First, we introduce two new reformulation convexification based hierarchies called <span class="monospace">RTC</span> and <span class="monospace">RSC</span> for which the rank <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M1" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.45912 9.49473" width="7.45912pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g50-101" d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"/></g></svg> continuous relaxations are denoted by <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.843001pt" id="M2" height="16.2317pt" version="1.1" viewBox="-0.0498162 -12.3887 21.7301 16.2317" width="21.7301pt"><g transform="matrix(.013,0,0,-0.013,1.579,-2.819)"><path id="g56-17" d="M490 563C409 598 330 631 258 673H233C161 631 81 597 0 563L14 533C89 551 168 576 245 598C320 575 400 551 476 533L490 563Z"/></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g50-81" d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"/></g><g transform="matrix(.0091,0,0,-0.0091,8.091,-5.872)"><use xlink:href="#g50-101"/></g><g transform="matrix(.0091,0,0,-0.0091,6.721,3.693)"><path id="g204-51" d="M195 0C211 1 222 12 223 28V37C222 54 211 62 195 65H158V273H240C289 273 333 241 333 193V120C333 51 364 -11 434 -11C489 -11 522 43 522 97C522 114 511 126 494 129H477C460 127 451 118 449 101C449 78 445 63 437 55C436 54 435 54 434 54C411 54 406 87 406 124V197C406 238 384 276 351 303C400 335 433 385 433 442C433 541 340 611 242 611H48C31 609 22 600 20 583V574C22 557 31 548 48 546H85V65H48C31 63 22 54 20 37V28C21 12 32 1 48 0H195ZM158 546H233C292 546 360 505 360 442S292 338 233 338H158V546Z"/></g><g transform="matrix(.0091,0,0,-0.0091,11.516,3.693)"><path id="g204-53" d="M134 28C137 11 146 2 162 0H363C379 1 390 12 391 28V37C390 54 379 62 363 65H299V546H425V480C427 463 436 454 453 452H470C487 454 496 463 498 480V583C496 600 487 609 470 611H54C37 609 28 600 26 583V480C28 463 37 454 54 452H71C87 455 98 463 99 480V546H226V65H162C146 63 137 54 134 37V28Z"/></g><g transform="matrix(.0091,0,0,-0.0091,16.312,3.693)"><path id="g204-36" d="M281 -11C384 -11 484 67 484 172C484 191 475 201 457 203H438C422 201 413 192 411 176C411 108 354 54 288 54C176 50 112 197 113 306C112 412 174 560 287 557C320 557 348 544 371 517S407 460 411 426C413 410 422 401 438 399H457C473 401 482 410 484 426V595C482 611 473 620 457 622H449C438 620 430 615 425 606L409 575C372 606 329 622 281 622C130 627 38 449 40 306C38 161 130 -16 281 -11Z"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.843001pt" id="M3" height="16.2317pt" version="1.1" viewBox="-0.0498162 -12.3887 21.7301 16.2317" width="21.7301pt"><g transform="matrix(.013,0,0,-0.013,1.579,-2.819)"><use xlink:href="#g56-17"/></g><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g50-81"/></g><g transform="matrix(.0091,0,0,-0.0091,8.091,-5.872)"><use xlink:href="#g50-101"/></g><g transform="matrix(.0091,0,0,-0.0091,6.721,3.693)"><use xlink:href="#g204-51"/></g><g transform="matrix(.0091,0,0,-0.0091,11.516,3.693)"><path id="g204-52" d="M52 16C55 1 64 -8 79 -11H88C108 -8 107 -2 122 33C163 4 219 -11 288 -11C388 -11 472 68 472 167C472 247 414 320 335 338L204 369C159 380 121 417 121 461C121 490 133 513 156 530C180 548 207 557 236 557C315 557 361 515 373 432C376 418 384 410 399 408H418C434 410 443 419 445 435V595C443 611 434 620 418 622H410C386 616 387 608 375 577C338 607 292 622 236 622C143 625 50 550 52 457C52 380 113 316 186 298L317 268C366 256 403 213 403 162C403 101 348 54 288 54C196 54 125 89 125 176C123 192 114 201 98 203H79C64 201 55 192 52 176V16Z"/></g><g transform="matrix(.0091,0,0,-0.0091,16.312,3.693)"><use xlink:href="#g204-36"/></g></svg>, respectively. These two hierarchies are obtained using two different convexification schemes: <i>term convexification</i> in the case of the <span class="monospace">RTC</span> hierarchy and <i>standard convexification</i> in the case of the <span class="monospace">RSC</span> hierarchy. Secondly, we compare the <i>strength</i> of these two hierarchies. We will prove that (i) the hierarchy <span class="monospace">RTC</span> is <i>equivalent</i> to the <span class="monospace">RLT</span> hierarchy of Sherali-Adams, (ii) the hierarchy <span class="monospace">RTC</span> dominates the hierarchy <span class="monospace">RSC</span>, and (iii) the hierarchy <span class="monospace">RSC</span> is dominated by the Lift-and-Project hierarchy. 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transform="matrix(.0091,0,0,-0.0091,9.659,-5.872)"><use xlink:href="#g50-101"/></g></svg> are convex, while <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.852201pt" id="M9" height="16.2409pt" version="1.1" viewBox="-0.0498162 -12.3887 15.536 16.2409" width="15.536pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-6"/></g><g transform="matrix(.0091,0,0,-0.0091,9.75,-5.872)"><use xlink:href="#g50-101"/></g><g transform="matrix(.0091,0,0,-0.0091,9.75,3.693)"><use xlink:href="#g50-117"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.852201pt" id="M10" height="16.2409pt" version="1.1" viewBox="-0.0498162 -12.3887 15.536 16.2409" width="15.536pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-6"/></g><g transform="matrix(.0091,0,0,-0.0091,9.75,-5.872)"><use xlink:href="#g50-101"/></g><g transform="matrix(.0091,0,0,-0.0091,9.75,3.693)"><use xlink:href="#g50-116"/></g></svg> are two nonconvex sets with empty interior (all these sets depend on the convexification step). The first inclusions allow, in some cases, an explicit characterization (in the space of the original variables) of the <span class="monospace">RLT</span> relaxations. Finally, we will discuss weak version of both <span class="monospace">RTC</span> and <span class="monospace">RSC</span> hierarchies and we will emphasize some connections between them.

