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The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer's decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer's own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks' capacities. [ABSTRACT FROM AUTHOR]

In today's competitive and environmentally conscious business landscape, companies constantly seek more efficient ways to conduct their daily operations. Horizontal Logistics Collaboration (HLC), in which firms at the same supply chain level share resources such as trucks and information, has proven effective in achieving synchronized deliveries, optimizing transport equipment usage, and reducing carbon footprint. This study implements HLC between two neighboring companies ordering different products from the same supplier. The study adopts the can-order policy, employing three threshold values to define each company's ordering policy and potential joint orders. To better reflect real-world operational aspects, a simulation-based optimization approach is employed, allowing experimentation with various realistic scenarios. The developed model assumes stochastic demand and lead time for both companies and assesses the benefits of HLC from both economic and environmental standpoints, one at a time. Computational experiments consistently demonstrate cost savings through collaboration, especially when both companies are similar with low unit holding costs. From an environmental standpoint, adopting the collaborative model can reduce carbon emissions by up to 27%, particularly when both companies are identical and have low demand and low products' weight. Statistical analysis using paired t-tests confirms the significant differences in cost and carbon emissions after implementing HLC. [ABSTRACT FROM AUTHOR]

This paper adopts a holistic approach to the integrated water supply chain system, considering water-related aspects including production, technology selection, distribution routes, and storage, among others. It also introduces a multi-period comprehensive mathematical model that assists decision makers in jointly optimizing a multitude of decisions pertaining to the water supply chain, ranging from strategic to tactical ones. In particular, the former address the installation of new desalination plants along with their operational capacity, capacity expansion of existing plants and infrastructure assets (storage and distribution), as well as the selection of the best-suited desalination technologies. On the other hand, tactical decisions consider issues such as the allocation of water resources among end users, production level of desalinated water at the different plants, and storage levels across various demand zones. All these decisions are being optimized in every period towards minimizing financial and environmental costs throughout the planning horizon. To illustrate the model's practical relevance and assess its validity, a case study focused on an Emirate in the United Arab Emirates (UAE). Results highlight the need for increased desalination capacity over the next 15 years to match growing demand. The study pinpoints the timings for desalination facility expansions, compensating for decreased capacity due to degradation or retirement. The study underscores the superiority of reverse osmosis technology over other desalination options. [ABSTRACT FROM AUTHOR]

Supply-chain-based organisations are nowadays facing intense pressure to abide to environmental regulatory requirements while they are striving to be responsive to customers' needs at the least cost possible. As supply chain activities are among the top contributors to carbon emissions, several recent research works have investigated the impact of carbon regulation policies on economic and environmental supply chain performance. This paper presents integrated economic and environmental models for the one-vendor one-buyer supply chain problem under a vendor managed consignment inventory (VMCI) arrangement. Through the developed models, we study the impacts of two carbon reduction policies, namely carbon cap and carbon tax policies, on supply chain wide costs and carbon emissions. We first provide a much simpler and more compact formulation for the basic single-vendor single-buyer supply chain under VMCI agreement. We also present an environmental-based VMCI model where reduction of carbon footprint is considered as the only objective function. We then extend these two basic models to include each of the two carbon emissions reduction policies. We identify structural properties for the optimal solutions of the two hybrid economic and environmental models and propose algorithms to generate optimal solutions. The results of the computational experiments reveal that the implementation of carbon reduction policies, through carbon cap and carbon tax, may call for the adjustment of the vendor's production and buyer's delivery quantities to reduce carbon footprint without significantly increasing the operational costs. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.06.025 Byline: Moncer A. Hariga (a), Abdulrahman Al-Ahmari (b), Abdel-Rahman A. Mohamed (b) Keywords: Inventory replenishment; Assortment; Space allocation; Optimization Abstract: In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer's profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model. Author Affiliation: (a) American University of Sharjah, Engineering Systems Management, P.O. Box 26666, Sharjah, United Arab Emirates (b) Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia Article History: Received 8 June 2005; Accepted 20 June 2006

This study considers a single vendor supplying a single retailer with a finished product packed in returnable transport items (RTIs), such as containers, pallets or crates, to facilitate its safe shipment. Once received at the retailer’s site, the RTIs are emptied, cleaned, repaired if needed and returned to the vendor to be used for the next shipment. Because of unexpected events, such as damage of RTIs and/or shortage of labour to empty RTIs, the RTI return time is considered stochastic in this study. In case the return of empty RTIs is delayed, the vendor has the option to rent RTIs from a nearby service provider to avoid disruptions in the delivery schedule and finished product shortages at the buyer’s premise. We formulate the problem of coordinating the flow of both the finished product and RTIs and minimising the supply chain wide costs as a mixed-integer non-linear programme. For a convex objective function, we develop an efficient solution procedure that generates the optimal replenishment cycle, the optimal number of RTIs and the optimal number of trucks. The general optimisation model and the solution procedure are illustrated for the case where the RTI return time is exponentially distributed. In addition, we conduct an experimental study to assess the impact of the problem parameters on the decision variables. It is found that renting RTIs is especially beneficial in case both shortage cost and the risk of late RTI returns are high. In addition, the average RTI return time is found to be critical for the performance of the supply chain. [ABSTRACT FROM PUBLISHER]

