A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

<table>Fraction of time server is on vacation—<svg height="9.875" id="M400" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
</text>
</g>
</g>
</svg> versus <svg height="16.700001" id="M401" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 426.13751 16.700001" width="426.13751" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.7)">
<g transform="translate(72,-58.64)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.9,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">(</tspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">𝑛</tspan>
<tspan style="font-size: 8.75px; " x="7.2641602" y="0">)</tspan>
</text>
<text transform="matrix(1,0,0,-1,-50.05,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑆</tspan>
<tspan style="font-size: 12.50px; " x="15.75378" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="27.794168" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="34.04567" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="40.297169" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="49.674419" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="58.651573" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="70.679459" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="76.930962" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="83.182457" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="92.559708" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="106.6756" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="118.71599" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="124.96748" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="131.21898" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="140.59624" y="0">𝜆</tspan>
<tspan style="font-size: 12.50px; " x="150.8362" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="162.86407" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="169.11559" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="178.49283" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="188.94534" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="200.98572" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="207.23723" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="210.36298" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="216.61447" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="225.99173" y="0">𝛾</tspan>
<tspan style="font-size: 12.50px; " x="235.81908" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="247.85947" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="254.11098" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="257.23672" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="263.48822" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="272.86548" y="0">𝜇</tspan>
<tspan style="font-size: 12.50px; " x="283.94312" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="295.98352" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="302.23502" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="305.36078" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="311.61227" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="314.73801" y="0">)</tspan>
</text>
</g>
</g>
</svg></table>

Modelling and Simulation in Engineering

fig12

Figure 12

Figure 12: A Perishable Inventory System with Postponed Demands and Multiple Server Vacations 