Business Analytics for Supply Chains and Operations: A Management Science Perspective
This page lists selected textual, mathematical and numerical corrections identified during the development of instructor presentation materials. The reference to each numbered equation, figure, table or section is more reliable than the standalone working-PDF page numbers.
Issue: “… solving management science challenges is often concerned with increasing revenues, and minimising costs may be achieved by determining …” runs two ideas together.
Proposed correction: “… concerned with increasing revenues and minimising costs. Costs may be reduced by determining …”.
Issue: “Profit per year z_a = 100k ⇒ v_a = z_a/p = 100k/25 = 4,000 engines”, and f₁₀₀ = 4k/20k = 20%. This ignores the fixed cost (and calls the contribution p). The daily number asked for in question 3 is not given, and the fixed cost appears as both C_f and c_f.
Proposed correction: v_a = (c_f + z_a)/(p − c_v) = (70k + 100k)/25 = 6,800 engines a year (≈ 31 a day over 220 days); f₁₀₀ = 6.8k/20k = 34%. Use c_f throughout.
Issue: Hillier and Lieberman (2015) is listed twice, as item 1 (‘Essential Management Science techniques’) and item 4 (‘A classic introduction into operational research’).
Proposed correction: Merge into one entry with both annotations.
Issue: Non-negativity is justified with “we are not outsourcing, which means we cannot have negative time or negative material”. The constraint concerns the decision variables.
Proposed correction: “Production quantities cannot be negative: x₁, x₂ ≥ 0.”
Issue: The opening paragraph is repeated almost word for word (“National grids, including electricity, gas, water …” and “National grids, which encompass electricity, gas, water …”).
Proposed correction: Delete one.
Issue: A stray \\cite{Ortuzar2024} sits outside the text.
Proposed correction: Remove it or cite it where intended.
Issue: The cost model is written as max; the double sum runs over i ∈ T, j ∈ F (sets swapped); both supply and demand are ≤, which with a cost objective would ship nothing; the non-negativity line lacks ∈ (“i {1, 2, 3}”).
Proposed correction: min Σᵢ∈F Σⱼ∈T cᵢⱼxᵢⱼ s.t. Σⱼ xᵢⱼ ≤ sᵢ (supply), Σᵢ xᵢⱼ = dⱼ (demand), xᵢⱼ ≥ 0, i ∈ {1,2,3}, j ∈ {A,B,C}.
Issue: Cost objective written as max, and the bounds are reversed relative to Code 6.6: supply is “= sᵢ” and demand “≤ dⱼ” (together with min, demand ≤ would allow zero deliveries).
Proposed correction: min …; supply Σⱼ xᵢⱼ ≤ sᵢ and demand Σᵢ xᵢⱼ = dⱼ, as in Code 6.6 (supply_lim, demand_lim).
Issue: TSP objective written as max (the text says minimise); the inner sum repeats the index i (“i ∈ N, i = 1..n, i ≠ j”).
Proposed correction: min Σᵢ∈N Σⱼ∈N, ⱼ≠ᵢ dᵢⱼ xᵢⱼ.
Issue: CVRP objective written as max and summed over i, j ∈ V only, which omits all depot arcs (14 of the 27 cost units in the reported solution).
Proposed correction: min Σᵢ∈N Σⱼ∈N, ⱼ≠ᵢ cᵢⱼxᵢⱼ, as in Code 6.10.
Issue: yᵢⱼ − pⱼxᵢ ≤ 0 uses the customer index on the facility capacity and bounds each pair separately, so a facility’s total shipments can exceed its capacity.
Proposed correction: Σⱼ∈C yᵢⱼ ≤ pᵢxᵢ, i ∈ F (Code 6.12 supply_ct).
Issue: s = (1/(n−1))√Σ(x̄ − xᵢ)² = 4.528/6 = 0.755 places 1/(n−1) outside the square root (and contradicts the definition on p. 22). Consequently “95% of the weeks … less than 3,242 units” is also wrong.
Proposed correction: s = √(20.5/6) = 1.848 (1,848 units); the 95% level under a normal assumption is ≈ 2,000 + 1.6449 × 1,848 ≈ 5,040 units.
Issue: d = D/t_w = 74.43 pallets; 24,000/306 = 78.43. R = 549.02 is only correct with 78.43, which the later examples use.
Proposed correction: d = 78.43 pallets per working day.
Issue: “The last ROP formula can be obtained by adding up the safety buffers”. The buffers are combined as the square root of the sum of squares (the variances add); the book’s own formula and the comparison 241.36 < 311.1 show this.
Proposed correction: “… by adding the variances of the two buffers: b = √(b₁² + b₂²) …”.
Issue: The inventory turnover ratio is defined as “the inventory’s sales price over its cost”.
Proposed correction: Cost of goods sold ÷ average inventory value (sometimes sales ÷ average inventory).
Issue: The plots are annotated ‘E(t)=3, E(x)=4 ⇒ ρ=0.75’ and ‘E(t)=4, E(x)=3 ⇒ ρ=1.33’. Read as expected interarrival and service times these give the opposite utilisations (ρ = E(x)/E(t)); the numbers are rates (the text: 3 arrivals and 4 services per hour).
Proposed correction: Annotate ‘λ = 3, μ = 4 ⇒ ρ = 0.75’ and ‘λ = 4, μ = 3 ⇒ ρ = 1.33’ (corrected copies are in the Part 1 deck assets).
Issue: “… for a 50% utilisation is one customer with P(x ≤ 1) ≅ .88, and for a 90% utilisation, there are nine customers with P(x ≤ 9) ≅ .38.” With P(X ≤ k) = 1 − ρ^(k+1): 0.75 and 0.65. (0.88 is P(X ≤ 2); 0.38 ≈ 0.9⁹.) The 68.4% for 75% is correct.
Proposed correction: P(X ≤ 1) = 0.75 and P(X ≤ 9) ≈ 0.65.
Issue: “The probability of μ customers being serviced is 1 − e^(−μ²)” evaluates the service-time CDF at x = μ, mixing a rate with a time; the values 63.2%, 98.2%, 22.2% depend on the time unit.
Proposed correction: Remove, or replace with: “the probability that a service finishes within its mean time 1/μ is 1 − e^(−1) ≈ 63.2%, for any μ”.
Issue: L_q = ρ/(1 − ρ) (that is L); the value shown, 8.1, is L_q = ρ²/(1 − ρ).
Proposed correction: L_q = ρ²/(1 − ρ) and update the cell formula description.
Issue: “41.25% of customers left, which is called the abandonment ratio (99/240 = 41.25%).” 99 is the number served; 151 left. Also 99 + 151 = 250, so 240 is the expected, not the observed, number of arrivals.
Proposed correction: Abandonment = 151 / 250 = 60.4% of resolved customers (served share 39.6%); state that 240 is the expected arrival count.
For technical discrepancies not shown here, an extended editorial register is being reviewed with Routledge. The existence of an observation does not imply that the published edition has yet been amended. © Wolfgang Garn, 2026.