scholarly journals Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times

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.

Optimization Methods for Lot-Sizing Problem in an Automated Foundry

2013 ◽  
Vol 58 (3) ◽  
pp. 863-866 ◽  
Author(s):  
J. Duda ◽  
A. Stawowy
Keyword(s):  
Production Planning ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Planning Problem ◽  
Lot Size ◽  
Mip Model ◽  
Production Planning Problem ◽  
Problem Instances

Abstract In the paper we studied a production planning problem in a mid-size foundry that provides tailor-made cast products in small lots for a large number of clients. Assuming that a production bottleneck is the furnace, a mixed-integer programming (MIP) model is proposed to determine the lot size of the items and the required alloys to be produced during each period of the finite planning horizon that is subdivided into smaller periods. As using an advanced commercial MIP solvers may be impractical for more complex and large problem instances, we proposed and compared a few computational intelligence heuristics i.e. tabu search, genetic algorithm and differential evolution. The examination showed that heuristic approaches can provide a good compromise between speed and quality of solutions and can be used in real-world production planning.

scholarly journals The integrated uncapacitated lot sizing and bin packing problem

2021 ◽  
Author(s):  
Natã Goulart ◽  
Thiago Ferreira de Noronha ◽  
Martin Gomez Ravetti ◽  
Mauricio Cardoso de Souza
Keyword(s):  
Bin Packing ◽  
Lot Sizing ◽  
Packing Problem ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Holding Costs ◽  
Bin Packing Problem ◽  
Combinatorial Relaxation ◽  
The Cost ◽  
Inventory Holding

In the integrated uncapacitated lot sizing and bin packing problem, we have to couple lot sizing decisions of replenishment from single product suppliers with bin packing decisions in the delivery of client orders. A client order is composed of quantities of each product, and the quantities of such an order must be delivered all together no later than a given period. The quantities of an order must all be packed in the same bin, and may be delivered in advance if it is advantageous in terms of costs. We assume a large enough set of homogeneous bins available at each period. The costs involved are setup and inventory holding costs and the cost to use a bin as well. All costs are variable in the planning horizon, and the objective is to minimize the total cost incurred. We propose mixed integer linear programming formulations and a combinatorial relaxation where it is no longer necessary to keep track of the specific bin where each order is packed. An aggregate delivering capacity is computed instead. We also propose heuristics using different strategies to couple the lot sizing and the bin packing subproblems. Computational experiments on instances with different configurations showed that the proposed methods are efficient ways to obtain small optimality gaps in reduced computational times.

Coordinating lot sizing and integrated production and distribution scheduling with batch delivery and holding cost

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Maedeh Bank ◽  
Mohammad Mahdavi Mazdeh ◽  
Mahdi Heydari ◽  
Ebrahim Teimoury
Keyword(s):  
Supply Chain ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Time Interval ◽  
Content Type ◽  
Integrated Production ◽  
Holding Costs ◽  
Integrated Production And Distribution ◽  
Distribution Scheduling ◽  
Production And Distribution

PurposeThe aim of this paper is to present a method for finding the optimum balance between sequence-dependent setup costs, holding costs, delivery costs and delay penalties in an integrated production–distribution system with lot sizing decisions.Design/methodology/approachTwo mixed integer linear programming models and an optimality property are proposed for the problem. Since the problem is NP-hard, a genetic algorithm reinforced with a heuristic is developed for solving the model in large-scale settings. The algorithm parameters are tuned using the Taguchi method.FindingsThe results obtained on randomly generated instances reveal a performance advantage for the proposed algorithm; it is shown that lot sizing can reduce the average cost of the supply chain up to 11.8%. Furthermore, the effects of different parameters and factors of the proposed model on supply chain costs are examined through a sensitivity analysis.Originality/valueAlthough integrated production and distribution scheduling in make-to-order industries has received a great deal of attention from researchers, most researchers in this area have treated each order as a job processed in an uninterrupted time interval, and no temporary holding costs are assumed. Even among the few studies where temporary holding costs are taken into consideration, none has examined the effect of splitting an order at the production stage (lot sizing) and the possibility of reducing costs through splitting. The present study is the first to take holding costs into consideration while incorporating lot sizing decisions in the operational production and distribution problem.

