E there are no lost sales inventory level on hand

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Unformatted text preview: l amount of demand that has has not been satisfied: • All backordered demand is eventually filled, i.e., there are no lost sales. • Inventory level = On-hand inventory - Backorder. • Inventory position = On-order inventory + Inventory level. • Order up-to level = S • the maximum inventory position we allow. • sometimes called the base stock level. What determines the inventory level? • Short answer: • • Inventory level at the end of a period = S - demand over (l+1) periods. Explanation via an example • with S = 6, l = 3, and 2 units on-hand, 2 on the way at the start of period 1 x3 x1 1 2 x4 x2 1 D1 2 D2 D3 D4 ? Meet the Service Target • Decide S to make in-stock probability ≥ α • Demand D over l+1 period • • Standard normal distribution Probability (D<S) is ! ! • µ=(l+1)λ, σ=sqrt((l+1)λ) p= S (l + 1) p (l + 1) ! square root law So the order up-to quantity S is S = (l + 1) + 1 (↵ ) p (l + 1) Choose the Service Target 1.Based on experience if no quantitative measures are available. 2.Quantitative Method • “Too much-too little” challenge: • If S is too high, then there are holding costs, Co = h • • If S is too low, then there are backorders, Cu = b • • h equal the holding cost per unit per period b equal the penalty per unit backordered Optimal in-stock probability • In-stock probability = critical ratio Cu b ↵= = Co + Cu h+b Part 4: News Vendor Model A review of News Vender problem • Profit function • demand of news paper: D • order quantity: q • order price: c • selling price: p • salvage value: s ⇡ (q ) = pE(mi...
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This document was uploaded on 01/28/2014.

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