Single Perishable Product Research Articles

Dynamic pricing for perishable product in the presence of low-carbon preference

ABSTRACT As countries worldwide strive to implement energy conservation and emission reduction measures, modeling consumers’ low-carbon preferences and purchasing decisions has become a crucial factor in implementing dynamic pricing strategies for firms. This paper investigates the dynamic pricing problems for a single perishable product and substitutable perishable products, respectively, where consumer is affected by low-carbon preference. We first propose the decision framework of consumer choice with low-carbon preference based on the multinomial logit model. On this basis, we establish dynamic pricing models by the dynamic programming method and obtain the optimal pricing strategies. We analytically show that consumer’s low-carbon preference has a positive effect on the optimal price for a single perishable product. Meanwhile, numerical examples illustrate that consumer’s low-carbon preference has a positive effect on the optimal prices for substitutable perishable products. Finally, we give some suggestions to increase firm’s revenue when consumer’s low-carbon preference is present.

Value of risk aversion in perishable products supply chain management

AbstractIn this paper, we study optimal procurement and inventory decisions for a supply chain with a single perishable product under demand uncertainty. To control risk, on the one hand, we use a risk-averse objective, and on the other hand, we utilize a chance constraint to satisfy demand with a high probability. We formulate the problem as a two-stage stochastic program with a chance constraint and risk-averse objective, where long-term decisions on pre-positioning products are made in the first stage, while recourse decisions on reallocation and emergency procurement are made in the second stage. To allow for different risk preferences, we incorporate conditional value-at-risk into the objective function and study its combination with the expectation or worst-case of the second-stage costs. To solve the resulting models, we develop various variants of the L-shaped method, based on dual and primal decomposition, and by leveraging the connection between the optimization of coherent risk measures and distributionally robust optimization. Through extensive numerical experiments, we demonstrate the value of risk aversion and present a comparative computational study on the performance of different algorithms.

Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost

Perishable products are very common, but managing inventory of perishable products can be very challenging for firms, especially in distribution systems, including multiple chain stores. In this environment, we consider a dynamic lot-sizing problem faced by a distribution center that dis-patches a single perishable product to multiple chain stores. Demand cannot be backlogged, but it does not have to be satisfied; unsatisfied demand means stockout (lost sale). The first step is to transform the total profit function into a special total cost function. Our next step is to explore the properties of the optimal solution and use them to formulate a dynamic programming algorithm to solve the problem. Furthermore, we establish forecast and decision horizon results, which help the operation manager to decide the precise forecast horizon in a rolling decision-making process. Based on the model setting and the methods of dynamic programming, we obtained two interesting findings: (1) the maximized profit objective function is equivalent to the minimized cost objective function, and (2) the famous zero inventory property conditionally holds in the inventory management of perishable products. On an extensive test bed, useful insights were obtained on the impact of the lifetime of the product and cost parameters on the total cost and length of the forecast horizon. Thus, the contributions of this study are as follows: (1) we explore two structure policies in an optimal solution to devise efficient algorithms to reduce computational complexity; (2) we provide a sufficient condition for forecasting and decision horizons; and (3) we determine that, for a given fixed cost, the median forecast horizon first increases with the lifetime of the product and stockout cost and then remains invariable when it reaches a certain level.

Innovative decision support tools for perishable food supply chain management

PurposeWe introduce decision support tools aimed at optimizing perishable food supply chain management, effectively balancing conflicting objectives such as the exporter’s product collection cost and the importer’s profit. This involves considering factors like perishability, selling price, discount rate, and order quantity to achieve optimal outcomes.Design/methodology/approachThis study considered a three-echelon supply chain comprising farmers, a single exporter, and a single importer providing a single, random-lifetime, perishable product under deterministic customer demand. The proposed mathematical model derived the optimal order quantity, selling price, and discount rate for the entire supply chain. This integrated optimization model treats both demand and supply sides as a multi-objective problem, employing a nonlinear program and a two-stage capacitated vehicle routing problem formulation. Numerical examples and a case study focusing on Thailand durian supply chain were conducted to illustrate the approach of the proposed model.FindingsTaking into account both the importer’s profit and the exporter’s product collection cost, the proposed integrated supply chain model and tools maximize profitability, minimizes waste, and meets demand by optimizing perishable product collection costs and proposing a discount system for selling prices.Research limitations/implicationsLimited to a single perishable product in a three-echelon international food supply chain. Future research can explore different products and supply chain contexts.Practical implicationsThe tools enhance decision-making for supply chain managers, improving efficiency, reducing costs, and enhancing customer satisfaction in the perishable food industry.Social implicationsThe proposed model aids in local workforce management by forecasting required manpower for upcoming seasons. By factoring in product quality and pricing, it ensures customers receive fresh products at fair prices. Furthermore, the near-zero waste concept enhances storage conditions at importers' facilities, contributing to improved environmental hygiene.Originality/valueThe integrated model and decision support tools offer a novel approach to address complexities and conflicting objectives in perishable food supply chains, providing practical insights for researchers and practitioners.

