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This chapter discusses a collaborative strategy for noncompetitive small- and medium-sized enterprises (SME's) aiming to reduce their logistics costs by means of a joint replenishment of multiple items. The proposed approach is an extension of the classical joint replenishment problem, named as a Stochastic Collaborative Joint Replenishment problem (S-CJRP) because it considers stochastic demand, warehouse and transport capacity constraints, and multiple buyers and vendors. Operating this method implies three main challenges: (1) determining the frequency with which each buyer should replenish the products; (2) allocating investments and benefits between partnering buyers; and (3) deciding whether to coordinate the supply chain internally or outsource its coordination. The S-CJRP is solved through a heuristic approach, which deals with uses of the Shapley Value Function to allocate the investments and benefits, and it explores the coordination through several simulation scenarios, all of which exhibit prospective cost reductions in inventory management. Preliminary results show that third-party logistics providers could be a valuable resource in coordinating SMEs along a supply chain.

This work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.

The demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.

The proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.

The results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.

The demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.

In a multi‐item environment with a joint set‐up cost structure considerable savings may be realised by co‐ordinating the replenishments. This article presents a unified survey of the inventory control literature designed to capture the models that fit in this frame. In general these models are complex and require a great deal of computational effort to obtain an exact solution. The literature relies mainly on heuristic procedures.

This paper aims to propose a supply model of periodic review with joint replenishment for multi-products grouped by several variables with random and time dependence demand.

The products are grouped by multivariate cluster analysis. The stochastic inventory model describes the random demand of each product, considering the temporal dependency through a generalized autoregressive moving average model. Stochastic programming for the total cost of inventory is obtained considering the expected value of the demand per unit of time.

The total costs for the products grouped with the proposed model are 6% lower than for the individual inventory policy. The expected shortage units decrease significantly in the proposed grouped model with temporary dependence. In addition, the proposal with temporary dependency has lower costs than when the independent and identically distributed demand is considered.

The proposed policy is exemplified with real-world data from a Chilean hospital, where the products (drugs) are segmented by grouping variables, forming clusters of drugs with homogeneous behavior within the groups and heterogeneous behavior between groups.

Integrated decision of pricing and inventory control for a deteriorating product is known as a good practice in revenue management discipline. The purpose of this paper is to formulate the problem of joint pricing and inventory decision in a manufacturer–retailer supply chain with deteriorating items and backlogging. Furthermore, the other purpose is to develop an efficient algorithm to obtain the equilibrium solution.

In this study, a manufacturer–retailer supply chain of a deteriorating product is considered. The retailer aims to maximize his profit, for which he jointly determines the retail price and replenishment cycle. In addition, the manufacturer should decide on the wholesale price to maximize her profit. Considering the problem as a manufacturer-Stackelberg game, the equilibrium solution is formulated and analyzed for both the manufacturer and the retailer. Moreover, two different procedures are developed to obtain the equilibrium solution. The first procedure is an exact procedure for the Taylor-approximated model and the second is a simulated annealing (SA)-embedded algorithm for the actual model.

It is found that Taylor-approximated procedure is more accurate than SA-embedded procedure. However, the latter is more time-efficient. Moreover, it is observed that the obtained solution is highly sensitive to demand parameters, while it is not the case for the cost parameters.

The paper models a real industrial problem, and its results could be used in analyzing any manufacturer–retailer supply chain with deteriorating items. Among others, the fruit and vegetable supply chains are more likely to have a similar setting, and this study’s results are applicable for such chains in food industry.

The purpose of this paper is to review and analyze the perishable inventory models along various dimensions such as its evolution, scope, demand, shelf life, replenishment policy, modeling techniques and research gaps.

In total, 418 relevant and scholarly articles of various researchers and practitioners during 1990-2016 were reviewed. They were critically analyzed along author profile, nature of perishability, research contributions of different countries, publication along time, research methodologies adopted, etc. to draw fruitful conclusions. The future research for perishable inventory modeling was also discussed and suggested.

There are plethora of perishable inventory studies with divergent objectives and scope. Besides demand and perishable rate in perishable inventory models, other factors such as price discount, allow shortage or not, inflation, time value of money and so on were found to be combined to make it more realistic. The modeling of inventory systems with two or more perishable items is limited. The multi-echelon inventory with centralized decision and information sharing is acquiring lot of importance because of supply chain integration in the competitive market.

Only peer-reviewed journals and conference papers were analyzed, whereas the manuals, reports, white papers and blood-related articles were excluded. Clustering of literature revealed that future studies should focus on stochastic modeling.

Stress had been laid to identify future research gaps that will help in developing realistic models. The present work will form a guideline to choose the appropriate methodology(s) and mathematical technique(s) in different situations with perishable inventory.

The current review analyzed 419 research papers available in the literature on perishable inventory modeling to summarize its current status and identify its potential future directions. Also the future research gaps were uncovered. This systemic review is strongly felt to fill the gap in the perishable inventory literature and help in formulating effective strategies to design of an effective and efficient inventory management system for perishable items.

