Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

A Note on "Stability of the Constant Cost Dynamic Lot Size Model" by K. Richter

In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution

Inventory Analytics

"Inventory Analytics provides a comprehensive and accessible introduction to the theory and practice of inventory control – a significant research area central to supply chain planning. The book outlines the foundations of inventory systems and surveys prescriptive analytics models for deterministic inventory control. It further discusses predictive analytics techniques for demand forecasting in inventory control and also examines prescriptive analytics models for stochastic inventory control. Inventory Analytics is the first book of its kind to adopt a practicable, Python-driven approach to illustrating theories and concepts via computational examples, with each model covered in the book accompanied by its Python code. Originating as a collection of self-contained lectures, Inventory Analytics will be an indispensable resource for practitioners, researchers, teachers, and students alike.

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

Application of Optimization Techniques in Corporate Cash Management

For any individual person or firm, there is a trade-off between carrying too much or too little cash on hand to meet the day-to-day transactions demand for cash. The BAT model, named after three eminent economists, Baumol, Allais, and Tobin, is the foundation for almost all cash management models in use today. The goal of the BAT model is to minimize the total costs involving the brokerage fees and the opportunity cost of interest lost on the cash held on hand. The brokerage fees are incurred in connection with the transactions for liquidating securities and converting them into cash. The opportunity cost of lost interest represents the income the firm could have earned by investing the cash in an interest-bearing asset instead of holding it on hand. In Chapter 1, a proof of the equivalency of the three seemingly different models of Baumol, Allais and Tobin is provided. The BAT model yields a square-root-formula that helps us determine the optimal level of cash to carry on hand. In practice the square-root-formula of the BAT model often leads to fractional number of transactions involving the liquidation of securities and also fractional number of time periods (days or weeks) in the cycle-time between two consecutive transactions. Therefore, the results are not useful from a managerial or implementation point of view. Mathematical methods for obtaining integer solutions both for the number of transactions and the number of time periods between two consecutive transactions under different scenarios are described in Chapters 2 and 3. In the basic version of the BAT model there is no provision for the use of short-term credit. However, in the case of individual persons as well as corporations, it is sometimes beneficial to borrow funds on a short-term basis and repay the loan as soon as the funds become available. An extended version of the BAT model that not only includes the flexibility of short-term borrowing as described in the Sastry-Ogden-Sundaram (SOS) model, but also incorporates the requirement for the firm to buy insurance on the maximum amount borrowed during any time interval is discussed in Chapter 4. Further, a generalized version of the BAT and SOS models with insurance requirement is presented in Chapter 5. These cash management models are often considered as derivatives of some of the optimization models well-known in the field of Inventory Control and Production Management. The similarities and differences between the two types of models are also highlighted in this Chapter. A single-period stochastic-demand cash management model is discussed in Chapter 6. In this model, the demand for cash is random and cannot be predicted in advance, but some past data is available. A formula is developed for the optimal amount of cash to be kept on hand at the beginning of the period with the goal of minimizing the total expected cost, given the interest rate at the beginning of the period and the interest rate that may be charged by the bank when the funds are borrowed on an emergency basis, should such a need arise. The BAT model is static in the sense that the parameter values remain constant from one period to the next. In contrast, in a multi-period dynamic (MPD) cash management model the transaction costs, interest rates and proportional charge rates vary from one period to the next. Mixed linear-integer programming techniques for solving the multi-period dynamic (MPD) cash management model are described in Chapter 7. Conclusions and suggestions for future research are presented in Chapter 8

The dynamic lot-sizing problem with convex economic production costs and setups

In this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver–Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner–Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner–Whitin algorithm turns out to be the best heuristic

Replenishment Decision Making with Permissible Shortage, Repairable Nonconforming Products and Random Equipment Failure

Abstract: This study is concerned with replenishment decision making with repairable nonconforming products, backordering and random equipment failure during production uptime. In real world manufacturing systems, due to different factors generation of nonconforming items and unexpected machine breakdown are inevitable. Also, in certain business environments various situations between vendor and buyer, the backordering of shortage stocks sometimes is permissible with extra cost involved. This study incorporates backlogging, random breakdown and rework into a production system, with the objective of determination of the optimal replenishment lot size and optimal level of backordering that minimizes the long-run average system costs. Mathematical modeling along with the renewal reward theorem is employed for deriving system cost function. Hessian matrix equations are used to prove its convexity. Research result can be directly adopted by practitioners in the production planning and control field to assist them in making their own robust production replenishment decision

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

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