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Questions tagged [operations-research]

Operations Research, sometimes known as Management Science or Decision Science, is the discipline of applying appropriate analytical methods to help those who run organisations make better decisions.

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NP-completeness of Nested Flexible Machine Scheduling with summaric job completion time

I have found an interesting scheduling problem called Flexible Machine Scheduling. As it was defined in a paper I was reading: According to: https://www.sciencedirect.com/science/article/pii/...
Mich Szyfel's user avatar
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12 views

Delay in timetabling with supplements and exponentially distributed disturbances

I am looking at the following problem in operations research: Suppose that a train is operated over two identical consecutive trips, where on each trip the train incurs an exponentially distributed ...
Caliondo's user avatar
2 votes
0 answers
50 views

How is this function piece-wise linear?

I encountered this lemma in a research paper related to End-to-End inventory management model. Please note that $d_{[t_1,t_2]} = \sum_{t=t_1}^{t_2} d_t$, where $d_t$ denotes demand at time instance t. ...
Abhilash Mishra's user avatar
1 vote
1 answer
25 views

Bound for expected value under Wasserstein metric

I'm reading a paper and the following result is presented: $$ (\mathbb{E}_{F}[\|\mathbf{X}\|^k])^{1/k} \leq (\mathbb{E}_{F_{0}}[\|\mathbf{X}\|^k])^{1/k} + \epsilon, \ \forall F\in\mathcal{B}_{p}(F_{0},...
rcescon's user avatar
  • 286
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1 answer
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Final tableau in Simplex Method with unknowns

I'm currently working on a problem involving the Simplex Method and I've reached a point where I'm stuck. I have the final tableau after all iterations of the simplex, but there are still unknowns ...
user avatar
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1 answer
19 views

Independence assumption for interarrival time [closed]

I am new to Queuing systems. There is an independent assumption made for the interarrival time. Can someone please explain to me why this assumption is true, can you provide me with an example? "...
romesh prasad's user avatar
1 vote
2 answers
94 views

Existence of Nash Equilibrium in a Game with Mixed Strategy Spaces

I am considering formulating an applied research problem as a simultaneous zero-sum game with two players. The first player's set of actions is an infinite and compact subset of $\mathbb{R}^n$, while ...
graphtheory123's user avatar
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20 views

Rake building through mixed integer programming

I have a problem. I need some helps. I have several coils with weight. I have to load coils on wagons. There are two types of wagons. The capacity of two types of wagons are 64 and 67 respectively. I ...
Manglu's user avatar
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1 answer
24 views

We define the normal direction of Ω. Now if Ω is convex, why it is equivalent to the following set?

Let $\Omega \subset \mathbb R^n$ be closed and $x^* \in \Omega$. Define the normal directions of $\Omega$ at $x^*$ is given by $N(x^*) = \{d\in \mathbb R^n|\limsup_{x\to^\Omega x^*} \frac{\langle d, ...
Harry's user avatar
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-1 votes
2 answers
57 views

Identify optimal product size configuration based on historical data and some constraints [closed]

We have historical data for the demand of a product. Product can be demanded in any quantity between 0-1000g and the historical data show the distribution of previous request sizes. We can only pack ...
user896201's user avatar
1 vote
1 answer
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Awkward Linear Programming Problem

This is a linear programming problem I was given in my semester examinations. The question is attached as an image. Given its size , I couldn't type it out. LPP problem So basically we have to come up ...
Mike Billings's user avatar
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M/M/c Queue Model Solutions for Average Waiting Time and Queue Length

I am seeking assistance with a queueing theory problem involving the M/M/c queue model from my textbook. I have attempted to solve the problem and would greatly appreciate it if someone could review ...
Ameer786's user avatar
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2 votes
0 answers
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Dynamic programming, prove function is monotone non-decreasing

