Production inventory control model for deteriorating complementary and substitute items with shortage

A combination of complementary and substitute products are very significant for any business industry to make all-round profit from various prospect. How deterioration affects complementary products or substitute products is discussed in this study. A deterministic production inventory control model for complementary and/or substitute items with a constant deterioration rate is studied. Here a shortage is also allowed. During shortage period, the demand of available item increases due to the shortage of substitute items. Similarly, the demand of available item decreases due to the shortage of complementary items during the said period. The demand is both price and stock dependent and the deteriorated items are salvaged. Here the total profit function consist of sales of product, inventory holding cost, green technology cost, carbon tax, production cost and salvage value. Numerical examples illustrate the theoretical results. The Pontryagin Maximum principle is used to solve the said optimal control inventory model. To justify the effectiveness of our model we check the sensitivity analysis. The results of this model are also graphically presented with the help of MATLAB software.