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For questions about dynamic programming, a mathematical optimization technique where the optimal solution to the problem is found by breaking it down to simpler sub-problems and solved recursively.

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This is a re-newed question with some further details. I am currently running a column-generation based solution approach which (right now), I am solving using Gurobi. Currently I am using a barrier ...
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I’m working on an optimization problem that I believe can be framed as a graph or flow problem, but I haven’t found a good existing formulation that scales efficiently. I’d like advice on how to model ...
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We define the all-subset-sum problem as follows. Given a set $S$ of positive integers and a target $T$, the goal is to find all the maximal distinct subsets of $S$ summing to $T$. A maximal set is a ...
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More comprehensively, what is the technical term of the situation in which the SDDP (stochastic dual dynamic programming) algorithm can solve a non-recoursable problem because the feasible actions ...
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I am struggling with the following problem. A college student has 7 days remaining before final examinations begin in her four courses, and she wants to allocate this study time as effectively as ...
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In the following inventory problem, there are $N$ units of inventory available at the beginning of the time horizon $T$. Each day $t\in T$, it is possible to sell one unit of the inventory at price $...
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I have a variation of the knapsack problem where each item has a profit ($p_i$), weight ($w_i$), and penalty ($t_i$). The objective is to maximize the summation of the selected items' profits minus ...
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Have there been any comprehensive surveys or meta-analyses examining the efficacy of various refueling algorithms(such as this or approximation algorithms etc) across varying graph distances? ...
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I have a problem that I haven't encountered before and would like to know if there is any literature on the problem - or maybe you can help me simplify my problem if you think I'm doing something ...
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I encountered this lemma in a research paper related to End-to-End inventory management model. Please note that $d_{[t_1,t_2]} = \sum_{t=t_1}^{t_2} d_i$, where $d_t$ denotes demand at time instance t. ...
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Consider the following problem \begin{equation} \begin{aligned} \min_{x,y,z} \quad & \sum_{i=0}^1 \sum_{j=0}^1 \sum_{k=0}^1 a_{ijk} \cdot f_{ijk}(x,y,z), \\ \textrm{s.t.} \quad &...
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I am studying Stochastic Dynamic Programming using Sheldon Ross's book, "Introduction to Stochastic Dynamic Programming." In the book, Ross defines a dynamic programming algorithm to ...
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I want to know if dynamic programming can generally find globaly optimal solutions for scheduling problems? I think this might be difficult as dynamic makes one at a time decisions without calculating ...
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I am using SDDP.jl for my research project and want to use continuous distribution, can I do so?
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I am using SDDP.jl for my research project in which I am developing a state-of-the-art actor critic algorithm which I am going to benchmark with SDDP but for it I need to plot graphs which require ...
Engr. Moiz Ahmad's user avatar
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There is an order batching problem. Given a set of orders, they need to be split into several batches, with a maximum order number of M per batch. Each order needs to be picked from multiple storage ...
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I am currently working on a paper in which I am statistically comparing dynamic optimization algorithms like SDDP, Actor-Critics etc. In this regard, should I be running SDDP algorithm for my ...
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I'm having trouble in solving this problem dealing with the Wagner's-Whitin Algorithm, because the holding and ordering costs are not given, we only have the optimal costs from the beginning to each ...
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I have a maximization problem as shown in the picture below. The output has a common shock z that follows a two-state Markov chain with a transition matrix Π. Does anyone know how I would go about ...
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Variation of the traditional lot-sizing problem - with some additional complexities: multiple suppliers (S1, S2, S3), with different procurement lead-time Suppliers have to be allocated based on a ...
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Consider the following model: \begin{align*} max \quad Z &= 19x_1 - 3x_1^2 + 5x_2^2 - x_2^4 + 4x_3 \\ & s.t. \quad x_1 + 3x_2 + 3x_3 \leq 7 \\ & \quad \quad \quad x_1,x_2,x_3 \geq 0 \end{...
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I have often wondered whether there is an optimal way to spend cash denominations. For example: Suppose that Bob needs to pay Jill \$5, Jane \$10, Billy \$3.50 and John \$45.75. Furthermore suppose ...
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How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable? Since the term control variable ...
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Suppose there is a dynamic program that the state of the problem grows over time (more info is added to the state of the problem over time) and at each time, we need all historical data, full history, ...
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A familiar dynamic programming algorithm for the binary knapsack problem $$ \begin{align} \text{maximize}\quad & v \cdot x \\ \text{subject to} \quad & w \cdot x \leq W \\ \quad&x_i \text{ ...