I am currently studying dynamic programming using the Bersketas book: Dynamic programming and optimal control, volume 1. The question is regarding the notation used, but is the following: The ...
h3ab74's user avatar
  • 143
1 vote
1 answer
199 views

Expected distance of the first and second nearest person to one of the 2 cars on a circle road with uniformly distributed locations

let $X=\min(x_{11},x_{12},...,x_{1n},x_{21},x_{22},...,x_{2n})$,such as,$X=x_{1k}$ and $Y=\min(x_{21},x_{22},...,x_{2,k-1},x_{2,k+1},...,x_{2n})$ and $\forall x_{ij}$ is i.i.d, uniform random variable ...
Randy's user avatar
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1 vote
1 answer
69 views

Examine whether the following set is a convex set [closed]

So i am an undergrad student and this question was asked in an assignment Examine if $\{(x, y)\in \Bbb R^2 \mid 2x+3y≤6,2x+3y≥6, x≥0, y≥0\}$ is a convex set After solving the constraints, we come to ...
Amoeba_37's user avatar
2 votes
1 answer
54 views

CCR model in DEA - proof of dual linear program

I am studying Data Envelopment Analysis and the CCR model from Cooper, W. W., Seiford, L. M., Tone, K., & Cooper, W. W. (2006). Introduction to data envelopment analysis and its uses : With DEA-...
MattTct's user avatar
  • 23
3 votes
0 answers
44 views

Finding the optimal policy of an MDP just solving the primal problem associated

I need to find a method that allows me to determine the optimal policy of a finite-horizon Markov Decision Process with a discount factor without solving the dual problem of the linear programming ...
chitranjan_iyengar_01's user avatar
1 vote
1 answer
51 views

Hardness of a Hybrid problem combining knapsack and scheduling

I am trying to prove whether the following problem is NP-hard or not: Items with a certain length arrive in a fixed sequence and must be assigned to one of two containers which are constrained in ...
Christian's user avatar
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1 answer
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Operations research | Employee availability problem

So I have a problem with school and I am not sure if it is a employee schedueling problem, here is the situation: We have to minimize the amount of employees at a non profit organization(Sanquin) and ...
Thijssie3032's user avatar
2 votes
1 answer
73 views

On the optimal operation of a small solar plant and a battery

You operate a small solar plant and a battery. Each day, you can decide how much energy (in kWh) to buy from the grid, sell to the grid, or generate from the solar plant. On day $i$, the price of ...
Lana's user avatar
  • 21
1 vote
0 answers
34 views

What is the Steady-State Condition of Birth-and-death Process?

Question: Determine for which values of $\mu$ a birth-and-death process with $\mu_n=\mu$ and $\lambda_n=2+\cos (n \pi)$ admits steady state probabilities $\left\{p_n\right\}_{n \geq 0}$. My thought: ...
JavaZero's user avatar
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24 views

optimal choice between another unit of expensive and more valuable product or cheaper but less valuable product

I have little knowledge of Operations Research so any directions to reading material book/online will be welcomed lets say that product A have price $p_A$, value(benefit) $v_A$ and we have number of ...
quester's user avatar
  • 617
1 vote
0 answers
26 views

Determining max number of clients a person can have on their caseload based on their schedule & client frequency

I'm not sure if it's possible, and to be clear math is not my strong suit (assume I only know basic high school math, and a handful of excel functions). I'm a therapist supervisor, and I've been given ...
user avatar
0 votes
0 answers
32 views

Probability analysis in passengers taking trains in a FCFS way under capacity constraint

Suppose there are two trains: Train 1 and Train 2 have different departure times ($t_1$ and $t_2$) and capacities ($c_1$ and $c_2$). There are two types of passengers, Type 1 with $d_1$ passengers ...
Yuzhen Feng's user avatar
-3 votes
2 answers
309 views

