R03_Medicine_ProductionPlanner.html — Excel LP Solver Dashboard
● Ready to Solve
Solver: Simplex LP (Two-Phase)  |  Variables: 36  |  Constraints: 48
L17 ƒx =MIN_COST(P5:G16, assumptions)
⚙️ Assumptions
📈 Demand Data
🔧 Solver Model
✅ Results
Legend:
Input cell (editable)
Formula / calculated
Solver result
A – Cost & Capacity Parameters
Parameter ValueUnitNotes
💰 Cost Assumptions
2 Regular Labour Cost $/unit Base wage rate
3 Overtime Premium % =B2*(1+B3/100)
4 Overhead / Fixed Cost $/unit Allocated overhead
5 Inventory Holding Cost $/unit/mo Storage + insurance
🏭 Production Capacity
7 Regular Production Cap units/mo Factory capacity (regular)
8 Overtime Cap units/mo Additional OT capacity
9 Warehouse / Storage Cap units Warehouse size limit
📦 Inventory Position
11 Initial Inventory (I₀) units On-hand at Jan 1

B – Derived Overtime Labour Cost (auto-calculated)
Item$/unitFormula
13Effective Overtime Labour Cost =Regular Labour × (1 + OT Premium%)
C – Raw Material Cost by Month
MonthRaw Mat
($/unit)		 Total Reg
($/unit)		Total OT
($/unit)
Note: Total Reg = Raw Mat + Regular Labour + Overhead
Total OT = Raw Mat + OT Labour + Overhead

D – Regression Equation (from Regression Eq sheet)
ParameterValueNotes
1Trend EquationForecast(t) = 1,456.16 + 10.11 × tt = period number (Jan 1992 = 1)
2R² (R-Squared)0.880188% of variation explained by trend
3Intercept (β₀)1,456.16Baseline sales at period 0
4Slope (β₁)10.11 units/periodAverage monthly growth
5Historical DataJan 1992 – Dec 2018324 monthly observations
6Forecast Year2019 (Periods 325–336)12 forecasted months
Forecasted Monthly Demand — 2019 (Edit values below)
Month Period
(t)		Forecasted Demand
(units)		 Seasonal Index
(ref)		 vs. Reg Cap
TOTAL — — —
📋 About Demand Data

Forecasted monthly demand for R03 Respiratory Medicine 2019, derived from the regression equation Forecast(t) = 1,456.16 + 10.11t × Seasonal Index.

Cells highlighted red indicate demand exceeds total capacity (Reg + OT).

Cells highlighted orange indicate demand exceeds regular capacity but OT can help.

The LP solver determines whether to use overtime and inventory to meet demand at minimum cost.


✓ Updated from corrected Excel
Total demand: 55,139 units (R² = 0.8801)
Period column shows regression period t. SI = seasonal index from 1992–2018 averages.
Solver Model Spreadsheet View
Month Demand
D(t)		 Reg Prod
P(t)		 Overtime
O(t)		 Inv End
I(t)		 Demand
Met?		 Monthly Cost
($)
TOTAL
Constraint Checker
MonthConstraintLHS ValueOpRHS (Limit)Status

⚙️ Solver Parameters

Set Objective:
$L$17 — Total Annual Cost
To:
By Changing Variable Cells:
$E$5:$G$16  (P₁…P₁₂, O₁…O₁₂, I₁…I₁₂)
Subject to the Constraints:
$E$24:$E$35 = $G$24:$G$35    [Demand Balance]
$E$36:$E$47 <= $G$36:$G$47   [Regular Capacity]
$E$48:$E$59 <= $G$48:$G$59   [Overtime Capacity]
$E$60:$E$71 <= $G$60:$G$71   [Storage Capacity]
$E$5:$G$16 >= 0                [Non-Negativity]
Select a Solving Method:
Solving Method: Select the LP Simplex engine for linear Solver Problems. This dashboard uses a Two-Phase Simplex algorithm implemented in JavaScript — identical logic to Excel Solver's Simplex LP engine.
Mathematical Formulation
Objective
Min Z = Σᵢ₌₁¹² [RegCostᵢ·Pᵢ + OTCostᵢ·Oᵢ + HoldCost·Iᵢ]
Constraints
I(t-1) + Pₜ + Oₜ − Iₜ = Dₜ    ∀t
Pₜ ≤ RegCap                 ∀t
Oₜ ≤ OTCap                  ∀t
Iₜ ≤ StoreCap                ∀t
Pₜ, Oₜ, Iₜ ≥ 0               ∀t
▶
Click Solve in the ribbon or Solver Model tab to generate results
Ready Variables: 36 (12P + 12O + 12I) Constraints: 48