36 EOQ Interactive Model

Figure 36.1 shows the annual costs against the order quantity for the parameters chosen with the sliders.

Economic Order Quantity

Explore how demand, ordering cost, and holding cost affect EOQ.

Code

viewof D = Inputs.range(
  [100, 5000],
  {
    value: 1200,
    step: 100,
    label: "Annual demand (D)"
  }
)

viewof S = Inputs.range(
  [5, 200],
  {
    value: 50,
    step: 5,
    label: "Ordering cost (S)"
  }
)

viewof H = Inputs.range(
  [1, 30],
  {
    value: 5,
    step: 1,
    label: "Annual holding cost (H)"
  }
)

Code

html`
<div class="eoq-formula">
Q* = √(2DS / H)
</div>

<div class="eoq-metrics">

  <div class="eoq-metric">
    <div class="eoq-number">
      ${Qstar.toFixed(1)}
    </div>
    <div class="eoq-label">
      Optimal order quantity
    </div>
  </div>

  <div class="eoq-metric">
    <div class="eoq-number">
      ${orderingCost.toFixed(0)}
    </div>
    <div class="eoq-label">
      Ordering cost
    </div>
  </div>

  <div class="eoq-metric">
    <div class="eoq-number">
      ${totalCost.toFixed(0)}
    </div>
    <div class="eoq-label">
      Total relevant cost
    </div>
  </div>

</div>
`

Code

quantities =
  Array.from(
    {length: 200},
    (_, i) => 10 + i * 10
  )

costData =
  quantities.map(Q => ({
    Q: Q,

    ordering:
      (D / Q) * S,

    holding:
      (Q / 2) * H,

    total:
      (D / Q) * S +
      (Q / 2) * H
  }))

Code

Plot.plot({

  height: 400,

  x: {
    label: "Order quantity Q"
  },

  y: {
    label: "Annual cost",
    grid: true
  },

  marks: [

    Plot.line(
      costData,
      {
        x: "Q",
        y: "ordering"
      }
    ),

    Plot.line(
      costData,
      {
        x: "Q",
        y: "holding"
      }
    ),

    Plot.line(
      costData,
      {
        x: "Q",
        y: "total",
        strokeWidth: 3
      }
    ),

    Plot.ruleX(
      [Qstar]
    ),

    Plot.dot(
      [{
        Q: Qstar,
        cost: totalCost
      }],
      {
        x: "Q",
        y: "cost",
        r: 6
      }
    )
  ]
})

Figure 36.1: Annual ordering, holding, and total costs against the order quantity. The vertical line and the dot mark the optimal order quantity.