In this paper we model a consignment (CS) and vendor-managed inventory (VMI) policy for a single vendor and multiple buyers supply chain with known demand. We study three vendor–buyers partnerships: (i) the vendor and the buyers act independently, (ii) the vendor enters in a vendor-managed inventory consignment (VMI&CS) partnership with the buyers and (iii) the vendor and the buyer belong to a vertically integrated firm where a single decision maker decides about the ordering policies. We use relationships (i) and (ii) to study the benefits of the VMI&CS agreement. We provide analytical and numerical results. We find that such an agreement is more beneficial when the vendor has a flexible capacity. It is also more attractive to buyers when they have significant order costs and the vendor's setup cost is not large. Finally we find that under VMI&CS the vendor will tend to make more frequent shipments with smaller lots. [ABSTRACT FROM PUBLISHER]

Abstract In response to the rising public concerns on environmental issues and the recently imposed governmental legislations and directives in this regard, companies nowadays ought to constantly adopt sustainable practices in their day-to-day operations. To that end, this paper seeks to optimize the replenishment strategy for a firm (e.g. retailer), who is facing a discrete time-varying demand for a temperature-sensitive (cold) product, while taking into account carbon emissions resulting from transportation and storage activities. In essence, the problem tackled herein is a variant of the classical dynamic lot-sizing problem (DLSP) for cold products with limited shelf life. To better resemble reality, we assume a stepwise cost function that is proportional to the number of fixed-capacity refrigerated trucks and cold stores used. We present three mathematical models, with the first being a cost minimization model, the second a carbon footprint minimization model, and the third a hybrid model that utilizes the carbon tax policy to jointly optimize both economic and environmental measures. We identify several structural properties of the optimal solution to the three models leading to the development of an exact solution algorithm based on the dynamic programming approach. The results of the computational experiments suggest that accounting for environmental aspects induces a change in the cost minimizing lot-sizing policy, resulting in a minor increase in the operational cost where the savings in the CO 2 related costs outweigh this minor increase. The two-way sensitivity analysis, conducted under randomized values of the demand, truck sizes, and cold stores capacities, indicates that higher savings in cost and carbon reductions are realized for increasing values of the carbon tax rate. Furthermore, on average, more cost savings and lower carbon emissions are also achieved when the values of the shelf life, truck size, and cold store capacity are increased. [ABSTRACT FROM AUTHOR]

Abstract: Resource leveling and time–cost tradeoff are among the most challenging optimization problems in project management. These two problems are usually addressed separately because each problem optimizes different objective functions. In this paper, we develop an integrated model that addresses both problems when activities are allowed to split for better utilization of resources. The formulated mixed integer linear program (MILP) model considers the tradeoff between the crashing‐dependent costs; direct and indirect costs, and resource utilization related costs; acquiring, releasing, and splitting costs. The model can be used as a decision tool to determine whether crashing is recommended when decision makers are also concerned with the better utilization of project's resources. A one‐way sensitivity analysis was conducted to assess total cost savings achieved through the integration of time–cost tradeoff and resource leveling problems. Another experimental study was undertaken to evaluate the performance of the MILP runtime. [ABSTRACT FROM AUTHOR]

Resource leveling aims at minimizing the resource usage fluctuations, which is accomplished by moving noncritical activities within their float. The project duration is fixed and is not affected by the leveling. Most of resource leveling techniques assumes that activities cannot be split. Although this assumption is valid for most construction activities, there are several activities that can be split to achieve better resource leveling. However, there is an added cost associated with splitting such as startup and restarting costs. This paper presents an optimization model for resource leveling that allows activity splitting and minimizes its associated costs. The objective is to level resources in a way that provides a tradeoff between the extra cost of acquiring and releasing resources versus the extra cost of activity splitting. The model can be used to determine at what values of the splitting cost, the preemption of an activity is recommended. One example problem is solved at the end of the paper in order to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

