A Two-Product Inventory Model with a Joint Ordering Policy

Inventory is one of the most visible and tangible aspects of doing business. This is the reason why most problems of a business often end up in inventory. Most inventory studies focus on a single type of product or item such that optimality decisions are arrived at for that single product. In this study, we create a scenario where two types of products are considered in such a way that there exists a joint ordering policy. A continuous review inventory model was developed but ended up with a single period review model for simplicity reasons. We tried to exhaust all main cost elements and fed them into the model in addition to investigating the possible limitations that may constrain the whole decision making process. Six constraints were found and a mathematical programming model was developed. We further went on to prove that the mathematical inventory-programming model developed minimises the total inventory cost in such a scenario. 1. Introduction The role of inventory management is to coordinate the actions of sales, marketing, production, and purchasing to ensure that the correct level of stocks is held to satisfy customer demand at the lowest possible costs; hence, aiming to balance out supply and demand by regulating the supply of goods in such a way that they match demand conditions as close as possible. Some demand conditions require the application of multiple replenishment orders in continuous-review inventory systems. Reference [1] highlighted that in such a study the concept of common demand for some products arises; for example, when a customer arrives at a shop that sells two brands of soft drinks, the customer would be satisfied by a particular brand with a certain probability. Also, when a supplier is the same for several products under consideration, the retailer will prefer to have simultaneous replenishment for all products due to several reasons like cost considerations and so forth. Researchers like [2] allowed shortages and assumed that the lost sale policy could be applied when studying such kind of demand conditions. Their demand was not deterministic but stochastic, following a Poisson distribution. Later, [3] developed optimal coordination policies for manufacturing and supply divisions. The authors considered a problem where the responsibility of the manufacturing division was to provide a sufficient amount of raw materials so that the required production level could be achieved. Reference [4] studied such demand conditions and it was under continuous review of multiproduct inventory systems. Like Mohebi and Posner [2], they