COORDINATED PRICING AND INVENTORY CONTROL WITH BATCH PRODUCTION AND ERLANG LEADTIMES

2014 ◽  
Vol 28 (4) ◽  
pp. 529-563 ◽  
Author(s):  
Zhan Pang ◽  
Frank Y. Chen
Keyword(s):  
Inventory Control ◽  
Arrival Rate ◽  
Inventory Level ◽  
Erlang Distribution ◽  
Selling Price ◽  
Lot Size ◽  
Batch Production ◽  
Pricing Policy ◽  
Reorder Point ◽  
Joint Pricing

This paper addresses a joint pricing and inventory control problem for a batch production system with random leadtimes. Assume that demand arrives according to a Poisson process with a price-dependent arrival rate. Each replenishment order contains a single batch of a fixed lot size. The replenishment leadtime follows an Erlang distribution, with the number of completed phases recording the delivery state of outstanding orders. The objective is to determine an optimal inventory-pricing policy that maximizes total expected discounted profit or long-run average profit. We first show that when there is at most one order outstanding at any point in time and that excess demand is lost, the optimal reorder policy can be characterized by a critical stock level and the optimal pricing decision is decreasing in the inventory level and delivery state. We then extend the analysis to mixed-Erlang leadtime distribution which can be used to approximate any random leadtime to any degree of accuracy. We further extend the analysis to allowing three outstanding orders where the optimal reorder point becomes state-dependent: the closer an outstanding order is to its arrival or the more orders are outstanding, the lower selling price is charged and the lower reorder point is chosen. Finally, we address the backlog case and show that the monotone pricing structure may not be true when the optimal reorder point is negative.

Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand

2021 ◽  
Author(s):  
Boxiao Chen ◽  
Xiuli Chao ◽  
Cong Shi
Keyword(s):  
Inventory Control ◽  
Learning Algorithm ◽  
Spline Approximation ◽  
Inventory Level ◽  
Selling Price ◽  
Profit Function ◽  
Sales Data ◽  
Demand Distribution ◽  
Joint Pricing ◽  
Exploration Phase

We consider a joint pricing and inventory control problem in which the customer’s response to selling price and the demand distribution are not known a priori. Unsatisfied demand is lost and unobserved, and the only available information for decision making is the observed sales data (also known as censored demand). Conventional approaches, such as stochastic approximation, online convex optimization, and continuum-armed bandit algorithms, cannot be employed, because neither the realized values of the profit function nor its derivatives are known. A major challenge of this problem lies in that the estimated profit function constructed from observed sales data is multimodal in price. We develop a nonparametric spline approximation–based learning algorithm. The algorithm separates the planning horizon into a disjoint exploration phase and an exploitation phase. During the exploration phase, a spline approximation of the demand-price function is constructed based on sales data, and then the corresponding surrogate optimization problem is solved on a sparse grid to obtain a pair of recommended price and target inventory level. During the exploitation phase, the algorithm implements the recommended strategies. We establish a (nearly) square-root regret rate, which (almost) matches the theoretical lower bound.

scholarly journals Decision makings in discount pricing policy for imperfect production system

2019 ◽  
Vol 29 (2) ◽  
pp. 273-293 ◽  
Author(s):  
Uttam Khedlekar ◽  
Ram Tiwari
Keyword(s):  
Production System ◽  
Hessian Matrix ◽  
Selling Price ◽  
Production Plan ◽  
Lot Size ◽  
Price Discount ◽  
Pricing Policy ◽  
Negative Power ◽  
Imperfect Production ◽  
On Demand

In this paper, we discussed the effects of discount price on demand and profit in a diminishing market. A production plan has been suggested for an imperfect production system. Here, demand is considered to be price sensitive and negative power function of the selling price. This problem is solved by optimization, using the Hessian matrix of order three. The main objective is to find the optimal expected average profit, optimal selling price, discount rate, backorder level, and lot-size. The recommendations are provided to offer a price discount for limited sale season on different occasions. A numerical example is presented to validate the model and is graphically illustrated accordingly.

scholarly journals Joint Optimal Pricing and Inventory Control for Deteriorating Items under Inflation and Customer Returns

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Maryam Ghoreishi ◽  
Alireza Arshsadi khamseh ◽  
Abolfazl Mirzazadeh
Keyword(s):  
Inventory Control ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Deteriorating Items ◽  
Selling Price ◽  
Total Profit ◽  
Customer Returns ◽  
Joint Pricing ◽  
Finite Time Horizon ◽  
Dependent Demand

