Pricing and inventory decisions for non-instantaneous deteriorating items with price and promotional effort stochastic demand

This study investigates an inventory model for a non-instantaneous deteriorating item with partial backlogging wherein the demand is stochastic in nature and depends on price and promotional effort whereas the deterioration rate is time proportional.Under these settings,a mathematical model is developed with the objective to maximise the expected profit per unit time by determining the optimal price and the length of replenishment cycle.Some useful theoretical results are established to deduce the optimal replenishment schedule.An effective algorithmic procedure is developed to find the optimal solutions to the proposed model.The applicability of the proposed model is illustrated by numerical example.Sensitivity analysis of the optimal solution with respect to key parameters has been carried out and the implications are discussed.The study indicates that though promotional effort stimulates the market demand,it is beneficial in an economic sense when it applies in a conservative manner.

A supply chain model for imperfect production system with stochastic lead time demand

This study deals an integrated manufacturer-buyer supply chain system for imperfect production under stochastic lead time demand.Here,defective rate has been followed as a function of production rate.Also,the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand rate.Buyer purchases the products from the manufacturer.Also,we assume that shortage during the lead time is permitted and demand during the shortage period is fully backordered.The objective is to derive the optimal production rate,ordering quantity and to maximize joint total profit.Basically,two different models for different probability distribution functions of stochastic lead time demand have been developed.Some numerical examples are provided to show the applicability of the proposed models comparing the optimum average profits.Finally,sensitive analysis,conclusion and future researches are presented.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.

ORDER DECISION MAKING BASED ON DIFFERENT STATEMENT STRATEGIES UNDER STOCHASTIC MARKET DEMAND

Based on the stochastic market demand, this paper considers the order decision-making strategies of the supply chain by introducing statement strategies. Consequently, the time-variant variance in the demands of the market is incorporated into the model. The retailer simultaneously determines the purchase time （i.e., lead time） and order quantity, and the manufacturer determines the statement strategy and the reserved profit rate. The results show that the no overtime statement strategy can induce the retailer to place more orders in advance by limiting the available order quantity within the available time. Finally, we also adopt numerical examples to support the conclusion of this paper.

The optimal strategies in the supply chain with stochastic demand sensitivity to carbon emission

With the increasing awareness of low-carbon environmental protection,consumers prefer to purchase low-carbon products.In this paper,a two-echelon low-carbon supply chain consisting of one manufacturer and one retailer in classic single-period model with emission-sensitive stochastic demand is investigated.Firstly,optimal results for the decentralized and centralized decisions in the basic model are presented respectively.It manifests the effect of double marginalization which shows not only a lower order quantity but also higher unit carbon emission.Then,we are going to discuss the introduction of a buyback and cost-sharing contract,and two main carbon emission regulations in the decentralized model.Finally,compared with the basic model,numerical examples are studied on the optimal solutions to the total profit for the supply chain,order quantity,and unit/total carbon emission as the demand sensitivity to carbon emission/green investment coefficient/demand variance varies respectively before reaching several significant conclusions.

Stochastic Joint Replenishment Optimization under Joint Inbound Operational Cost

With e-commerce concentrating retailers and customers onto one platform,logistics companies(e.g.,JD Logistics)have launched integrated supply chain solutions for corporate customers(e.g.,online retailers)with warehousing,transportation,last-mile delivery,and other value-added services.The platform’s concentration of business flows leads to the consolidation of logistics resources,which allows us to coordinate supply chain operations across different corporate customers.This paper studies the stochastic joint replenishment problem of coordinating multiple suppliers and multiple products to gain the economies of scale of the replenishment setup cost and the warehouse inbound operational cost.To this end,we develop stochastic joint replenishment models based on the general-integer policy(SJRM-GIP)for the multi-supplier and multi-product problems and further reformulate the resulted nonlinear optimization models into equivalent mixed integer second-order conic programs(MISOCPs)when the inbound operational cost takes the square-root form.Then,we propose generalized Benders decomposition(GBD)algorithms to solve the MISOCPs by exploiting the Lagrangian duality,convexity,and submodularity of the sub-problems.To reduce the computational burden of the SJRM-GIP,we further propose an SJRM based on the power-of-two policy and extend the proposed GBD algorithms.Extensive numerical experiments based on practical datasets show that the stochastic joint replenishment across multiple suppliers and multiple products would deliver 13∼20%cost savings compared to the independent replenishment benchmark,and on average the proposed GBD algorithm based on the enhanced gradient cut can achieve more than 90%computational time reduction for large-size problem instances compared to the Gurobi solver.The power-of-two policy is capable of providing high-quality solutions with high computational efficiency.

A case study on sample average approximation method for stochastic supply chain network design problem

This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.

CAPACITY COMMITMENT AND PRICING FOR SUBSTITUTABLE PRODUCTS UNDER COMPETITION

Capacity acquisition and pricing decisions are a company＇s long-term strategic decisions. However, demand uncertainty and substitutability of multiple products cause the difficulty to solve capacity and pricing decision problems. In this paper, we address a multiple product pricing and multiple resource capacity acquisition problem with demand.uncertainties and competition. The company needs to determine capacity commitment for each resource and product prices before demands are realized so that the total profit is maximized. If the demand exceeds the committed capacity, extra amounts can be purchased from the spot market. Variable unit production costs, capacity acquisition and maintenance costs are considered. We first analyze a single company basic problem and find the optimal solutions on prices and capacity. Based on the single company model, we address the two-product, two-firm capacity commitment and pricing problem considering across product and across company price competition factors. The existence and uniqueness of equilibrium on price and capacity commitment are proved, and then we extended the results to the multiple product, multiple company case.