Comparing the outdate quantities for quantity based and useful lifetime based fixed lifetime inventory models

Introduction

The ordering policy of a fixed lifetime inventory system is an expression that tells the inventory manager when to order and how much to order. Some ordering policies are based on the quantity of items on hand while others are based on the number of useful lifetimes remaining on the quantity on hand. The goal of a good ordering policy is to minimize the outdate and shortage quantities. The egg inventory (chicken eggs) is our focus in this work. The useful, safe and high quality lifetime of chicken eggs is four (4) weeks. Eggs can be stored through any of the following ways; refrigerated, hard-boiled or unrefrigerated. Refrigerated eggs remain consumable 4 weeks from the time of purchase. Hard-boiled eggs are best consumed 1 week, if placed in the refrigerator, whether peeled or unpeeled while unrefrigerated eggs are best consumed two weeks from the time of purchase. After 4 weeks, the eggs go bad and are no longer safe for consumption. There are three simple test that can be conducted to determine if the eggs are good or bad.

The float test: place the egg in a bowl of water. A fresh egg will sink to the bottom on its side. An older egg, still safe for consumption will stand on one end while a bad egg will floats to the top.

The

smell test: on breaking a bad or rotten egg, there will be a distinct sulfur smell that is poisonous to humans.

Appearance

broken eggs with a pink or iridescent white should be discarded In this work, we shall compare three ordering policies on the egg inventory, our aim is to determine which ordering policy minimizes the outdate quantity. The ordering policies to be considered are the ordering policy by (Chiu, 1994) [1] , the ordering policy by (Fries, 1975) [2] and the ordering policy by (Izevbizua et al., 2021) [3] . The ordering polices, base the decision to reorder on the quantity of items on hand while the ordering policy, base the decision to reorder on the number of useful lifetime remaining on the items on hand in inventory. Two of the biggest problems of the fixed lifetimes inventory system (like the egg inventory) is the quantity of outdates and the shortages associated with the inventory system. Outdates refer to items in inventory whose useful lifetime is over (that is expired items) and shortage refer to situation where inventory managers cannot meet the customers demand. Expired items are dangerous for consumption and leads to loss of revenue while shortages can lead to lost of customers goodwill. The goal of every inventory manger is to minimize these two occurrences. Next we briefly discuss the three ordering policies and run a simulation on them.

ordering policy: the policy was developed by (Chiu, 1994) [1] and has been used by authors like (Izevbizua et al., 2021; Izevbizua et al., 2019; Liu et al., 1999) [3,4,5] in the literature. The policy states that is ordered whenever on hand inventory drops to . The decision to order is based on the on hand inventory dropping to . The reorder frequency is determined by demand, if demand is low, the reorder frequency is low and if demand is high the reorder frequency is high. When demand is low, it takes longer time for items to drop to the reorder point and this can lead to outdates. The policy is easy to implement and can be applied to small, medium and larger scare businesses. The total cost function obtained by (Chiu, 1994) [1] is given in equation (1) Substituting in equation ( 1) gives

The ordering policy was used by (Fries, 1975) [2] to obtain the optimal ordering policy for perishable commodities with fixed lifetime. The quantity of items ordered is not fixed and new orders arrive inventory every period. The total cost function obtained by (Fries, 1975) [2] is given as

The ordering policy was designed by (Izevbizua et al., 2021) [3] . The policy is based on the number of useful lifetime remaining on the items on hand and the quantity ordered is not fixed. The cost function as obtained by (Izevbizua et al., 2021) [3] is Using the same set of conditions for three models, a 30 weeks simulation was carried out and the results for each model is as shown. 1 shows a 30 weeks ordering policy for egg, where the quantity order and the reorder point . New orders are placed only when on hand inventory drops to 10. From the table, 50 creates of eggs arrived, week 1 and 25 was used to meet demand. The demand for the second week was 15, reducing on hand inventory to 10 and a new order placed. With a useful lifetime of 4 weeks, any create not used to meet demand by the end of the fourth week expires and must be discarded.

References

1. Chiu HN. An approximation to the continuous review inventory model with perishable items and lead times. European journal of operations research. 1994;87:93-103.
2. Izevbizua O, Batubo TB. A new ordering policy for the fixed lifetime inventory system. The journal of the Mathematical Association of Nigeria. 2021;48(1):38-44.
3. Applied Mathematics. 2026;11(10):20-25. doi: http s://www.doi.org/10.22271/maths.2026.v11.i10a.2712 International Journal of Statistics and Applied Mathematics https://www.mathsjournal.com 24561452, 2026, 11(10), Downloaded from https://www.doi.org/10.22271/maths.2026.v11.i10a.2712 by International Journal of Statistics and Applied Mathematics on [06/10/2026]. See the Terms and Conditions (https://www.mathsjournal.com) for rules of use; OA articles are governed by the applicable Creative Commons License