Pricing joint products in liner shipping

Fronthaul and backhaul shipping trips share the same round-trip voyage costs. The pricing strategies for the two trips are critical to the performance of liner operators, as well as the trade volume. This paper analyses the pricing strategies for the two trips in liner shipping based on different levels of demand imbalance. The critical condition is found when demand imbalance causes trade imbalance, and the optimal pricing strategies and the relationship between fronthaul and backhaul prices in both balanced trade and imbalanced trade are identified. Using the properties derived from theoretical analysis and employing Johansen's vector error correction model, the relationships between fronthaul and backhaul container freight rates for the Trans-Pacific, Trans-Atlantic and Euro-Asia routes were tested, and the critical trade imbalance ratios that disintegrate the freight rates for both directions were identified.