Commonly shared logistics services help manufacturing companies to cut down redundant logistics investments while enhance the overall service quality. Such service-sharing mode has been naturally adopted by group companies to form the so-called headquarter-managed centralized distribution center (HQ-CDC). The HQ-CDC manages the common inventories for the group’s subsidiaries and provides shared storage services to the subsidiaries through appropriate sizing, pricing and common replenishment. Apart from seeking a global optimal solution for the whole group, the purpose of this paper is to investigate balanced solutions between the HQ-CDC and the subsidiaries.

Two decision models are formulated. Integrated model where the group company makes all-in-one decision to determine the space allocation, price setting and the material replenishment on behalf of HQ-CDC and subsidiaries. Bilevel programming model where HQ-CDC and subsidiaries make decisions sequentially to draw a balance between their local objectives. From the perspective of result analysis, the integrated model will develop a managerial benchmark which minimizes the group company’s total cost, while the bilevel programming model could be used to measure the interactive effects between local objectives as well as their final effect on the total objective.

Through comparing the numerical results of the two models, two major findings are obtained. First, the HQ-CDC’s profit is noticeably improved in the bilevel programming model as compared to the integrated model. However, the improvement of HQ-CDC’s profit triggers the cost increasing of subsidiaries. Second, the analyses of different sizing and pricing policies reveal that the implementation of the leased space leads to a more flexible space utilization in the HQ-CDC and the reduced group company’s total cost especially in face of large demand and high demand fluctuation.

Several classical game-based decision models are to be introduced to examine the more complex relationships between the HQ-CDC and the subsidiaries, such as Nash Game model or Stackelberg Game model, and more complete and meaningful managerial implications may be found through result comparison with the integrated model. The analytical solutions may be developed to achieve more accurate results, but the mathematical models may have to be with easier structure or tighter assumptions.

The group company should take a comprehensive consideration on both cost and profit before choosing the decision framework and the coordination strategy. HQ-CDC prefers a more flexible space usage strategy to avoid idle space and to increase the space utilization. The subsidiaries with high demand uncertainties should burden a part of cost to induce the subsidiaries with steady demands to coordinate. Tanshipments should be encouraged in HQ-CDC to reduce the aggregate inventory level as well as to maintain the customer service level.

The proposed decision frameworks and warehousing policies provide guidance for the managers in group companies to choose the proper policy and for the subsidiaries to better coordinate.

This research studies the services sharing on the warehouse sizing, pricing and common replenishment in a HQ-CDC. The interactive decisions between the HQ-CDC and the subsidiaries are formulated in a bilevel programming model and then analyzed under various practical scenarios.

The increasing popularity of ERP solutions has provided dietary supplement manufacturing companies with modules to manage pricing and inventory. However, the decisions made by these modules are often independent and rely on deterministic forecasts. This paper studies a multi-product dietary supplement manufacturing system under stochastic demands. The purpose is to maximize the long-run expected profit by jointly considering pricing and inventory strategies.

The authors investigate both the general cases and three special cases including stable demand, negligible backlog and instantaneous replenishment. A two-stage algorithm named PAS is proposed. In the strategy construction stage, the constructed objective bounds are combined to provide estimates which then help to derive the optimal product prices. In the system operation stage, replenishment decisions are further made based on the prices generated from the previous stage.

It is proved that base-stock policy is optimal for the studied system, and the optimal based-stock level is provided. The global optimal strategies are obtained for three important special cases. For the general case, theoretical objective bounds are established. These bounds provide quick and reliable performance estimates for practical applications.

Very few studies have jointly considered pricing and inventory strategies with uncertainty demands in the dietary supplement industry. The PAS algorithm developed integrates these decisions and consistently generates high-quality solutions even under highly varying demands. Such algorithm could be a valuable add-on to the pricing and inventory management modules in ERP systems.

The purpose of this paper is to maximize the average profit of the supply chain by calculating the order quantity, the number of shipments during the production time of the vendor, the number of shipments during the supply cycle of the vendor and the time when the retailer’s inventory level reaches to zero.

A production and inventory model for degrading commodities with stochastic demand and two-level partial trade credit in a supply chain is presented. The model’s applicability and the processes' feasibility for solving are verified by GAMS software with BARON.

The impact of the model’s parameters on the vendor and retailer’s average profit was found through sensitivity analysis. The effect of the model’s parameters on the supply chain’s average profit was also found. Moreover, the reasons for this effect were given.

First, decision-makers may use this model to increase the supply chain's average profit. Second, the proposed model takes a general form. Third, the policymakers can also adjust the model’s parameters according to their preferences to get the desired results.

First, this paper develops an inventory and production model for perishable goods. Second, it is believed that the demand is random because the demand is affected by many factors, which make the study more realistic. Third, this paper studies production and inventory problems from the supply chain perspective. Finally, the interest for partial trade credit is calculated. The interest caused by stochastic shortages is also considered and calculated.

Carbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers.

This paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software.

This paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model.

This study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.