Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product’s demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation.The analysis of results helps supply chain managers to take right decision in different demand and service level situations

Production distribution planning in a multiechelon supply chain using carbon policies: A review and reflections

Sustainability of a supply chain has gained more attention from economists, environmentalists, consumers, manufacturers, government and the academia. In this paper, the literature survey has been performed on production allocation problem in a multi-echelon supply chain with carbon policies. With web-based search engines such as Scopus and Web of Science several resources such as journals, conference proceedings and books are selected and reviewed. It is observed from the literature that the mentioned problem traces the progression of carbon policies in a supply chain over the past 22 years to provide substantiation for Green Supply Chain. The research papers are then analyzed and categorized to construct the useful foundation of previous studies. Moreover, the importance of this problem in recent years needs has been highlighted by mentioning the gaps in the literature. Further, at the end of the paper, several future work directions in this area also suggested.(undefined)info:eu-repo/semantics/publishedVersio

Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

Optimization Models for Cost Efficient and Environmentally Friendly Supply Chain Management

This dissertation aims to provide models which will help companies make sustainable logistics management and transportation decisions. These models are extensions of the economic lot sizing model with the availability of multiple replenishment modes. The objective of the models is to minimize total replenishment costs and emissions. The study provides applications of these models on contemporary supply chain problems. Initially, the impact of carbon regulatory mechanisms on the replenishment decisions are analyzed for a biomass supply chain under fixed charge replenishment costs. Then, models are extended to consider multiple-setups replenishment costs for age dependent perishable products. For a cost minimization objective, solution algorithms are proposed to solve cases where one, two or multiple replenishment modes are available. Finally, using a bi-objective model, tradeoffs in costs and emissions are analyzed in a perishable product supply chain

Stochastic Lot Sizing for Shareholder Wealth Maximisation under Carbon Footprint Management

Fulltext in http://www.jiii.org/index.php?m=content&c=index&a=show&catid=41&id=141There is a growing consensus that human beings must cut greenhouse gas emissions to mitigate global warming and the resultant impacts on the environment. However, production optimisation has rarely taken this issue into consideration, often leading to environmentally unsustainable operation decisions. This paper presents a lot sizing batch optimisation model for a stochastic make-to-order production environment under the carbon emission trading mechanism—currently the most effective market-based carbon emission controlling system, with an aim to maximise the long-term sustainable interests of corporate owners, well-known as the shareholder wealth. To more closely reflect the real-world manufacturing environment, the proposed model adopts general distributions, instead of unrealistic theoretical assumptions, for random variables. We apply the model to investigate the impacts of the carbon emission trading mechanism on shareholder wealth, and test its hedging capability against a series of risk factors. The analytical results provide insights into production optimisation with carbon footprint management.International Conference on Industrial Engineering and Applications (ICIEA 2014), Sydney, Australia, 29-30 May 2014. In Journal of Industrial and Intelligent Information, 2015, v. 3 n. 1, p. 1-

A production planning problem with lost sales and nonlinear convex production cost function under carbon emission restrictions

In this paper, a finite-horizon production planning problem with possible lost sales under several carbon emission restrictions is investigated. The studied model is deterministic with known demands which may not necessarily be met as lost sales are also allowed to provide reasonable flexibility with carbon emission restrictions. The problem is modeled as mixed integer nonlinear programming which has been reformulated in conic-quadratic form for convex cases. The problem is numerically investigated with respect to the costs incurred, the amount of carbon emissions and the magnitude of resulting demand losses. These issues are considered under different carbon restriction policies imposed over several block of periods over the planning horizon. Different carbon cap policies are defined and examined to with wide range of parameter sets to observe how different policies affect the amount of emission, cost and lost sales as the main KPI's set in this study. Numerical examples and their corresponding observations and managerial insights are provided accordingly

Programming problems on time scales: Theory and computation

In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases in between. Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and dual models have been established using the time scales approach. Third, state-constraints separated linear programming primal and dual models on time scales are considered. Fourth, linear fractional primal and dual models have been constructed on time scales. Fifth, quadratic programming problems are formulated using the time scales technique. Sixth, quadratic fractional programming problems have been constructed using a hybrid of the parametric approach and the time scales technique. In addition, for each class of these programming problems the weak duality theorem and the optimality conditions theorem are established for arbitrary time scales, while the strong duality theorem is given for isolated time scales to ensure that our formulation is indeed a perfect formulation. Furthermore, examples for the most well-known isolated time scales are given to illustrate the main results --Abstract, page iv

Optimal Lot Sizing for Perishable Products under Strict Carbon Cap Policy considering Stochastic Demand and Energy Usage cost

In this paper, we have considered stochastic demand for perishable items under strict carbon cap policy and energy usage. Perishable foods like meat, poultry, fish, dairy products etc. which are likely to spoil if not kept refrigerated. So that we related to the energy usage for maintaining perishable items at certain climate conditions where the inventory is stocked. Due to the nature of perishable product starts to decay at certain time, so that vendor provide a discount for the product in demand rate. We model the system into two stage, On first stage holds fresh items as non-discount period and second stage as older items as discount period nearer to expiration. A mathematical model is developed to determine the optimal order quantity, reorder point and number of shipments in a two-echelon supply chain considering partial backorders. The objective is to minimize the total expected supply chain cost while satisfying the carbon emission constraint. A numerical example is given to illustrate the solution procedure

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time