Hacene Ouzia

Two New Reformulation Convexification Based Hierarchies for 0-1&#x2009;MIPs

This paper presents a new hybrid of Bat Algorithm (BA) based on Mutual Information (MI) and Naive Bayes called BAMI. In BAMI, MI was used to identify promising features which could potentially accelerate the process of finding the best known solution. The promising features were then used to replace several of the randomly selected features during the search initialization. BAMI was tested over twelve datasets and compared against the standard Bat Algorithm guided by Naive Bayes (BANV). The results showed that BAMI outperformed BANV in all datasets in terms of computational time. The statistical test indicated that BAMI has significantly lower computational time than BANV in six out of twelve datasets, while maintaining the effectiveness. The results also showed that BAMI performance was not affected by the number of features or samples in the dataset. Finally, BAMI was able to find the best known solutions with limited number of iterations.

Ahmed Majid Taha

Soong-Der Chen

Aida Mustapha

Bat Algorithm Based Hybrid Filter-Wrapper Approach

We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate probability generating function from which the joint distribution of queue and server content at departure epoch of a batch is extracted and presented in terms of roots of the characteristic equation. We also obtain the joint distribution of queue and server content at arbitrary epoch. Finally, the utility of analytical results is demonstrated by the inclusion of some numerical examples which also includes the investigation of multiple zeros.

U. C. Gupta

S. Pradhan

Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

This paper proposes three numerical algorithms based on Karmarkar&#x2019;s interior point technique for solving
nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar
idea and linearization of the objective function. The second and third algorithms are modification of
the first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemes
are tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithms
are more efficient and converge to the correct optimal solution, while the KKY algorithm fails in
some cases. Numerical results are given to illustrate the performance of the proposed algorithms.

Sakineh Tahmasebzadeh

Hamidreza Navidi

Alaeddin Malek

Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems

We examine the relationship between strategic positioning of firms and their production efficiency.  Firms with competitive advantages based on either cost leadership or differentiation are able to outperform their competitors. Firms pursuing a cost leadership strategy seek to be the lowest cost producer, primarily by minimizing inputs for a given level of output, thus concentrating on increasing the efficiency of their production processes. On the other hand, firms that pursue a differentiation strategy rely on innovation, brand development, marketing, and so forth to achieve competitive advantages; therefore such firms do not place high emphasis on production efficiency. Thus the importance of production efficiency for the success of a firm depends on the strategic positioning of the firm.  We apply DEA to an archival data for a large sample of publicly listed firms to investigate the importance of production efficiency for firms based on their strategic positioning. We provide empirical evidence that firms pursuing a cost leadership strategy attribute higher importance to production efficiency, while firms pursuing differentiation strategy attribute less importance to production efficiency.