Bi-level pricing and inventory strategies for perishable products in a competitive supply chain

This paper aims to develop a new bi-level game model for joint pricing and inventory decisions in a competitive supply chain consisting of a dominant manufacturer, who produces single perishable product from deteriorating raw materials, and two follower retailers who face nonlinear price-dependent demand and operate under Cournot assumptions. Three levels of warehousing including raw material warehouse, final product warehouse, and retail warehouses with exponential deterioration rates are considered to explore the joint impact of deterioration rate and price elasticity on the equilibrium inventory decisions. A Stackelberg–Nash–Cournot model is developed to seek the equilibrium prices, quantities, and replenishment cycles and is solved through an exact methodology. A numerical example is presented to validate the proposed model and comprehensive sensitivity analyses are carried out to measure the impact of the model’s key parameters including the deterioration rate in the producer’s and the retailers’ warehouses, the retail and competitor price elasticity, and the market scale on the equilibrium.

Modelling and solving the bi-objective production–transportation problem with time windows and social sustainability

Abstract We model and solve the production routing problem (PRP) with time windows, product deterioration and split delivery. A bi-objective PRP model for a single perishable product, which is subject to deterioration, is presented. The two objectives represent the economic and social aspects of sustainability, whereas the environmental impact is enforced by incorporating ad-hoc constraints. The economic dimension of sustainability consists of minimizing the costs related to the production, setup, holding, transportation and lateness penalty. The social responsibilities are modelled through maximizing the total freshness of the delivered products at all nodes over the planning horizon. The outcomes of our formulation are represented by the lot sizes, and the amounts of product to be delivered, as well as the routing at each planning period. To solve the resulting problem, we develop an interval robust possibilistic approach, and we carry out an experimental study and a sensitivity analysis. Finally, we further validate our optimization model and solution method using a real-life case of a food factory producing a product that is subject to perishability and deterioration.

Dynamic channel control and pricing of a single perishable product on multiple distribution channels

This paper studies dynamic channel control and pricing of a single perishable product distributed through multiple channels with the objective of maximizing the total expected profit over a finite horizon. We consider two types of commissions, namely proportional and fixed commissions, on the third-party channels and utilize stylized linear functions to characterize dependent demand flows from different channels. We show that, the magnitude of the opportunity cost of capacity uniquely determines the optimal channel control, at any given inventory level and periods to go. Consequently, we are able to derive the optimal price offered on each channel as a function of the opportunity cost of capacity in closed form. This significantly reduces the computational complexity of the stochastic dynamic program when parameters are constant with time. When channels are independent, we provide a necessary and sufficient condition for the optimality of a nested channel control policy by commission rates. The same condition is also sufficient for the optimality of the nested channel control policy in a distribution system with two dependent channels. We then characterize the structural properties of the optimal pricing and channel control policies. Finally, we explore the impact of the substitution effect on the channel control through numerical studies and gain managerial insights.

Profit Optimization for Zero Ending Inventories Dynamic Pricing Model under Stochastic Demand and Fixed Lifetime Product

Abstract We consider a single perishable product under a compound Poisson demand with a price sensitive intensity and a continuous batch size distribution. A model of a dynamic retail price control with an adjustable coefficient is proposed providing almost surely zero ending inventories at the end of the product’s lifetime. To obtain probabilistic characteristics of the selling process and the expected profit a diffusion approximation of the demand process is used. The task of the expected profit optimization with respect to the coefficient and lot size for a linear intensity-of-price dependence is solved.