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Question: How to establish an explicit characterization of both the optimal value functions and the optimal control policy for a controlled random walk? Background: Assume our system is a perfectly-...
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I aim to solve the following Bellman equation: \begin{equation} v(\vec{s}) = \min_{\vec{x} \in \Xi_{\vec{s}}} \big\{c(\vec{s}, \vec{x}) + \lambda \times \sum_{\vec{s}^{'}\in S} p(\vec{s}^{'} | \...
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The shortest path problem with resource constraints is a common subproblem when doing column generation. It is often solved with a labeling algorithm. The procedure is very well explained here and ...
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I have a question that has been bothering me for a while: In our OR-introduction course, we introduce the concept of Dynamic Programming via backward recursion: Working backwards from a final state (...
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There is a factory that produces one unit of stock uniformly so that $q$ units of stock are produced during a day. The warehouse near a factory has the maximal capacity of $q$ items, i.e. a daily ...
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If we consider the dynamic lot sizing problem with: $d_i$ as the demand per period $i$ and denote $\sum_{i=1}^t d_i$ being the total demand up to period $t$, where $t$ can take values $1, \dots, T$ ...
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Based on Markov chain context, we say a stochastic process is Markovian if the state at time $t+1$, $S_{t+1}$ just depends on the state in the previous step, that is, $\Pr\left( S_{t+1}|S_1, S_2, \...
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I want to formulate a game of darts as a dynamic program again. This question is closely related to my previous post where I wanted to minimize the number of throws to reach checkout. Now the goal is ...
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I am modelling a stochastic dynamic program but because I need to store all information related to former sales, the state of the dynamic program increases and potentially it can growth so much which ...
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I'm new to the field of sequential decision making. I got intrigued by a stochastic shortest path problem, described in Chapter 5 of this book by W. Powell. Consider the following stochastic shortest ...
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I want to formulate a game of darts as a dynamic program. The goal is to minimize the number of darts thrown while reaching checkout. A dart player has a score s. If his score is s = ...
HJA24's user avatar
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I was thinking about exact methods for solving the Time Dependent TSP (TDTSP). Clearly, it is at least as complex as TSP because it extends TSP, but why is it for exact approaches that difficult to ...
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Mostly when I search dynamic programming in google I get : dynamic programming (DP) in python, in C++, in java from web pages like geekforgeeks, litecode, codechef, and so on. But in the operation ...
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We wish to apply dynamic programming techniques to find the optimal betting strategy for a pool to wager on the outcome of the NCAA men's basketball tournament 64 teams compete in a single elimination ...
user620842's user avatar
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I have a problem that I must formulate as a DP problem and solve. A hospital is split up into 4 sections, each section has 1 or 2 or 3 backup generators. We have to maximize the likelihood that no ...
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I’m not sure if I’m wording this right but in a nutshell, my problem is: I’m modelling potential actions a boat owner can do to their boat. Let’s say he wants to know over the 50 year lifespan of the ...
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I need to formulate the following problem as a Mixed Integer Linear Programming problem A farmer needs to establish a 17-year business plan where he will decide when to sell or buy a new truck. The ...
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I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges") [...][the use of the term "relaxation"] is historical. The outcome of a relaxation ...
Alexey's user avatar
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I am going to buy a family car at the beginning of the New Year. I am going to stay in the UK for the next 4 years. I am considering the possibility of being a customer of company A which sells ...
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Consider $m$ knapsack and $n$ items. With each knapsack $j$ associated a capacity $c(j)$ and with each item $i$ associated a profit $p(i,j)$ (that depends on the knapsack, so it's not exactly the ...
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I am wondering what are the fastest ways(faster than classical dynamic programming) to solve the knapsack problem (to optimality) with $n$ items when $n$ is nearly equal to $10000$ ? Apart from ...
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I am going to buy a family car at the beginning of the New Year. I am going to stay in the UK for the next 4 years. I am considering the possibility of being a customer of company A which sells BMW ...
Slim Shady's user avatar
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Could someone please show how he uses dynamic programming to solve for minimum cost of getting from 1 to 6? Is it recommended to use dynamic programming to solve this? Edit: I know that dynamic ...
Slim Shady's user avatar
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A company will be using a new technology for 5 years. For this purpose a specialized machine is required. The company currently has one, which will be 2-year old at the beginning of next year. The ...
Slim Shady's user avatar
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A library must build shelving to shelve $200$ 4-inch high books, $100$ 8-inch high books, and $80$ 12-inch high books. Each book is 0.5-inch thick. The library has several ways to store books. ...
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