Shipment Policies for Products with Fixed Shelf Lives: Impact on Profits and Waste

Problem definition: Our research is motivated by the product expiration problem in consumer packaged goods retailing, which creates substantial landfill waste and drains firm profits. We analyze shipment policies (i.e., the rules to determine the quantity and age composition of inventory to ship from a warehouse to a retail location) and their impact on profits and waste. Academic/practical relevance: The same firm often bears the cost of expiration at the warehouse and the retail store, which is why the problem necessitates a supply chain perspective. The ship oldest first (SOF) policy (commonly referred to as first in, first out) is advocated by industry experts to manage product shelf lives. Although its optimality in a single location is well established in the literature, it has not been studied in the context of a two-stage supply chain. Methodology: We conduct empirical analysis on a real-life data set to motivate the relevance of our problem. Then, we formulate an infinite horizon dynamic programming problem with stochastic demand for which we obtain analytical and numerical results. Results: The SOF policy is found to always minimize waste at the warehouse and total waste (warehouse and retail level combined) and under certain practically unlikely conditions, to maximize profits. However, in most practical applications, it is suboptimal, and the optimal policy is shown to have a complex structure. We analyze deterministic and myopic versions of our problem in order to generate insights on the trade-off between the issuing cost and the expiration cost. Then, we develop heuristic policies based on the myopic analysis of the problem, which are shown to perform well in terms of profits, waste, and product freshness; in our numerical analysis, the best such heuristic yields a median optimality gap of 9.5% versus 21% for SOF, pantry life of 69% versus 56% for SOF, and retail waste of 4% versus 10% for SOF. Managerial implications: The SOF policy is shown to generate high waste at the retail store, where waste is more likely to be disposed of at landfills as opposed to being donated; therefore, it may have an adverse impact on the environment. Our results also show that it is not effective at managing shelf lives in the supply chain, contrary to what practitioners argue, as evidenced by poor pantry life leading to excessive waste at the household level. Our analysis also questions the value of flow-through stocking systems to facilitate SOF as we show that firms can gain much more from improving their issuing policies.

Interactive Multiobjective Procedure for Mixed Problems and Its Application to Capacity Planning

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered structures and their scalarization. The aim of the paper is to present an interactive procedure with trade-offs for mixed problems, which helps the decision-maker to make a final decision. Its basic advantage consists of simplicity: after having obtained the solution proposed, the decision-maker should determine whether it is satisfactory and if not, how it should be improved by indicating the criteria whose values should be improved, the criteria whose values cannot be made worse, and the criteria whose values can be made worse. The procedure is applied in solving capacity planning treated as a mixed dynamic programming problem.

A Hilbert transform approach for controlled jump-diffusions with financial applications

We propose a new computational method for a class of controlled jump-diffusions for financial applications. In the first step of our method, we apply piecewise constant policy approximation where we partition the time horizon into small time intervals and the control is constant on each interval. In the second step, we develop a Hilbert transform approach to solve a discrete time dynamic programming problem. We provide rigorous error bounds for the piecewise constant policy approximation for controlled jump-diffusions, generalizing previous results for diffusions. We also apply our method to solve two classical types of financial problems: option pricing under uncertain volatility and/or correlation models and optimal investment, including utility maximization and mean-variance portfolio selection. Through various numerical examples, we demonstrate the properties of our method and show that it is a computationally efficient choice for low-dimensional problems. Our method also compares favorably with some popular approaches.

Search for all solutions to the dynamic programming problem if their multicriteria estimates coincide

Among the mathematical methods used in economics, a prominent place is occupied by the dynamic programming method, with the help of which the optimal control of multi-stage processes is organized. The disadvantage of this method is the impossibility of calculating all solutions to the problem if their criteria-based estimates coincide. The fact of the existence of several optimal trajectories of a multi-step process may mean that the task is not set correctly, in the sense that the assigned criteria do not fully characterize the system under study. This means that the traditional method of dynamic programming needs to be refined in case of the existence of several optimal trajectories with the same value of the criterion. This article proposes the most general version of such refinement, namely, a multi-criteria numerical scheme is generalized. For a more visual representation of calculations and the result of the study, we will describe the discrete dynamic programming problem in terms of graph theory. In this case, it reduces to the problem of finding the optimal path on a directed graph. To solve it, a three-stage algorithm is proposed, the composition of which includes the following steps. The first stage is the construction of optimal criteria estimates for paths from the initial vertex to all the others. To perform this stage, the most universal method is the multicriteria version of the Ford – Bellman method. The second stage is the construction of a graph of optimal paths. In the original graph, arcs are selected that are part of the optimal paths. Of these, using the original algorithm, a subgraph is formed in which all paths are optimal. It is analytically proved that this algorithm gives the correct result (correct). The third stage is enumeration of all paths in the constructed subgraph. Numerical experiments showed that the proposed three-stage method works efficiently on oriented graphs of any type in a sufficiently large range of dimensions. The proposed algorithm with minimal changes can be used to solve an arbitrary discrete dynamic programming problem.

THE CALCULATION OF THE LIFETIME OF THE EQUIPMENT WITH APPLICATION OF DYNAMIC PROGRAMMING

The dynamic programming problem for finding the optimal operating period and equipment replacement time using a combination of graphical and calculation methods of economic analysis is considered.

Modeling M Warehouse N Manpower-Team Allocation Problem Using Dynamic Programming Approach

In this research, a dynamic programming-based approach is deployed to model and solve the manpower allocation problem for warehouses. The authors specifically evolve the detailed model for M warehouses and N teams (available for allocation to these warehouses). Profitability is considered as a performance measure for the allocation problem. The warehouses and manpower-team are modelled as stages and states respectively within the dynamic programming problem structure. Owing to the rather abstract nature of such allocation problems possessing Markovian properties and having similarities with stage-gate type of a problem, dynamic programming approach is deployed. The study results in recommending key decisions in workforce allocation for organizations such as retailers operating multiple warehouses.

Simulation System of Technological Support of Automated Complex

Mathematical modeling of technical and technological systems and processes occurring in these systems can be interpreted as multi-step processes of solving managerial problems, where the application of classical methods for obtaining numerical results is possible. In particular, it is practical to apply the theory of dynamic programming based on the use of functional equations and the optimality principle to solve the problem of resource allocation. In the formulation and solution of the dynamic programming problem, the process is divided into stages in time, and at each stage decisions at which the goal is achieved are made. In our case, homogeneous stages are considered, and the use of the optimality principle leads to the fact that a decision made at each stage is the best regarding the entire process.

Fuzzy Dynamic Programming Problem for Single Additive Constraint with Additively Separable Return by Means of Trapezoidal Membership Functions

Dynamic Programming Problem (DPP) is a multivariable optimization problem is decomposed into a series of stages, optimization being done at each stage with respect to one variable only. DP stands a suitable quantitative study procedure that can be used to explain various optimization problems. It deals through reasonably large as well as complex problems; in addition, it involves creating a sequence of interconnected decisions. The technique offers an efficient procedure for defining optimal arrangement of decisions. Throughout this chapter, solving procedure completely deliberate about as Fuzzy Dynamic Programming Problem for single additive constraint with additively separable return with the support of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of Fuzzy Dynamic Programming Problem (FDPP). The fuzzified version of the problem has been stated with the support of a numerical example for both linear and nonlinear fuzzy optimal solutions and it is associated to showing that the proposed procedure offers an efficient tool for handling the dynamic programming problem instead of classical procedures. As a final point the optimal solution with in the form of fuzzy numbers and justified its solution with in the description of trapezoidal fuzzy membership functions.