Embedding the production policy in location-allocation decisions

This paper investigates how the production policy, as well as other factors, affect the facility location-allocation decisions. We focus on a p-median location problem in which one single perishable product is to be produced and shipped to a set of users. The time-correlated demands of the clients are generated by autoregressive processes, and they are forecasted from historical data. Empirically, we show that: (i) embedding the production policy in the location-allocation decision problem may lead to a facilities-clients assignment which does not necessarily correspond to the minimum cost allocation, but produces better profits, (ii) taking into account the autocorrelation of the demand can significantly improve the performance of the supply chain, and (iii) the variability of the demand strongly affects the performance of the supply chain, so a careful choice of production strategy is especially recommended in this case.

Joint pricing and lot-sizing for a perishable item under two-level trade credit with multiple demand classes

Abstract This paper addresses the differential pricing and lot-sizing problem for a perishable item with multiple demand classes under a two-level trade credit. The distributer sells a single perishable product at different prices to various markets and offers a varied credit period to customers. In the proposed model: (1) the demand rate at each market depends on the selling price, credit period and the price of other complementary and substitute products and (2) the time and temperature parameters affect the deterioration rate. A bi-objective model is developed, which aims to jointly maximize the total profit and minimize the total inventory to assess the supply chain’s inventory performance with multiple demand classes under switching cost constraints. Since most of the parameters are imprecise in nature, a tailored possibilistic programming method based upon the fuzzy measure Me is devised to construct the deterministic counterpart. Several theoretical results are derived which demonstrate the existence and uniqueness of the solution. An efficient search procedure based on the model’s properties is developed to find the pricing and lot-sizing decisions. Then, an efficient multi-objective programming method is used to find efficient compromise solutions. Finally, illustrative examples along with a number of sensitivity analyses are provided to show applicability of the proposed approach and study the influence of key parameters on the model’s performance.

Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer–retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.

Prices, profits and market shares of two competing retailers under consumer information asymmetry

Abstract Access to consumer information is a key factor in a firm’s ability to compete. We assume a duopoly of two firms, where each is located at a different point in a market with a single perishable product. Consumers are assumed to be heterogeneous in their readiness to buy products with different levels of freshness and in their physical distance from each retailer. One retailer among the two (retailer A) has accurate information about the locations of consumers and their sensitivities to freshness (i.e., their distributions). A non-cooperative game is used to model the competition and to develop optimization models for each retailer according to the information they have about consumers. We conclude that lost sales or leftovers on the part of the uninformed retailer are a possible outcome of information asymmetry, even under a deterministic scenario. We show that each of the best response functions is unique and increases with the opponent's price. A pure strategy Nash equilibrium is shown to exist. Through a numerical example, we show that the optimal profit of retailer A increases when the retailer who lacks accurate information (retailer B) assumes that consumers are less sensitive to freshness than they are in reality. This result is interesting, as it shows that the estimations of the uninformed retailer have a significant effect on the competitor's profits.

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.

A genetic algorithm-Taguchi based approach to inventory routing problem of a single perishable product with transshipment

In this paper we present a model of inventory routing problem with transshipment in the presence of a single perishable product. In this problem, vehicle routing and inventory decisions are made simultaneously over the planning horizon to meet customer’s demand under maximum level policy. Products are deteriorated at the exponential rate during the time they are stored in the depot or customer’s warehouse. Due to the NP-hard nature of the model, we propose a genetic algorithm based approach to solve the problem. Moreover, the proposed algorithm parameters are determined using Taguchi design approach to achieve the best solution. Besides, a numerical example is used to illustrate the validity of the model. To the best of our knowledge, this is the first study that incorporates perishability of the products into inventory routing problem with transshipment, in which the products stocked in the depot or warehouses spoil due to their nature and also environmental issues.

A single perishable product from a single-producer and multiple-buyer's model for Weibull deterioration with time dependent demand and allowable shortage

The attention of this study is derived from a single perishable product from a single producer and multi-buyers, production-inventory model for deteriorating items with time dependent demand and allowable shortage. A mathematical model incorporating the costs of both the producer and the buyers is developed. A sensitivity analysis of relevant cost function of this model is to minimise the integrated total cost per year more easily. All these practical aspects are incorporated into the model with the purpose of making it more realistic.