Hsihui Chang

Guy D. Fernando

Arindam Tripathy

An Empirical Study of Strategic Positioning and Production Efficiency

This paper presents a switching strategy between the admission control and the pricing control policies in a queueing system with two types of customers. For an arriving first-type customer, the decision maker has an option on which policy to choose between the two control policies; that is, one determines whether or not to admit the customer&#x2019;s request for the service (admission control) or decides a price of the customer&#x2019;s request and offers it to the customer (pricing control). The second-type customers are only served when no first-type customers are present in the system in order to prevent the system from being idle. This would yield an extra income, which we refer to as the sideline profit. The so-called search cost, which is a cost paid to search for customers, creates the search option on whether to continue the search or not. We clarify the properties of the optimal switching strategy as well as the optimal search policy in relation to the sideline profit in order to maximize the total expected net profit. In particular, we show that when the sideline profit is sufficiently large, the two optimal switching thresholds exist with respect to the number of first-type customers in the system.

Jae-Dong Son

Optimal Switching Strategy between Admission Control and Pricing Control Policies with Two Types of Customers and Search Costs

The present paper aims to address the flow-shop sequence-dependent group scheduling problem with learning effect (FSDGSLE). The objective function to be minimized is the total completion time, that is, the makespan. The workers are required to carry out manually the set-up operations on each group to be loaded on the generic machine. The operators skills improve over time due to the learning effects; therefore the set-up time of a group under learning effect decreases depending on the order the group is worked in. In order to effectively cope with the issue at hand, a mathematical model and a hybrid metaheuristic procedure integrating features from genetic algorithms (GA) have been developed. A well-known problem benchmark risen from literature, made by two-, three- and six-machine instances, has been taken as reference for assessing performances of such approach against the two most recent algorithms presented by literature on the FSDGS issue. The obtained results, also supported by a properly developed ANOVA analysis, demonstrate the superiority of the proposed hybrid metaheuristic in tackling the FSDGSLE problem under investigation.

Sergio Fichera

Antonio Costa

Fulvio Cappadonna

Scheduling Jobs Families with Learning Effect on the Setup

This paper describes a method developed to schedule the preventive maintenance tasks of the generation and desalination units in separate and linked cogeneration plants provided that all the necessary maintenance and production constraints are satisfied. The proposed methodology is used to generate two preventing maintenance schedules, one for electricity and the other for distiller. Two types of crossover operators were adopted, 2-point and 4-point. The objective function of the model is to maximize the available number of operational units in each plant. The results obtained were satisfying the problem parameters. However, 4-point slightly produce better solution than 2-point ones for both electricity and water distiller. The performance as well as the effectiveness of the genetic algorithm in solving preventive maintenance scheduling is applied and tested on a real system of 21 units for electricity and 21 units for water. The results presented here show a great potential for utility applications for effective energy management over a time horizon of 52 weeks. The model presented is an effective decision tool that optimizes the solution of the maintenance scheduling problem for cogeneration plants under maintenance and production constraints.

Khaled Alhamad

Mohsen Alardhi

Abdulla Almazrouee

Preventive Maintenance Scheduling for Multicogeneration Plants with Production Constraints Using Genetic Algorithms

This paper investigates equilibrium formation in the passenger traffic model. First, we propose an estimation technique for the distribution of incoming passengers at each stop with respect to subsequent stops of a route based on
available information on incoming and outgoing passengers. Second, we employ the obtained information on passenger traffic
to introduce a game-theoretic model of passenger traffic distribution with respect to transport facilities.

