Optimizing price, lot size and backordering level for products with imperfect quality, different holding costs and non-linear demand

In this paper, the authors propose a non-linear cost function based on ecological considerations for lot-size planning. The classical approaches of lot-size optimization, the Wagner-Whitin algorithm and the Part-Period Balancing heuristic, are enhanced with so-called eco-factors. These eco-enhanced approaches combined with eco-balancing help to reduce overall production costs. Simultaneously, the environmental impact is also reduced.

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Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times

Applied Sciences ◽

10.3390/app112311210 ◽

2021 ◽

Vol 11 (23) ◽

pp. 11210

Author(s):

Mohammed Alnahhal ◽

Diane Ahrens ◽

Bashir Salah

Keyword(s):

Lot Sizing ◽

Planning Horizon ◽

Service Level ◽

Mixed Integer ◽

Lot Size ◽

Dynamic Planning ◽

Holding Costs ◽

Delivery Times ◽

Mip Model ◽

Total Inventory

This study investigates replenishment planning in the case of discrete delivery time, where demand is seasonal. The study is motivated by a case study of a soft drinks company in Germany, where data concerning demand are obtained for a whole year. The investigation focused on one type of apple juice that experiences a peak in demand during the summer. The lot-sizing problem reduces the ordering and the total inventory holding costs using a mixed-integer programming (MIP) model. Both the lot size and cycle time are variable over the planning horizon. To obtain results faster, a dynamic programming (DP) model was developed, and run using R software. The model was run every week to update the plan according to the current inventory size. The DP model was run on a personal computer 35 times to represent dynamic planning. The CPU time was only a few seconds. Results showed that initial planning is difficult to follow, especially after week 30, and the service level was only 92%. Dynamic planning reached a higher service level of 100%. This study is the first to investigate discrete delivery times, opening the door for further investigations in the future in other industries.

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A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

RAIRO - Operations Research ◽

10.1051/ro/2021020 ◽

2021 ◽

Vol 55 (2) ◽

pp. 723-744

Author(s):

Sujit Kumar De ◽

Gour Chandra Mahata

Keyword(s):

Deterministic Model ◽

Classical Method ◽

Profit Maximization ◽

Extensive Study ◽

Inventory Model ◽

Purchasing Cost ◽

Imperfect Quality ◽

Holding Costs ◽

Fuzzy Environment ◽

Imperfect Items

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

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