A multi-period location model with transportation economies-of-scale and perishable inventory

In this paper, we propose a multi-period location model with transportation economies-of-scale that distributes a single perishable product. The problem involves a single supplier, a layer of potential facility locations, and a layer of retailers. Each facility is assumed to practice cross-docking and each retailer faces a constant demand rate in each planning period. A Zero-Inventory-Ordering (ZIO) inventory policy is assumed to be adopted at each retailer. The demand at each retailer must be satisfied by the end of the planning horizon, although backlogging is allowed in the intermediate periods. The decisions to be made comprise the location of facilities, the allocation of retailers to the open facilities with single-sourcing, and the logistics shipping plan over time for the open facilities and the retailers allocated to them. The goal is to minimize the total cost that includes (1) the fixed setup cost for locating facilities, (2) the inbound cost at the open facilities, (3) the transportation cost from the facilities to the retailers (which is assumed to be an economies-of-scale function), and (4) the inventory cost at the retailers. We first formulate the problem as a mixed integer nonlinear programming model. By effectively utilizing the structural properties of the cost functions and combining with the ZIO, we show how to linearize the nonlinear cost components. The results of a set of numerical experiments performed on randomly generated medium-sized problem instances are reported.

An Integrated Model for Production and Distribution Planning of Perishable Products with Inventory and Routing Considerations

In many conventional supply chains, production planning and distribution planning are treated separately. However, it is now demonstrated that they are mutually related problems that must be tackled in an integrated way. Hence, in this paper a new integrated production and distribution planning model for perishable products is formulated. The proposed model considers a supply chain network consisting of a production facility and multiple distribution centers. The facility produces a single perishable product that is storable only for predetermined periods. A homogenous fleet of vehicles is responsible for delivering the product from facility to distribution centers. The decisions to be made are the production quantities, the distribution centers that must be visited, and the quantities to be delivered to them. The objective is to minimize the total cost, where the trip minimization is considered simultaneously. As the proposed formulation is computationally complex, a heuristic method is developed to tackle the problem. In the developed method, the problem is divided into production submodel and distribution submodel. The production submodel is solved using LINGO, and a particle swarm heuristic is developed to tackle distribution submodel. Efficiency of the algorithm is proved through a number of randomly generated test problems.

Retailing policy for perishable item sold from two bins with mixed issuing policy

This paper deals with a retailer who sells single perishable product in two bins. The fresh items are sold at a list price in the primary bin and the unsold items that have reached a certain allowed age are transferred to the secondary bin to be sold at a discount price. It is assumed that the demand is affected by inventory level, selling price, product freshness, and demand leakage caused by the price difference of two bins. Also, products are sold under mixed issuing policy which is defined as a weighted sum of Last-In-First-Out and First-In First-Out issuing policy. With the objective of maximizing the retailer's profit, we develop mathematical models for the following two cases: (1) opening primary shop only and (2) opening both primary shop and secondary shop. Noting that the objective function is too complicated to possess a closed-form optimal solution, a solution procedure is developed based on Tabu search. The validity of the model is shown by solving an example problem and the sensitivity study is performed on the system parameters.

Risk-sensitive dynamic pricing for a single perishable product

We show that the monotone structures of dynamic pricing for a single perishable product under risk-neutrality are preserved under risk-sensitivity with the additive general utility and atemporal exponential utility functions. We also show that the optimal price is decreasing over the degree of risk-sensitivity under the exponential class of both additive and atemporal utility functions.

Managing Slow‐Moving Perishables in the Grocery Industry

We address the value of information and value of centralized control in the context of a two‐echelon, serial supply chain with one retailer and one supplier that provide a single perishable product to consumers. Our analysis is relevant for managing slow‐moving perishable products with fixed lot sizes and expiration dates of a week or less. We evaluate two supply chain structures. In the first structure, referred to as decentralized information sharing, the retailer shares its demand, inventory, and ordering policy with the supplier, yet both facilities make their own profit‐maximizing replenishment decisions. In the second structure, centralized control, incentives are aligned and the replenishment decisions are coordinated. The latter supply chain structure corresponds to the industry practices of company‐owned stores or vendor‐managed inventory. We measure the value of information and value of centralized control as the marginal improvement in expected profits that a supply chain achieves relative to the case when no information is shared and decision making is decentralized. Key assumptions of our model include stochastic demand, lost sales, and fixed order quantities. We establish the importance of information sharing and centralized control in the supply chain and identify conditions under which benefits are realized. As opposed to previous work on the value of information, the major benefit in our setting is driven by the supplier's ability to provide the retailer with fresher product. By isolating the benefit by firm, we show that sharing information is not always Pareto‐improving for both supply chain partners in the decentralized setting.