V. M. Bure

V. V. Mazalov

A. V. Melnik

N. V. Plaksina

Passenger Traffic Evaluation and Price Formation on the Transportation Services Market

We attempt to derive the steady-state distribution of the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.2392pt" id="M1" height="11.9171pt" version="1.1" viewBox="-0.0498162 -9.6779 43.6163 11.9171" width="43.6163pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-78" d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"/></g><g transform="matrix(.0135,0,0,-0.0135,13.347,0)"><path id="g113-48" d="M368 703H309L44 -163H104L368 703Z"/></g><g transform="matrix(.0135,0,0,-0.0135,18.934,0)"><use xlink:href="#g113-78"/></g><g transform="matrix(.0135,0,0,-0.0135,32.282,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.0135,0,0,-0.0135,37.869,0)"><path id="g113-100" d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"/></g></svg> queueing-inventory system with positive service time. First we analyze the case of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2130003pt" id="M2" height="8.91176pt" version="1.1" viewBox="-0.0498162 -8.69876 27.701 8.91176" width="27.701pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-100"/></g><g transform="matrix(.0135,0,0,-0.0135,9.29,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.0135,0,0,-0.0135,21.028,0)"><path id="g113-51" d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"/></g></svg> servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.3616pt" id="M3" height="12.0395pt" version="1.1" viewBox="-0.0498162 -9.6779 29.7997 12.0395" width="29.7997pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.0135,0,0,-0.0135,4.688,0)"><path id="g113-116" d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"/></g><g transform="matrix(.0135,0,0,-0.0135,9.768,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"/></g><g transform="matrix(.0135,0,0,-0.0135,15.128,0)"><path id="g113-82" d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"/></g><g transform="matrix(.0135,0,0,-0.0135,24.91,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg> policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.3616pt" id="M4" height="12.0395pt" version="1.1" viewBox="-0.0498162 -9.6779 29.7997 12.0395" width="29.7997pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.0135,0,0,-0.0135,4.688,0)"><use xlink:href="#g113-116"/></g><g transform="matrix(.0135,0,0,-0.0135,9.768,0)"><use xlink:href="#g113-45"/></g><g transform="matrix(.0135,0,0,-0.0135,15.128,0)"><use xlink:href="#g113-82"/></g><g transform="matrix(.0135,0,0,-0.0135,24.91,0)"><use xlink:href="#g113-42"/></g></svg> and the corresponding expected minimum cost are computed. As in the case of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.2392pt" id="M5" height="11.9171pt" version="1.1" viewBox="-0.0498162 -9.6779 43.6163 11.9171" width="43.6163pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-78"/></g><g transform="matrix(.0135,0,0,-0.0135,13.347,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.0135,0,0,-0.0135,18.934,0)"><use xlink:href="#g113-78"/></g><g transform="matrix(.0135,0,0,-0.0135,32.282,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.0135,0,0,-0.0135,37.869,0)"><use xlink:href="#g113-100"/></g></svg> retrial queue with <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-1.16493pt" id="M6" height="9.86369pt" version="1.1" viewBox="-0.0498162 -8.69876 27.701 9.86369" width="27.701pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-100"/></g><g transform="matrix(.0135,0,0,-0.0135,9.29,0)"><path id="g117-94" d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"/></g><g transform="matrix(.0135,0,0,-0.0135,21.028,0)"><path id="g113-52" d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"/></g></svg>, we conjecture that <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.2392pt" id="M7" height="11.9171pt" version="1.1" viewBox="-0.0498162 -9.6779 43.6163 11.9171" width="43.6163pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-78"/></g><g transform="matrix(.0135,0,0,-0.0135,13.347,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.0135,0,0,-0.0135,18.934,0)"><use xlink:href="#g113-78"/></g><g transform="matrix(.0135,0,0,-0.0135,32.282,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.0135,0,0,-0.0135,37.869,0)"><use xlink:href="#g113-100"/></g></svg> for <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-1.16493pt" id="M8" height="9.86369pt" version="1.1" viewBox="-0.0498162 -8.69876 27.701 9.86369" width="27.701pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-100"/></g><g transform="matrix(.0135,0,0,-0.0135,9.29,0)"><use xlink:href="#g117-94"/></g><g transform="matrix(.0135,0,0,-0.0135,21.028,0)"><use xlink:href="#g113-52"/></g></svg>, queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutive <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129903pt" id="M9" height="6.42315pt" version="1.1" viewBox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-116"/></g></svg> to <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129903pt" id="M10" height="6.42315pt" version="1.1" viewBox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-116"/></g></svg> transitions of the inventory level (i.e., the first return time to <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129903pt" id="M11" height="6.42315pt" version="1.1" viewBox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-116"/></g></svg>) is computed. We also obtain several system performance measures.

A. Krishnamoorthy

R. Manikandan

Dhanya Shajin

Analysis of a Multiserver Queueing-Inventory System

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Advances in Operations Research publishes original research and review articles contributing to the theory and methodology of operational research.

Advances in Operations Research