This paper studies the effect of inflation and customer returns on joint pricing and inventory control for deteriorating items. We adopt a price and time dependent demand function, also the customer returns are considered as a function of both price and demand. Shortage is allowed and partially backlogged. The main objective is determining the optimal selling price, the optimal replenishment cycles, and the order quantity simultaneously such that the present value of total profit in a finite time horizon is maximized. An algorithm has been presented to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

Two phases inventory model with variable cycle length under discount policy

2020 ◽  
Vol 54 (1) ◽  
pp. 1-18
Author(s):  
Brojeswar Pal ◽  
Subhankar Adhikari
Keyword(s):  
Optimality Criteria ◽  
Inventory Model ◽  
Linear Functions ◽  
Inventory Level ◽  
Second Phase ◽  
Selling Price ◽  
Lot Size ◽  
Power Functions ◽  
Demand Rate ◽  
Two Phases

This study deals with single stage inventory model where two phases are involved in an inventory cycle. In the first phase of the cycle, demand depends on both of inventory level and selling price while in the second, the demand depends on price only. Discount policy in selling price is offered in the second phase and inventory level at the end of the cycle is taken to be zero. Two models have been constructed on infinite time horizon. In the first model the demand rate is taken as the sum of two linear functions of inventory level and selling price and, in the second model, it is taken as a product of two power functions of inventory level and selling price. Our objective is to maximize average profit by considering ordering lot size and selling price as decision variables. Numerical examples of each model have been provided. The optimality criteria for the solutions are also checked by both graphically and numerically. Sensitivity analysis for different parameters in both models has been discussed in details to check the feasibility of the models.

Multi-objective particle swarm optimisation approach for production-inventory control systems

2018 ◽  
Vol 13 (4) ◽  
pp. 1037-1056 ◽  
Author(s):  
Huthaifa AL-Khazraji ◽  
Colin Cole ◽  
William Guo
Keyword(s):  
Control System ◽  
Control Systems ◽  
Inventory Control ◽  
Dynamic Performance ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Inventory Level ◽  
Content Type ◽  
Multi Objective ◽  
Production Inventory

Purpose This paper aims to optimise the dynamic performance of production–inventory control systems in terms of minimisation variance ratio between the order rate and the consumption, and minimisation the integral of absolute error between the actual and the target level of inventory by incorporating the Pareto optimality into particle swarm optimisation (PSO). Design/method/approach The production–inventory control system is modelled and optimised via control theory and simulations. The dynamics of a production–inventory control system are modelled through continuous time differential equations and Laplace transformations. The simulation design is conducted by using the state–space model of the system. The results of multi-objective particle swarm optimisation (MOPSO) are compared with published results obtained from weighted genetic algorithm (WGA) optimisation. Findings The results obtained from the MOPSO optimisation process ensure that the performance is systematically better than the WGA in terms of reducing the order variability (bullwhip effect) and improving the inventory responsiveness (customer service level) under the same operational conditions. Research limitations/implications This research is limited to optimising the dynamics of a single product, single-retailer single-manufacturer process with zero desired inventory level. Originality/value PSO is widely used and popular in many industrial applications. This research shows a unique application of PSO in optimising the dynamic performance of production–inventory control systems.

scholarly journals ANALISIS PENETAPAN HARGA JUAL PRODUK PADA PT.WICAKSANA OVERSEASINTERNASIONAL CABANG MEDAN

2018 ◽  
Author(s):  
STIM Sukma
Keyword(s):  
Data Collection ◽  
Selling Price ◽  
Pricing Policy ◽  
Marketing Department ◽  
Volume Increase ◽  
Purchasing Decision ◽  
Qualitative Descriptive ◽  
Research Findings ◽  
The Right ◽  
Descriptive Method

The purpose of this study was to determine the pricing policy applied by selling PT.Wicaksana Overseas Internasional.Analisis data in this study using qualitative descriptive method and data collection by observation and interviews. These results indicate that the right pricing will affect the volume increase in sales and satisfaction to consumers. Because prices affect the volume of sales and the purchasing decision. Therefore, setting the selling price of products made by the International Overseas PT.Wicaksana already running well by doing and observation visit directly into the field, and conduct periodic surveys in the field and carried out by the marketing department who has been given the task by the leadership and results of the research findings discussed in the meeting and obtained conclusions and results that have been agreed. This means that pricing in the International Overseas PT.Wicaksana doing some process so that pricing is done going well and accepted by consumers.

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