Environmentally sustainable stochastic procurement model

2018 ◽  
Vol 29 (3) ◽  
pp. 472-498 ◽  
Author(s):  
Harpreet Kaur ◽  
Surya Prakash Singh
Keyword(s):  
Carbon Emissions ◽  
Environmental Sustainability ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Business Environment ◽  
Manufacturing Firms ◽  
Mixed Integer ◽  
Content Type ◽  
Environmentally Sustainable ◽  
Procurement Planning

Purpose Procurement planning has always been a huge and challenging activity for business firms, especially in manufacturing. With government legislations about global concern over carbon emissions, the manufacturing firms are enforced to regulate and reduce the emissions caused throughout the supply chain. It is observed that procurement and logistics activities in manufacturing firms contribute heavily toward carbon emissions. Moreover, highly dynamic and uncertain business environment with uncertainty in parameters such as demand, supplier and carrier capacity adds to the complexity in procurement planning. The paper aims to discuss these issues. Design/methodology/approach This paper is a novel attempt to model environmentally sustainable stochastic procurement (ESSP) problem as a mixed-integer non-linear program. The ESSP optimizes the procurement plan of the firm including lot-sizing, supplier and carrier selection by addressing uncertainty and environmental sustainability. The model applies chance-constrained-based approach to address the uncertain parameters. Findings The proposed ESSP model is solved optimally for 30 data sets to validate the proposed ESSP and is further demonstrated using three illustrations solved optimally in LINGO 10. Originality/value The ESSP model simultaneously minimizes total procurement cost and carbon emissions over the entire planning horizon considering uncertain demand, supplier and carrier capacity.

Some Studies in Multi-Storage Inventory System

2016 ◽  
pp. 176-200
Author(s):  
Shyamal Kumar Mondal
Keyword(s):  
Planning Horizon ◽  
Inventory System ◽  
Mixed Integer ◽  
Lot Size ◽  
Continuous Release ◽  
Demand Rate ◽  
Cycle Lengths ◽  
Holding Cost ◽  
Inventory Holding ◽  
And Storage

In this chapter, a multi-storage inventory system has been considered to develop a deterministic inventory model in finite planning horizon. Realistically, it is shown that due to large stock and insufficient space of existing own warehouse (OW); excess items are stored in single rented warehouse (RW). Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. Here, the replenishment cycle lengths are of equal length, the demand rate is a continuous linear increasing function of time and partially backlogged shortages are allowed in all cycles. In each cycle, the replenishment cost is assumed to be dependent linearly on lot size and the stocks of RW are also transported to OW in continuous release pattern. The model is formulated as a constrained non-linear mixed integer cost objective function under single management. Finally, results with a sensitivity analysis have been shown with the help of a real coded GA.

scholarly journals MATERIAL REQUIREMENT PLANNING UNTUK MEMENUHI PRODUKSI PADA CV. BANGUN CIPTA ARTHA DI BADUNG

2020 ◽  
Vol 9 (2) ◽  
pp. 426
Author(s):  
I Made Sugita Yasa ◽  
Kastawan Mandala
Keyword(s):  
Inventory Management ◽  
Lot Sizing ◽  
Raw Materials ◽  
Raw Material ◽  
Exact Order ◽  
Lot Size ◽  
Inventory Costs ◽  
Material Requirement Planning ◽  
Material Requirement ◽  
Total Inventory

Inventory management without Material Requirement systems in CV. Bangun Cipta Artha resulted in the lot size for each order of raw materials not optimal. One concept that can be used to plan and control raw materials is the Material Requirement Planning. This study is to determine the number of sizes of raw material orders, the exact order time, the method that produces the lowest cost for each raw material, and the effect of using MRP on inventory costs. This research conducted on 160x200cm spring bed products. Data was analyzed by making production master schedules, determining net requirements, determining lot size, and making MRP tables. Based on the results, the determination the best lot sizing is the order quantiy period which results in a total inventory cost of Rp. 26,475,220 where the total cost is lower, compared to lot for lot method which Rp. 43,464,000. part period balancing Rp. 33,106,576, and conventional method Rp.49,472,912. Keywords: Material Requirement Planning (MRP), Sizing Lot, Lot For Lot, Balancing Part Period, Period Order Quantiy