Ratio vs. Difference

The naturals: $\{1, 2, 3, ... \}$ $2 - 1 = 1$ and $\frac{2}{1} = 2$ $3 - 2 = 1$ and $\frac{3}{2} = 1.5$ $4 - 3 = 1$ and $\frac{4}{3} = 1.333...$ . . . $167834632 - 167834631 = 1$ and $\frac{167834632}{...
Hudjefa's user avatar
  • 983
1 vote
0 answers
68 views

Optimizing the portfolio in modern portfolio theory

I am trying to understand some aspects of the modern portfolio theory, which has brought me to a point I don't fully understand. I would appreciate any hep/suggestions/references. Lets assume that the ...
Seyed Mohsen Ayyoubzadeh's user avatar
1 vote
1 answer
81 views

Optimization of Dynamic Warehouse Delivery

I have an optimization problem for the delivery of boxes between warehouse and production lines within a small facility. I need to determine how many transport vehicles and utilities to buy, such that ...
user18463824's user avatar
1 vote
1 answer
60 views

Constraint formulation for variable cleaning times - MILP optimization

I have a Mixed Integer Linear Problem where I want to schedule the production of different orders ($O$) in which in each order, there is only one product ($P$) produced. Each order can be produced ...
Ignacio Aristimuño's user avatar
5 votes
0 answers
210 views

Linear sum assignment -- faster algorithms for a structured cost matrix?

The Hungarian algorithm for the linear sum assignment problem with dimension $n$ has complexity $O(n^3)$. Can the complexity be improved if one is able to assume that the cost matrix is structured? I ...
calmcc's user avatar
  • 261
1 vote
1 answer
68 views

Why do we choose the maximum value instead of minimum?

Vogel's method selects the corresponding variable through a penalty. There is a penalty for each row and column and is the subtraction between the two lowest costs (in absolute value). We must select ...
Nothing's user avatar
  • 11
2 votes
0 answers
52 views

Geometric Proof About Constrained Minimization Problem

I got the following problem, but I have difficulties understanding part of its solution. I would really appreciate it if someone could explain it for me! Problem Present a geometric proof that in the ...
Beerus's user avatar
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1 vote
1 answer
24 views

Particle Swarm: Restart a stalled particle near the "global best" or the particle's "local best" position?

I am working on an implementation of Particle Swarm that intelligently restarts a particle when its velocity reaches zero, so the particle can find a new starting point and continue its search. This ...
KJ7LNW's user avatar
  • 277
0 votes
1 answer
34 views

Maximizing Neighboring Count in a Sequential Grid Placement: A Combinatorial Optimization Problem [closed]

Given a 20x20 grid and an initial value of N = 0, we follow a certain strategy to place a piece into each cell of the grid sequentially. Upon each placement of a piece, we calculate the number of ...
Lantern's user avatar
1 vote
0 answers
31 views

Recent and interesting application of infinite series or inifite sequence in the optimization theory or any other area

I'm looking for an interesting application of Sequences and Series (theory from mathematical analysis) in the field of Operational Research, in particular involving combinatorics or linear ...
Eduardo Silva's user avatar
3 votes
1 answer
61 views

Managing warehouse based on how likely it is that products are ordered together

I am trying to solve a rather difficult issue at my job right now. We are interested in installing a set of automatic trays in our warehouse, each of which can hold $N \in \{5, 6, \dots, 20 \}$ unique ...
Owen S's user avatar
  • 31
0 votes
0 answers
114 views

How to model the update-delay of observable variable in a model?

