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Optimal ordering quantities for substitutable items under joint replenishment with cost of substitution

Mishra V. K., Shanker K.

Operations Research and Decisions

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2017

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Vol. 27, No. 1

77--104

EN

An inventory system of two mutually substitutable items has been studied where an item is out of stock, demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted item. The demands are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle, in order to take advantage of joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. The critical value of the substitution rate is defined to help in deciding the optimal value of decision parameters. Extensive numerical experimentation is carried out, which shows that prior knowledge of the critical value of the substitution rate helps to minimize the total inventory cost. Sensitivity analysis is carried out for the improvement in the optimal total cost with substitution as compared to the case without substitution to draw insights into the behaviour of the model.

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Optimal ordering quantities for substitutable deteriorating items under joint replenishment

Mishraa V., Shankerb K.

Control and Cybernetics

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2017

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Vol. 46, no. 1

49--70

EN

In this paper, we study an inventory system for two substitutable deteriorating items where when an item is out of stock, the demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. The level of inventory of both items deplete due to combined eﬀect of demand fulﬁlment and deterioration. The rates of demand and deterioration are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle so as to take advantage of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. An extensive numerical analysis is carried out to illustrate the parameters of the model. The results indicate that there is substantial improvement in the optimal total cost of the inventory system with substitution over the case without substitution.

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Adaptive inventory control system for material items with continuous non-stationary demand

Krajčovič M., Plinta D.

Management and Production Engineering Review

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2014

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Vol. 5, No. 1

11--20

EN

This paper describes an algorithm of dynamic inventory control system for large numbers of material items with continuous non-stationary demand. It uses principles of pull inventory control systems, statistical inventory analysis and joint replenishment inventory systems. This algorithm was processed in software module (VBA for Excel) and applied in practice. The target of described algorithm is to keep an optimum inventory level and optimum customer service level in terms of inventory control of items with non-stationary demand.