Production Planning Considering Transfer Lot Size

2010 ◽  
Vol 44-47 ◽  
pp. 552-556
Author(s):  
Zhi Cong Zhang ◽  
Kai Shun Hu ◽  
Hui Yu Huang ◽  
Shuai Li
Keyword(s):  
Production Planning ◽  
Performance Measures ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Production Plan ◽  
Lot Size ◽  
Planning And Scheduling ◽  
Production Planning And Scheduling ◽  
Lot Sizing Problem ◽  
Plan Change

Traditional methods conduct production planning and scheduling separately and solve transfer lot sizing problem between these two steps. Unfortunately, this may result in infeasibility in planning and scheduling. We take into account transfer lot size in production planning to obtain the consistency and to eliminate the gap between planning and real production. We present the detailed Transfer Lot-Based Model with mixed integer programming. Experiments show that performance measures of a production plan change remarkably with increasing of transfer lot size.

scholarly journals A fix-and-optimize heuristic for the capacitated multi-item stochastic lot-sizing problem

2020 ◽  
Vol 11 (1) ◽  
pp. 41-51
Author(s):  
M. Edib Gurkan ◽  
Huseyin Tunc
Keyword(s):  
Lot Sizing ◽  
Numerical Study ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Solution Approach ◽  
Decomposition Scheme ◽  
Lot Sizing Problem ◽  
Single Production ◽  
Capacitated Lot Sizing ◽  
Cost Efficient

This study addresses the stochastic multi-item capacitated lot-sizing problem. Here, it is assumed that all items are produced on a single production resource and unmet demands are backlogged. The literature shows that the deterministic version of this problem is NP-Hard. We consider the case where period demands are time-varying random variables. The objective is to determine the minimum expected cost production plan so as to meet stochastic period demands over the planning horizon. We extend the mixed integer programming formulation introduced in the literature to capture the problem under consideration. Further, we propose a fix-and-optimize heuristic building on an item-period oriented decomposition scheme. We then conduct a numerical study to evaluate the performance of the proposed heuristic as compared to the heuristic introduced by Tempelmeier and Hilger [16]. The results clearly show that the proposed fix-and-optimize heuristic arises as both cost-efficient and time-efficient solution approach as compared to the benchmark heuristic.

Combinatorial Heuristics for Inventory Routing Problems

2021 ◽  
Author(s):  
Ziye Tang ◽  
Yang Jiao ◽  
R. Ravi
Keyword(s):  
Steiner Tree ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Inventory Routing ◽  
Optimal Solutions ◽  
Routing Problem ◽  
Holding Costs ◽  
Prize Collecting ◽  
Finite Time Horizon

We consider the deterministic inventory routing problem over a discrete finite time horizon. Given clients on a metric, each with daily demands that must be delivered from a depot and holding costs over the planning horizon, an optimal solution selects a set of daily tours through a subset of clients to deliver all demands before they are due and minimizes the total holding and tour routing costs over the horizon. In the capacitated case, a limited number of vehicles are available, where each vehicle makes at most one trip per day. Each trip from the depot is allowed to carry a limited amount of supply to deliver. We develop fast heuristics for both cases by solving a family of prize-collecting Steiner tree instances. Computational experiments show our heuristics can find near-optimal solutions for both cases and substantially reduce the runtime compared with a pure mixed integer programming formulation approach.

scholarly journals A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 878 ◽  
Author(s):  
Yajaira Cardona-Valdés ◽  
Samuel Nucamendi-Guillén ◽  
Rodrigo E. Peimbert-García ◽  
Gustavo Macedo-Barragán ◽  
Eduardo Díaz-Medina
Keyword(s):  
Lot Sizing ◽  
Mixed Integer ◽  
Lot Size ◽  
Penalty Cost ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
Batch Ordering ◽  
New Formulation ◽  
Production Resources

This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

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