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Economies of scale : The concept of making goods according to economy of scale is relevant when we have set up cost, hodling cost, change over cost, fixed cost, etc. The different costs mentioned would either be fixed or would vary depending on the quantum of production. Hence it would make sense to increase the batch size of production in order to compensate the fixed cost component. In doing so one should also remember that the variable cost component also increases. So a compromise on the total number of goods is made which would result in increasing the revenues and at the same time decrease the input cost, so that the profit is maximized. Economies of scales also make sense when there are discounts, change of technology which increases the rate of production substantially, etc.

Variability : Variability can be either predictable or unpredictable. The concept of variability can be present when one orders good, procures them, tries to do a demand analysis of the quantum of goods required, explores cost of inventory depending on its fluctuation, examines the cost of goods being procured, evaluates the existing demand and supply of the goods in the existing markets, etc. These type of variability effects the planning of the production system and a judicious choice of well thought out plans helps one to achieve the objective at hand.

Conflicting Interests : In making a decision like how many goods to supply, from where to get the goods dependning on quality, how fast to get the products delievered, etc., would always result in different plans which may not be at concurrence with each other. Hence to plan a production system in detail and have a well thought out supply chain mechanism in place would results in many situations where conflicts arise. But the main emphasis of the production planning system should always be to have some concrete objective(s) of the production planning system in mind so that it/they can be met without being bothered about any individual objective, however practical it may be.

Single period model

Assume you have a single period for which you need to order a demand , where demand , per unit production cost is , per unit shortage cost or penalty is , per unit holding cost is , per unit left over stock cost is . Now if  is the stock level after ordering, then, , where  is the optimum stock level. In case one is interested to find the buffer stock, then its value is given by the quantity . If  is the crucial factor, then the optimal objective function value can be written as , where  and  is the unit normal loss function. In case we have discontinuous product or distribution function, then . On the other hand if demand distribution is known in its functional form but the parameters are unknown, then one assumes some priors to solve such problems.