Typical models for determining the economic production quantity (EPQ) assume perfect product quality and perfect production processes. Deteriorating processes may affect production systems in several ways. They may decrease the quality of the items produced, cause production stoppage and breakdowns and/or reduce the production rate due to production process inefficiency. The purpose of this paper is to present an EPQ model that incorporates the effect of shifts in production rate on lot sizing decisions due to speed losses. The cycle starts with a certain production rate and after a random time, the production rate shifts to a lower value. A mathematical model to determine the optimal production policy under these conditions is developed and analyzed. Numerical examples are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In most deterministic and stochastic inventory models encountered in the literature, the optimal policy is determined on the basis of the assumption that lead-time is a given parameter. However, lead-time is composed of several controllable components such as run time, setup time, waiting time, moving time, and lot size inspection time. In this paper, we study a stochastic inventory continuous review system with lead-time depending on lot size and setup time. We assume that the lead-time can be expressed as the product of productive time and a given non-productive factor that reflects the portion of the lead-time such as waiting and moving times. For general demand distributions, the resulting mathematical model is too complex to be solved analytically. For such distributions, we developed an Awesim simulation model for the continuous review system with lot size and lead-time interaction. This simulation model is interfaced with an optimization procedure based on a proposed partial enumeration method to search for the least-cost lot size and reorder point. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of determining optimum inspection schedules for a single deteriorating production system with a predetermined replacement cycle. It is assumed that, at different discrete points in time over the fixed planning horizon, the facility is inspected to detect its operating state and then it goes over an imperfect preventive maintenance routine to enhance its operating performance. Moreover, the facility undergoes minimal repair once detected in an “out-of-control” state. We also adopt the concept of discounted cash flow analysis to account properly for the effect of time value of money on the inspection policies. Under these settings, we formulate the discounted integrated inspection-maintenance problem as a dynamic programming model with general time to failure distribution. After illustrating the model with a numerical example, we perform sensitivity analysis to investigate the effects of some input parameters on the expected present worth and the number of inspections. [ABSTRACT FROM AUTHOR]

Addresses a deterministic maintenance-scheduling problem for a group of non-identical machines. The problem is formulated as a mixed integer non-linear program which is approached heuristically. In the model formulation, it is assumed that a major overhaul brings the machine back to its new condition, whereas a minor overhaul restores it to a specified operating condition. An iterative solution procedure is developed to obtain a near-optimal cyclic overhaul schedule. Presents a worked example to illustrate the proposed solution method. [ABSTRACT FROM AUTHOR]

The Warehouse Scheduling Problem is a deterministic multi-item inventory problem with a restriction on warehouse floor space available. We formulate a mixed integer nonlinear programming problem for the objective of minimizing long run inventory holding and order costs per unit of time. We integrate algorithms for staggering orders, described in companion papers, with a heuristic to choose the order sequences. The result is called Sequenced Staggering. We describe a new algorithm to generate order frequencies, called the powers-of-two-factor-of-three technique, as a generalization of Roundy's roundoff technique for powers-of- two policies. We report on a computational study of four hybrid algorithms for solving the warehouse scheduling problem, including the competing algorithm of Gallego, Queyranne, and Simchi-Levi. Based on these results, we recommend the combination of powers-of-two frequencies with Sequenced Staggering. [ABSTRACT FROM AUTHOR]

We consider the problem of scheduling the delivery of n products into a warehouse with limited space under the assumptions of continuous demands at constant rates, infinite horizon, and no backorders. The delivery schedule is described by a cyclic schedule with time-varying lot sizes. The order frequencies and the order sequence are assumed to be given. We formulate a linear program that determines delivery times relative to the cycle length to minimize the relative maximum space used and show that the optimal solution is characterized by filling the warehouse at each order. We bound the optimal solution by using a worst-case analysis and give conditions under which the linear program has the same optimal solution as a quadratic program that minimizes the holding cost. Under general conditions, we derive a bound on the cost penalty that results when using the optimal solution of the linear program as a solution to the quadratic program. Finally, we complete a solution to the nonlinear lot-sizing model by determining the best cycle length corresponding to the solution to the linear program and present a bound on a quality of this solution. [ABSTRACT FROM AUTHOR]

It is common practice in most inventory systems to hold excess stocks in a rented warehouse (RW) whenever the storage capacity of the owned warehouse (OW) is insufficient. Therefore, the purpose of this paper is to study the effect of renting more storage space on the optimal ordering policy in a stochastic single-period setting. We show that the optimal ordering quantity obtained from the single-period, two-warehouse model is smaller than the ordering quantity of the unconstrained classical newsboy problem. We additionally present various properties of the optimal ordering policy. The model is also extended to the fixed cost case, where depending on the level of the initial inventory, a fixed ordering charge is incurred at the start of the period. In addition, we analyse both models with and without fixed ordering cost under the distribution-free approach in which the form of the demand distribution is not required to be specified. Numerical examples are also included to illustrate the developed models in this paper. [ABSTRACT FROM AUTHOR]