A Multi-Item Probabilistic Inventory Model that Considers Expiration Factor, All Unit Discount Policy and Warehouse Capacity Constraints


  • Roland Y.H. Silitonga Program Studi Logistik Institut Teknologi Harapan Bangsa Bandung
  • Leo Rama Kristiana Program Studi Logistik Institut Teknologi Harapan Bangsa Bandung
  • Tabita Anette Parley




probabilistic inventory model, all unit discount, perishable, warehouse capacity


The characteristics considered in this study are probabilistic demand, perishable products, and warehouse constraints for multi-item inventory models. This condition occurs in several industries that consider perishable factors and warehouse constraints, namely companies that produce food, food sales agents, and retail that sell goods to end customers. The Karush-Kuhn-Tucker Condition approach was used to solve the warehouse capacity problem to find the optimum point of a constrained function. The results of the developed inventory model provide two optimal ordering times, namely ordering time-based on warehouse capacity and joint order time, and the two ordering time values ​​will be compared to determine which ordering time is optimal. In addition, the sensitivity analysis to the model was done to analyse the total inventory costs in a planning horizon, the time between goods ordering from one cycle to the next cycle, and the number of items that will expire. The parameters to be changed for the sensitivity test were warehouse constraint, a fraction of good condition goods, holding costs per unit per period, and all unit discount factors. The sensitivity analysis was done to see the behaviour of the total cost, time to order changes, and the quantity of perished products. The result of model testing and sensitivity analysis showed that total cost, based on joint order, is sensitive to the fraction of good condition products, discount, and holding cost.  The joint order was not sensitive to the warehouse capacity. In general, the model was perceived as able to describe the behaviour of the model components.


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