Heuristic analyses of separate and bundling sales for complimentary products under consignment stock policy

•We develop two JELS models under VMI-CS policy for two-complementary products.•Two nonlinear mixed-integer models for bundling and separate sales are proposed.•The concavity of the objective functions is studied and two algorithms are proposed.•Some applicable and management guidelines are obtained from the numerical study.•It is shown that in bundling, the SC members benefit from the economy of scale. In the real world, various products are displayed simultaneously on the shelf; therefore, their demands/prices affect each other. This paper aims at studying a joint economic lot-sizing model with two complementary products in a supply chain consisting of a vendor and a buyer. The vendor sends items to the buyer's warehouse in equal-size batches applying vendor-managed inventory with consignment stock policy. The buyer stocks items at the warehouse and on the shelf. Two mixed-integer nonlinear models that consider bundling and separate sales have been proposed and solved through different solution algorithms such that the profit is maximized. The concavity of both models' objective functions is investigated and the effect of considering complementation between products and bundling strategy is studied. Numerical experiments indicate that the bundle's marginal profit is greater than a single product's marginal profit. Moreover, the supply chain members can also take advantage of economies of scale in bundling sales.