facilities are absent, respectively. Consumer service facilities are also critical, as profit declines by 10.99% without them. Similarly, profit decreases by 7.65% in the absence of advertisement facilities and by 3.70% when setup costs reduction is not considered. The findings also indicate that the absence of free delivery reduces profit by 2.25%.
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Nandita Barman, Adrijit Goswami, Biswajit Sarkar, Mitali Sarkar. Service oriented dual channel supply chain system with stochastic lead time and variable demand[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 716-753. doi: 10.3934/jimo.2026026
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