INFO: I have asked the same question last week at CS (here), but there is not even a single comment, so I am posting it here in hope someone might help with literature or approach. I have a problem ...
a_confused_engineer's user avatar
1 vote
2 answers
56 views

Expressing locally linear in terms of integer programming

A locally linear graph $G=(V,E)$ is a graph whose adjacent vertices have exactly one common neighbor, i. e. $$\forall(\{i,j\}\in E)\exists!(k\in V):\{i,k\}\in E\wedge\{j,k\}\in E$$ I'm trying to ...
Bertrand Haskell's user avatar
1 vote
2 answers
38 views

Linear Programming for suppliers grouping

I have a set of suppliers each one with a set of products to be picked up with a certain quantity. The objective is to know what suppliers to group with each other in order to minimize the distance ...
Mohamed_98's user avatar
1 vote
2 answers
177 views

Max condition in Integer programming and MILP

Assume you have 2 binary variables $b$ and $c$. Suppose you want another binary variable, $a$ to be $\max(b,c)$ always. How would you represent this in the constraints of an integer program or of a ...
Anonymous Bunny's user avatar
1 vote
1 answer
75 views

Operations research invert pyramid problem in minimum steps mathematical intutive solution to reach optimal solution

A (two-dimensional) pyramid is constructed in four layers: The bottom layer consists of (equally spaced) dots 1, 2, 3, and 4; the next layer includes dots 5, 6, and 7; the following layer has dots 8 ...
Akansha Banerjee's user avatar
1 vote
1 answer
35 views

Minimizing maximum distance for integer case

I am working with different facility location models giving its single (only one center help a demand zone) and multi-source models (multiple centers can help a demand zone). My decision variables are ...
Noah's user avatar
  • 159
0 votes
1 answer
110 views

Crossing the bridge puzzle mathematical solution

I have been trying to understand the mathematical solution to the Operation Research crossing the bridge puzzle. I was reading and trying to understand the solution given in the following paper http://...
Akansha Banerjee's user avatar
1 vote
1 answer
72 views

Minimizing the cost of generating a certain amount of power

I am working on electricity generation. I have $n$ motors and must produce a given amount of power: Let the rotational speed of the $i$-th motor be denoted by $\omega_i$. For each motor, there is a ...
Miguff's user avatar
  • 11
0 votes
0 answers
16 views

Prove commutative of entanglement of two natural numbers.

I have defined an operation for entanglement of two natural numbers. It is: $a$ T $b$ Example part 1 of 3: $$ 13 \\ 24 \ \ \ \ $$ $$1 * 4$$ Example part 2 of 3: $$ 13\\ 24 $$ $$1 * 2 + 3 * 4$$ ...
Michal's user avatar
  • 149
0 votes
2 answers
68 views

Model legal shift constraints

I need your help. My decision variable $b_{fds}$ indicates whether a fireman $f$ works shift $s$ on day $d$. I need two constraints: a) No more than 5 consecutive working days b) At least 2 ...
HulliSeb's user avatar
0 votes
2 answers
114 views

Modelling a shift change

I have the following problem. I am currently modeling shift schedules. There is the variable $x_{itk}$ which tells whether the cashier $i$ completes the shift $k$ on day $t$. Now I want to model the ...
manofthousandnames's user avatar
0 votes
2 answers
75 views

Linear program for non-zero combination of solutions

I am creating a linear program to find the optimal solution that is a combination of $3$ variables but due the constraints I have the optimal solution is just a combination of a non-zero value of one ...
Marcelo Endurance Albuquerque's user avatar
1 vote
2 answers
120 views

Problem with case distinction in a programming problem

Good evening, I have the following problem. I want to create a duty roster and model performance losses. For this I have introduced the binary variable $l_{it}$, which takes the value 1 when the shift ...
themaneater22's user avatar
1 vote
1 answer
40 views

How to efficiently solve a set of precedence networks at the same time?

I'm having a problem where I have a set of precedence networks. Each networks consists of a number of nodes which have a duration, and type. There are also a number of workers, who each have a type ...
IsolatedSushi's user avatar
1 vote
0 answers
390 views

Lagrangian function and first order necessary optimality conditions

I am given the following equality constrained convex QP. $$\min_x \frac{1}{2}x'Hx+g'x$$ $$st. A'x+b=0$$ with $H\succ 0$. I want to find the Lagrangian function for this problem and the first order ...
sarah johnson's user avatar

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